%   ORIGINAL: h4/words/dimindex__30
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/ASCIInumbers/UNHEX__primitive__def: h4/ASCIInumbers/UNHEX = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\UNHEX a. h4/bool/literal__case (\v. h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I h4/num/0) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND (v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) h4/bool/ARB)))))))))))))))))))))) a)
% Assm: h4/ASCIInumbers/HEX__primitive__def: h4/ASCIInumbers/HEX = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\HEX a. h4/bool/literal__case (\v. h4/bool/COND (v = h4/num/0) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND (v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) h4/bool/ARB)))))))))))))))) a)
% Assm: h4/ASCIInumbers/UNHEX__def_c20: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm: h4/ASCIInumbers/UNHEX__def_c14: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm: h4/ASCIInumbers/HEX__def_c14: h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))
% Assm: h4/string/isLower__def: !c. h4/string/isLower c <=> h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))
% Assm: h4/ASCIInumbers/HEX__ind: !P. P h4/num/0 /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ (!v18. P v18) ==> (!v. P v)
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/numeral/numeral__distrib_c19: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm: h4/numeral/numeral__eq_c5: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT1 m <=> F
% Assm: h4/numeral/numeral__eq_c7: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT2 m <=> n = m
% Assm: h4/bool/literal__case__THM: !x f. h4/bool/literal__case f x = f x
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/numeral/numeral__eq_c6: !n m. h4/arithmetic/BIT1 n = h4/arithmetic/BIT1 m <=> n = m
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/numeral/numeral__eq_c4: !n m. h4/arithmetic/BIT1 n = h4/arithmetic/BIT2 m <=> F
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/words/dimindex__28: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm: h4/words/dimindex__6: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/string/CHAR__EQ__THM: !c2 c1. c1 = c2 <=> h4/string/ORD c1 = h4/string/ORD c2
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/numeral/numeral__lt_c6: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/string/ORD__CHR: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) <=> h4/string/ORD (h4/string/CHR r) = r
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c4: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/fcp/index__one: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/numeral__bit/iDUB__NUMERAL: !i. h4/numeral/iDUB (h4/arithmetic/NUMERAL i) = h4/arithmetic/NUMERAL (h4/numeral/iDUB i)
% Assm: h4/fcp/index__bit1: h4/fcp/dimindex h4/bool/the__value = h4/bool/COND (h4/pred__set/FINITE h4/pred__set/UNIV) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/numeral/numeral__add_c7: !n. h4/num/SUC (h4/arithmetic/_2B n h4/arithmetic/ZERO) = h4/num/SUC n
% Assm: h4/fcp/index__bit0: h4/fcp/dimindex h4/bool/the__value = h4/bool/COND (h4/pred__set/FINITE h4/pred__set/UNIV) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/TIMES2: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm: h4/fcp/finite__one: h4/pred__set/FINITE h4/pred__set/UNIV
% Assm: h4/numeral/iDUB__removal_c0: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm: h4/numeral/numeral__add_c4: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/iDUB0: !x. h4/numeral/iDUB x = h4/arithmetic/_2B x x
% Assm: h4/ASCIInumbers/HEX__def_c9: h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm: h4/ASCIInumbers/UNHEX__def_c19: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm: h4/ASCIInumbers/HEX__def_c8: h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm: h4/ASCIInumbers/HEX__def_c13: h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))
% Assm: h4/ASCIInumbers/HEX__def_c6: h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm: h4/ASCIInumbers/UNHEX__def_c6: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/ASCIInumbers/HEX__def_c7: h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm: h4/fcp/finite__bit1: h4/pred__set/FINITE h4/pred__set/UNIV <=> h4/pred__set/FINITE h4/pred__set/UNIV
% Assm: h4/string/isSpace__def: !c. h4/string/isSpace c <=> h4/string/ORD c = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) \/ h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm: h4/string/isDigit__def: !c. h4/string/isDigit c <=> h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm: h4/ASCIInumbers/UNHEX__def_c13: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm: h4/ASCIInumbers/UNHEX__def_c9: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/ASCIInumbers/UNHEX__def_c8: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/ASCIInumbers/UNHEX__def_c7: h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/string/isHexDigit__def: !c. h4/string/isHexDigit c <=> h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))) \/ h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) \/ h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))
% Assm: h4/ASCIInumbers/UNHEX__ind: !P. P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (!v24. P v24) ==> (!v. P v)
% Assm: h4/fcp/finite__bit0: h4/pred__set/FINITE h4/pred__set/UNIV <=> h4/pred__set/FINITE h4/pred__set/UNIV
% Assm: h4/numeral/iDUB__removal_c1: !n. h4/numeral/iDUB (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT2 (h4/arithmetic/BIT1 n)
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/words/dimindex__12: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm: h4/words/dimindex__24: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm: h4/words/dimindex__11: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm: h4/words/dimindex__5: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/words/dimindex__20: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/words/dimindex__10: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/words/dimindex__9: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/relation/WF__INDUCTION__THM: !R. h4/relation/WF R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/numeral/numeral__suc_c1: !n. h4/num/SUC (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 n
% Assm: h4/words/dimword__20: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))))))))))))))
% Assm: h4/words/dimword__5: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/words/INT__MIN__10: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))
% Assm: h4/numeral/numeral__suc_c2: !n. h4/num/SUC (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 (h4/num/SUC n)
% Assm: h4/numeral/numeral__texp__help_c2: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT2 n) acc = h4/numeral/texp__help (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 acc)
% Assm: h4/numeral/numeral__texp__help_c1: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT1 n) acc = h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 acc)
% Assm: h4/numeral/numeral__pre_c2: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 n)) = h4/arithmetic/BIT2 (h4/prim__rec/PRE (h4/arithmetic/BIT1 n))
% Assm: h4/numeral/numeral__pre_c1: h4/prim__rec/PRE (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__texp__help_c0: !acc. h4/numeral/texp__help h4/arithmetic/ZERO acc = h4/arithmetic/BIT2 acc
% Assm: h4/words/dimword__IS__TWICE__INT__MIN: h4/words/dimword h4/bool/the__value = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/words/INT__MIN h4/bool/the__value)
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% Assm: h4/numeral/DIV2__BIT1: !x. h4/arithmetic/DIV2 (h4/arithmetic/BIT1 x) = x
% Assm: h4/numeral/enumeral__mult_c5: !y x. h4/arithmetic/_2A (h4/arithmetic/BIT2 x) (h4/arithmetic/BIT2 y) = h4/bool/LET (\m. h4/bool/LET (\n. h4/bool/COND (h4/arithmetic/ODD m) (h4/numeral/texp__help (h4/arithmetic/DIV2 m) (h4/prim__rec/PRE (h4/arithmetic/BIT2 y))) (h4/bool/COND (h4/arithmetic/ODD n) (h4/numeral/texp__help (h4/arithmetic/DIV2 n) (h4/prim__rec/PRE (h4/arithmetic/BIT2 x))) (h4/numeral/internal__mult (h4/arithmetic/BIT2 x) (h4/arithmetic/BIT2 y)))) (h4/numeral/exactlog (h4/arithmetic/BIT2 y))) (h4/numeral/exactlog (h4/arithmetic/BIT2 x))
% Assm: h4/numeral/exactlog__def_c2: !n. h4/numeral/exactlog (h4/arithmetic/BIT2 n) = h4/bool/LET (\x. h4/bool/COND (x = h4/arithmetic/ZERO) h4/arithmetic/ZERO (h4/arithmetic/BIT1 x)) (h4/numeral/onecount n h4/arithmetic/ZERO)
% Assm: h4/numeral/onecount__def_c1: !x n. h4/numeral/onecount (h4/arithmetic/BIT1 n) x = h4/numeral/onecount n (h4/num/SUC x)
% Assm: h4/numeral/onecount__def_c0: !x. h4/numeral/onecount h4/arithmetic/ZERO x = x
% Assm: h4/numeral/numeral__evenodd_c3: ~h4/arithmetic/ODD h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__pre_c4: !n. h4/prim__rec/PRE (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 n
% Assm: h4/numeral/numeral__evenodd_c5: !n. h4/arithmetic/ODD (h4/arithmetic/BIT1 n)
% Assm: h4/numeral/numeral__distrib_c5: !n m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2A n m)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/numeral/numeral__pre_c3: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 n)) = h4/arithmetic/BIT2 (h4/arithmetic/BIT1 n)
% Assm: h4/words/INT__MIN__20: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))))))))))))
% Assm: h4/words/INT__MIN__5: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/words/INT__MIN__def: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/numeral/TWO__EXP__THM_c1: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = h4/arithmetic/NUMERAL (h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) h4/arithmetic/ZERO)
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Goal: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_ASCIInumberss_UNHEXu_u_primitiveu_u_def]: !_3. (!v. ?v. (v <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (?v'. (v' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (?v''. (v'' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (?v'''. (v''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (?v''''. (v'''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (?v'''''. (v''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (?v''''''. (v'''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ (?v'''''''. (v''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ (?v''''''''. (v'''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ (?v'''''''''. (v''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ (?v''''''''''. (v'''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ (?v'''''''''''. (v''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ (?v''''''''''''. (v'''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v'''''''''''''. (v''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v''''''''''''''. (v'''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v'''''''''''''''. (v''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v''''''''''''''''. (v'''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v'''''''''''''''''. (v''''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v''''''''''''''''''. (v'''''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v'''''''''''''''''''. (v''''''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v''''''''''''''''''''. (v'''''''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ (?v'''''''''''''''''''''. (v''''''''''''''''''''' <=> v = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ _3 v = h4/bool/COND v''''''''''''''''''''' (h4/combin/I h4/num/0) (h4/bool/COND v'''''''''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/bool/COND v''''''''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/bool/COND v'''''''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/bool/COND v''''''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/bool/COND v'''''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/bool/COND v''''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/bool/COND v'''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND v''''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND v'''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND v''''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND v'''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v''''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v'''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v''''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v'''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (h4/bool/COND v''''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/bool/COND v'''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v''' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v'' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v' (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bool/COND v (h4/combin/I (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) h4/bool/ARB))))))))))))))))))))))))))))))))))))))))))) ==> (!_2. (!a. happ _2 a = h4/bool/literal__case _3 a) ==> (!_1. (!UNHEX. happ _1 UNHEX = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/ASCIInumbers/UNHEX = h4/relation/WFREC (h4/min/_40 _0) _1)))
% Assm [h4s_ASCIInumberss_HEXu_u_primitiveu_u_def]: !_3. (!v. ?v. (v <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ (?v'. (v' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ (?v''. (v'' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ (?v'''. (v''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ (?v''''. (v'''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ (?v'''''. (v''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ (?v''''''. (v'''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ (?v'''''''. (v''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ (?v''''''''. (v'''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ (?v'''''''''. (v''''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) /\ (?v''''''''''. (v'''''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) /\ (?v'''''''''''. (v''''''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ (?v''''''''''''. (v'''''''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ (?v'''''''''''''. (v''''''''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ (?v''''''''''''''. (v'''''''''''''' <=> v = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ (?v'''''''''''''''. (v''''''''''''''' <=> v = h4/num/0) /\ happ _3 v = h4/bool/COND v''''''''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v'''''''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v''''''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v'''''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v''''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v'''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v''''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v'''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v''''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v'''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) (h4/bool/COND v''''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND v'''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND v''' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND v'' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND v' (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) (h4/bool/COND v (h4/combin/I (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) h4/bool/ARB))))))))))))))))))))))))))))))) ==> (!_2. (!a. happ _2 a = h4/bool/literal__case _3 a) ==> (!_1. (!HEX. happ _1 HEX = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/ASCIInumbers/HEX = h4/relation/WFREC (h4/min/_40 _0) _1)))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c20]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c14]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm [h4s_ASCIInumberss_HEXu_u_defu_c14]: happ h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))
% Assm [h4s_strings_isLoweru_u_def]: !c. h4/string/isLower c <=> h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))
% Assm [h4s_ASCIInumberss_HEXu_u_ind]: !P. happ P h4/num/0 /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) /\ happ P (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ (!v18. happ P v18) ==> (!v. happ P v)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_numerals_numeralu_u_distribu_c19]: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm [h4s_numerals_numeralu_u_equ_c5]: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT1 m <=> F
% Assm [h4s_numerals_numeralu_u_equ_c7]: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT2 m <=> n = m
% Assm [h4s_bools_literalu_u_caseu_u_THM]: !x f. h4/bool/literal__case f x = happ f x
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_numerals_numeralu_u_equ_c6]: !n m. h4/arithmetic/BIT1 n = h4/arithmetic/BIT1 m <=> n = m
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_numerals_numeralu_u_equ_c4]: !n m. h4/arithmetic/BIT1 n = h4/arithmetic/BIT2 m <=> F
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_wordss_dimindexu_u_28]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm [h4s_wordss_dimindexu_u_6]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_strings_CHARu_u_EQu_u_THM]: !c2 c1. c1 = c2 <=> h4/string/ORD c1 = h4/string/ORD c2
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c6]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_strings_ORDu_u_CHR]: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) <=> h4/string/ORD (h4/string/CHR r) = r
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_ltu_c4]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_fcps_indexu_u_one]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_numeralu_u_bits_iDUBu_u_NUMERAL]: !i. h4/numeral/iDUB (h4/arithmetic/NUMERAL i) = h4/arithmetic/NUMERAL (h4/numeral/iDUB i)
% Assm [h4s_fcps_indexu_u_bit1]: h4/fcp/dimindex h4/bool/the__value = h4/bool/COND (h4/pred__set/FINITE h4/pred__set/UNIV) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_numerals_numeralu_u_addu_c7]: !n. h4/num/SUC (h4/arithmetic/_2B n h4/arithmetic/ZERO) = h4/num/SUC n
% Assm [h4s_fcps_indexu_u_bit0]: h4/fcp/dimindex h4/bool/the__value = h4/bool/COND (h4/pred__set/FINITE h4/pred__set/UNIV) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_TIMES2]: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm [h4s_fcps_finiteu_u_one]: h4/pred__set/FINITE h4/pred__set/UNIV
% Assm [h4s_numerals_iDUBu_u_removalu_c0]: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm [h4s_numerals_numeralu_u_addu_c4]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_iDUB0]: !x. h4/numeral/iDUB x = h4/arithmetic/_2B x x
% Assm [h4s_ASCIInumberss_HEXu_u_defu_c9]: happ h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c19]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm [h4s_ASCIInumberss_HEXu_u_defu_c8]: happ h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm [h4s_ASCIInumberss_HEXu_u_defu_c13]: happ h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))
% Assm [h4s_ASCIInumberss_HEXu_u_defu_c6]: happ h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c6]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_ASCIInumberss_HEXu_u_defu_c7]: happ h4/ASCIInumbers/HEX (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) = h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm [h4s_fcps_finiteu_u_bit1]: h4/pred__set/FINITE h4/pred__set/UNIV <=> h4/pred__set/FINITE h4/pred__set/UNIV
% Assm [h4s_strings_isSpaceu_u_def]: !c. h4/string/isSpace c <=> h4/string/ORD c = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) \/ h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm [h4s_strings_isDigitu_u_def]: !c. h4/string/isDigit c <=> h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c13]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c9]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c8]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_ASCIInumberss_UNHEXu_u_defu_c7]: happ h4/ASCIInumbers/UNHEX (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_strings_isHexDigitu_u_def]: !c. h4/string/isHexDigit c <=> h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))) \/ h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) \/ h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) (h4/string/ORD c) /\ h4/arithmetic/_3C_3D (h4/string/ORD c) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))
% Assm [h4s_ASCIInumberss_UNHEXu_u_ind]: !P. happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ happ P (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))) /\ (!v24. happ P v24) ==> (!v. happ P v)
% Assm [h4s_fcps_finiteu_u_bit0]: h4/pred__set/FINITE h4/pred__set/UNIV <=> h4/pred__set/FINITE h4/pred__set/UNIV
% Assm [h4s_numerals_iDUBu_u_removalu_c1]: !n. h4/numeral/iDUB (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT2 (h4/arithmetic/BIT1 n)
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_wordss_dimindexu_u_12]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm [h4s_wordss_dimindexu_u_24]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm [h4s_wordss_dimindexu_u_11]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))
% Assm [h4s_wordss_dimindexu_u_5]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_wordss_dimindexu_u_20]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_wordss_dimindexu_u_10]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_wordss_dimindexu_u_9]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_relations_WFu_u_INDUCTIONu_u_THM]: !R. h4/relation/WF R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P x))
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_numerals_numeralu_u_sucu_c1]: !n. h4/num/SUC (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 n
% Assm [h4s_wordss_dimwordu_u_20]: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))))))))))))))
% Assm [h4s_wordss_dimwordu_u_5]: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_wordss_INTu_u_MINu_u_10]: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))
% Assm [h4s_numerals_numeralu_u_sucu_c2]: !n. h4/num/SUC (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 (h4/num/SUC n)
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c2]: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT2 n) acc = h4/numeral/texp__help (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 acc)
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c1]: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT1 n) acc = h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 acc)
% Assm [h4s_numerals_numeralu_u_preu_c2]: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 n)) = h4/arithmetic/BIT2 (h4/prim__rec/PRE (h4/arithmetic/BIT1 n))
% Assm [h4s_numerals_numeralu_u_preu_c1]: h4/prim__rec/PRE (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c0]: !acc. h4/numeral/texp__help h4/arithmetic/ZERO acc = h4/arithmetic/BIT2 acc
% Assm [h4s_wordss_dimwordu_u_ISu_u_TWICEu_u_INTu_u_MIN]: h4/words/dimword h4/bool/the__value = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/words/INT__MIN h4/bool/the__value)
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% Assm [h4s_numerals_DIV2u_u_BIT1]: !x. h4/arithmetic/DIV2 (h4/arithmetic/BIT1 x) = x
% Assm [h4s_numerals_enumeralu_u_multu_c5]: !_1. (!m x y n. happ (happ (happ (happ _1 m) x) y) n = h4/bool/COND (h4/arithmetic/ODD m) (h4/numeral/texp__help (h4/arithmetic/DIV2 m) (h4/prim__rec/PRE (h4/arithmetic/BIT2 y))) (h4/bool/COND (h4/arithmetic/ODD n) (h4/numeral/texp__help (h4/arithmetic/DIV2 n) (h4/prim__rec/PRE (h4/arithmetic/BIT2 x))) (h4/numeral/internal__mult (h4/arithmetic/BIT2 x) (h4/arithmetic/BIT2 y)))) ==> (!_0. (!x y m. happ (happ (happ _0 x) y) m = h4/bool/LET (happ (happ (happ _1 m) x) y) (h4/numeral/exactlog (h4/arithmetic/BIT2 y))) ==> (!y x. h4/arithmetic/_2A (h4/arithmetic/BIT2 x) (h4/arithmetic/BIT2 y) = h4/bool/LET (happ (happ _0 x) y) (h4/numeral/exactlog (h4/arithmetic/BIT2 x))))
% Assm [h4s_numerals_exactlogu_u_defu_c2]: !_0. (!x. ?v. (v <=> x = h4/arithmetic/ZERO) /\ happ _0 x = h4/bool/COND v h4/arithmetic/ZERO (h4/arithmetic/BIT1 x)) ==> (!n. h4/numeral/exactlog (h4/arithmetic/BIT2 n) = h4/bool/LET _0 (h4/numeral/onecount n h4/arithmetic/ZERO))
% Assm [h4s_numerals_onecountu_u_defu_c1]: !x n. h4/numeral/onecount (h4/arithmetic/BIT1 n) x = h4/numeral/onecount n (h4/num/SUC x)
% Assm [h4s_numerals_onecountu_u_defu_c0]: !x. h4/numeral/onecount h4/arithmetic/ZERO x = x
% Assm [h4s_numerals_numeralu_u_evenoddu_c3]: ~h4/arithmetic/ODD h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_preu_c4]: !n. h4/prim__rec/PRE (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 n
% Assm [h4s_numerals_numeralu_u_evenoddu_c5]: !n. h4/arithmetic/ODD (h4/arithmetic/BIT1 n)
% Assm [h4s_numerals_numeralu_u_distribu_c5]: !n m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2A n m)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_numerals_numeralu_u_preu_c3]: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 n)) = h4/arithmetic/BIT2 (h4/arithmetic/BIT1 n)
% Assm [h4s_wordss_INTu_u_MINu_u_20]: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))))))))))))
% Assm [h4s_wordss_INTu_u_MINu_u_5]: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_wordss_INTu_u_MINu_u_def]: h4/words/INT__MIN h4/bool/the__value = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_numerals_TWOu_u_EXPu_u_THMu_c1]: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = h4/arithmetic/NUMERAL (h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) h4/arithmetic/ZERO)
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Goal: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1217832,TV_Q1217828]: ![V_f, V_g]: (![V_x]: s(TV_Q1217828,happ(s(t_fun(TV_Q1217832,TV_Q1217828),V_f),s(TV_Q1217832,V_x))) = s(TV_Q1217828,happ(s(t_fun(TV_Q1217832,TV_Q1217828),V_g),s(TV_Q1217832,V_x))) => s(t_fun(TV_Q1217832,TV_Q1217828),V_f) = s(t_fun(TV_Q1217832,TV_Q1217828),V_g))).
fof(ah4s_ASCIInumberss_UNHEXu_u_primitiveu_u_def, axiom, ![V_uu_3]: (![V_v]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_]: ((p(s(t_bool,V_vi_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_]: ((p(s(t_bool,V_vi_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_strings_char,V_v) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) & s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_uu_3),s(t_h4s_strings_char,V_v))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_i_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v0),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),s(t_h4s_nums_num,h4s_bools_arb))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) => ![V_uu_2]: (![V_a]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_uu_2),s(t_h4s_strings_char,V_a))) = s(t_h4s_nums_num,h4s_bools_literalu_u_case(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_uu_3),s(t_h4s_strings_char,V_a))) => ![V_uu_1]: (![V_UNHEX]: s(t_fun(t_h4s_strings_char,t_h4s_nums_num),happ(s(t_fun(t_fun(t_h4s_strings_char,t_h4s_nums_num),t_fun(t_h4s_strings_char,t_h4s_nums_num)),V_uu_1),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_UNHEX))) = s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_bool)),V_R))) => s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex) = s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_relations_wfrec(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_strings_char,t_h4s_nums_num),t_fun(t_h4s_strings_char,t_h4s_nums_num)),V_uu_1)))))))).
fof(ah4s_ASCIInumberss_HEXu_u_primitiveu_u_def, axiom, ![V_uu_3]: (![V_v]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_]: ((p(s(t_bool,V_vi_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_]: ((p(s(t_bool,V_vi_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & ?[V_vi_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))) & ?[V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_)) <=> s(t_h4s_nums_num,V_v) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_uu_3),s(t_h4s_nums_num,V_v))) = s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_i_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))),s(t_h4s_strings_char,h4s_bools_cond(s(t_bool,V_v0),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))),s(t_h4s_strings_char,h4s_bools_arb))))))))))))))))))))))))))))))))))))))))))))))))) => ![V_uu_2]: (![V_a]: s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_uu_2),s(t_h4s_nums_num,V_a))) = s(t_h4s_strings_char,h4s_bools_literalu_u_case(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_uu_3),s(t_h4s_nums_num,V_a))) => ![V_uu_1]: (![V_HEX]: s(t_fun(t_h4s_nums_num,t_h4s_strings_char),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_strings_char),t_fun(t_h4s_nums_num,t_h4s_strings_char)),V_uu_1),s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_HEX))) = s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R))) => s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex) = s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_relations_wfrec(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_nums_num,t_h4s_strings_char),t_fun(t_h4s_nums_num,t_h4s_strings_char)),V_uu_1)))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c20, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c14, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ASCIInumberss_HEXu_u_defu_c14, axiom, s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))).
fof(ah4s_strings_isLoweru_u_def, axiom, ![V_c]: (p(s(t_bool,h4s_strings_islower(s(t_h4s_strings_char,V_c)))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c)))))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))))).
fof(ah4s_ASCIInumberss_HEXu_u_ind, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))) & ![V_v18]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_v18)))))))))))))))))))) => ![V_v]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_v)))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_relations_WFu_u_EMPTYu_u_REL, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_numerals_numeralu_u_distribu_c19, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_numerals_numeralu_u_equ_c5, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_equ_c7, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_bools_literalu_u_caseu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_literalu_u_case(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_numerals_numeralu_u_equ_c6, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_numerals_numeralu_u_equ_c4, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m)))))) <=> ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_wordss_dimindexu_u_28, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_ones_one))))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_wordss_dimindexu_u_6, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_ones_one))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_strings_CHARu_u_EQu_u_THM, axiom, ![V_c2, V_c1]: (s(t_h4s_strings_char,V_c1) = s(t_h4s_strings_char,V_c2) <=> s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c1))) = s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c2))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_ltu_c6, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_strings_ORDu_u_CHR, axiom, ![V_r]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_r),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))))) <=> s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c4, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_c17, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_fcps_indexu_u_one, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_ones_one),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_numeralu_u_bits_iDUBu_u_NUMERAL, axiom, ![V_i]: s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_i))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_i)))))).
fof(ah4s_fcps_indexu_u_bit1, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit1(TV_u_27a)),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_numerals_numeralu_u_addu_c7, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))).
fof(ah4s_fcps_indexu_u_bit0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(TV_u_27a)),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_TIMES2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))).
fof(ah4s_fcps_finiteu_u_one, axiom, p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_ones_one,t_bool),h4s_predu_u_sets_univ))))).
fof(ah4s_numerals_iDUBu_u_removalu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_addu_c4, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_iDUB0, axiom, ![V_x]: s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_x)))).
fof(ah4s_ASCIInumberss_HEXu_u_defu_c9, axiom, s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c19, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ASCIInumberss_HEXu_u_defu_c8, axiom, s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
fof(ah4s_ASCIInumberss_HEXu_u_defu_c13, axiom, s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))).
fof(ah4s_ASCIInumberss_HEXu_u_defu_c6, axiom, s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c6, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_ASCIInumberss_HEXu_u_defu_c7, axiom, s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),h4s_asciinumberss_hex),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
fof(ah4s_fcps_finiteu_u_bit1, axiom, ![TV_u_27a]: s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool),h4s_predu_u_sets_univ))) = s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))).
fof(ah4s_strings_isSpaceu_u_def, axiom, ![V_c]: (p(s(t_bool,h4s_strings_isspace(s(t_h4s_strings_char,V_c)))) <=> (s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c)))))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
fof(ah4s_strings_isDigitu_u_def, axiom, ![V_c]: (p(s(t_bool,h4s_strings_isdigit(s(t_h4s_strings_char,V_c)))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c)))))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c13, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c9, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c8, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_defu_c7, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_strings_isHexDigitu_u_def, axiom, ![V_c]: (p(s(t_bool,h4s_strings_ishexdigit(s(t_h4s_strings_char,V_c)))) <=> ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c)))))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))) | ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c)))))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c)))))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_c))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))))))).
fof(ah4s_ASCIInumberss_UNHEXu_u_ind, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))) & ![V_v24]: p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,V_v24)))))))))))))))))))))))))) => ![V_v]: p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_strings_char,V_v)))))).
fof(ah4s_fcps_finiteu_u_bit0, axiom, ![TV_u_27a]: s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_fcps_bit0(TV_u_27a),t_bool),h4s_predu_u_sets_univ))) = s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))).
fof(ah4s_numerals_iDUBu_u_removalu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_sucu_c0, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_wordss_dimindexu_u_12, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_ones_one)))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_wordss_dimindexu_u_24, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_ones_one))))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_wordss_dimindexu_u_11, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_wordss_dimindexu_u_5, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_wordss_dimindexu_u_20, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_wordss_dimindexu_u_10, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_wordss_dimindexu_u_9, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ?[V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_relations_WFu_u_INDUCTIONu_u_THM, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_P]: (![V_x]: (![V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_numerals_numeralu_u_sucu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n)))).
fof(ah4s_wordss_dimwordu_u_20, axiom, s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))))))))))))))))))))))))))).
fof(ah4s_wordss_dimwordu_u_5, axiom, s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))).
fof(ah4s_wordss_INTu_u_MINu_u_10, axiom, s(t_h4s_nums_num,h4s_wordss_intu_u_min(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))))).
fof(ah4s_numerals_numeralu_u_sucu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c2, axiom, ![V_n, V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_acc)))))).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c1, axiom, ![V_n, V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_acc)))))).
fof(ah4s_numerals_numeralu_u_preu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_numerals_numeralu_u_preu_c1, axiom, s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c0, axiom, ![V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_acc)))).
fof(ah4s_wordss_dimwordu_u_ISu_u_TWICEu_u_INTu_u_MIN, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_wordss_intu_u_min(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))).
fof(ah4s_bools_LETu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
fof(ah4s_numerals_DIV2u_u_BIT1, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numerals_enumeralu_u_multu_c5, axiom, ![V_uu_1]: (![V_m, V_x, V_y, V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_1),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_y))))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_x))))))),s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_y))))))))) => ![V_uu_0]: (![V_x, V_y, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_0),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_1),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,h4s_numerals_exactlog(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_y))))))) => ![V_y, V_x]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_y))))) = s(t_h4s_nums_num,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_0),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,h4s_numerals_exactlog(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_x)))))))))).
fof(ah4s_numerals_exactlogu_u_defu_c2, axiom, ![V_uu_0]: (![V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_x) = s(t_h4s_nums_num,h4s_arithmetics_zero)) & s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_uu_0),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x)))))) => ![V_n]: s(t_h4s_nums_num,h4s_numerals_exactlog(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_uu_0),s(t_h4s_nums_num,h4s_numerals_onecount(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))))).
fof(ah4s_numerals_onecountu_u_defu_c1, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_numerals_onecount(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_numerals_onecount(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_x)))))).
fof(ah4s_numerals_onecountu_u_defu_c0, axiom, ![V_x]: s(t_h4s_nums_num,h4s_numerals_onecount(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numerals_numeralu_u_evenoddu_c3, axiom, ~ (p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_numerals_numeralu_u_preu_c4, axiom, ![V_n]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_evenoddu_c5, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_distribu_c5, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_numerals_numeralu_u_preu_c3, axiom, ![V_n]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_wordss_INTu_u_MINu_u_20, axiom, s(t_h4s_nums_num,h4s_wordss_intu_u_min(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))))))))))))))))))))))))).
fof(ah4s_wordss_INTu_u_MINu_u_5, axiom, s(t_h4s_nums_num,h4s_wordss_intu_u_min(s(t_h4s_bools_itself(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_wordss_INTu_u_MINu_u_def, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_wordss_intu_u_min(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_numerals_TWOu_u_EXPu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_wordss_dimindexu_u_30, conjecture, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_ones_one))))),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
