%   ORIGINAL: h4/quantHeuristics/LIST__LENGTH__10_c101
% 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/quantHeuristics/LIST__LENGTH__3_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c59: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c17: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c31: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__COMPARE__1_c1: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/arithmetic/GREATER__DEF: !n m. h4/arithmetic/_3E m n <=> h4/prim__rec/_3C n m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/list/LENGTH__EQ__NUM__compute_c0: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/arithmetic/SUB__EQUAL__0: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm: h4/list/LENGTH__EQ__NUM__compute_c1: !n l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) <=> (?h l_27. h4/list/LENGTH l_27 = h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ l = h4/list/CONS h l_27)
% Assm: h4/quantHeuristics/LENGTH__LE__NUM: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) <=> (?l1 l2. h4/list/LENGTH l1 = n /\ l = h4/list/APPEND l1 l2)
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/list/LENGTH__EQ__NUM__compute_c2: !n l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n) <=> (?h l_27. h4/list/LENGTH l_27 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) /\ l = h4/list/CONS h l_27)
% Assm: h4/numeral/numeral__distrib_c14: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm: h4/numeral/iSUB__THM_c3: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/iDUB__removal_c0: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% 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
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% 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__distrib_c8: !n m. h4/arithmetic/_2D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m)
% 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__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__suc_c1: !n. h4/num/SUC (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 n
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 l_27)))))))
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c59: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 l_27))))))
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c45: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 l_27)))))))
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c17: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 l_27))))))
% 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__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7 e8 e9 e10. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 (h4/list/CONS e8 (h4/list/CONS e9 (h4/list/CONS e10 l_27))))))))))
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c17: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7 e8 e9. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 (h4/list/CONS e8 (h4/list/CONS e9 l_27)))))))))
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c73: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 l_27)))))
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 l_27)))))
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c31: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 l_27)))))
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c45: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c87: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm: h4/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c31: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7 e8. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 (h4/list/CONS e8 l_27))))))))
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c17: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c45: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c31: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c73: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c17: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c87: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c45: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c17: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c59: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c3: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c31: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c31: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/quantHeuristics/LIST__LENGTH__0_c3: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c17: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c59: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c73: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c101: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c45: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm: h4/numeral/numeral__distrib_c24: !n. h4/arithmetic/_3E (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% 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/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/list/LENGTH__NIL: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/arithmetic/NOT__GREATER__EQ: !n m. ~h4/arithmetic/_3E_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/NOT__GREATER: !n m. ~h4/arithmetic/_3E m n <=> h4/arithmetic/_3C_3D m n
% Assm: h4/arithmetic/LESS__EQ__0: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm: h4/arithmetic/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/numeral/iZ0: !x. h4/numeral/iZ x = x
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/arithmetic/MULT__CLAUSES_c0: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/arithmetic/SUB__0_c0: !m. h4/arithmetic/_2D h4/num/0 m = h4/num/0
% Assm: h4/arithmetic/MULT__CLAUSES_c1: !m. h4/arithmetic/_2A m h4/num/0 = h4/num/0
% Assm: h4/arithmetic/SUB__0_c1: !m. h4/arithmetic/_2D m h4/num/0 = m
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/arithmetic/LESS__0__CASES: !m. h4/num/0 = m \/ h4/prim__rec/_3C h4/num/0 m
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c3: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/GREATER__OR__EQ: !n m. h4/arithmetic/_3E_3D m n <=> h4/arithmetic/_3E m n \/ m = n
% Goal: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
%   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_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c59]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c17]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c31]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_COMPAREu_u_1u_c1]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_arithmetics_GREATERu_u_DEF]: !n m. h4/arithmetic/_3E m n <=> h4/prim__rec/_3C n m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c0]: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm [h4s_arithmetics_SUBu_u_EQUALu_u_0]: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c1]: !n l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) <=> (?h l_27. h4/list/LENGTH l_27 = h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ l = h4/list/CONS h l_27)
% Assm [h4s_quantHeuristicss_LENGTHu_u_LEu_u_NUM]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) <=> (?l1 l2. h4/list/LENGTH l1 = n /\ l = h4/list/APPEND l1 l2)
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c2]: !n l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n) <=> (?h l_27. h4/list/LENGTH l_27 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) /\ l = h4/list/CONS h l_27)
% Assm [h4s_numerals_numeralu_u_distribu_c14]: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm [h4s_numerals_iSUBu_u_THMu_c3]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_iDUBu_u_removalu_c0]: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% 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_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
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% 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_distribu_c8]: !n m. h4/arithmetic/_2D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m)
% 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_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_sucu_c1]: !n. h4/num/SUC (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 n
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 l_27)))))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c59]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 l_27))))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c45]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 l_27)))))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c17]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5 e6. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 l_27))))))
% 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_ltu_c1]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7 e8 e9 e10. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 (h4/list/CONS e8 (h4/list/CONS e9 (h4/list/CONS e10 l_27))))))))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c17]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7 e8 e9. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 (h4/list/CONS e8 (h4/list/CONS e9 l_27)))))))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c73]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 l_27)))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 l_27)))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c31]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4 e5. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 l_27)))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c45]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c87]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm [h4s_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c31]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4 e5 e6 e7 e8. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 (h4/list/CONS e5 (h4/list/CONS e6 (h4/list/CONS e7 (h4/list/CONS e8 l_27))))))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c17]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2 e3 e4. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 (h4/list/CONS e4 l_27))))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c45]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c31]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c73]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c17]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c87]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c45]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c17]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c59]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c3]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c31]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) h4/num/0 <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c31]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_0u_c3]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c17]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c59]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c73]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c101]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c45]: !l. h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> l = h4/list/NIL
% Assm [h4s_numerals_numeralu_u_distribu_c24]: !n. h4/arithmetic/_3E (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% 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_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_lists_LENGTHu_u_NIL]: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_arithmetics_NOTu_u_GREATERu_u_EQ]: !n m. ~h4/arithmetic/_3E_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_NOTu_u_GREATER]: !n m. ~h4/arithmetic/_3E m n <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_0]: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm [h4s_arithmetics_GREATERu_u_EQ]: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_numerals_iZ0]: !x. h4/numeral/iZ x = x
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_arithmetics_SUBu_u_0u_c0]: !m. h4/arithmetic/_2D h4/num/0 m = h4/num/0
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2A m h4/num/0 = h4/num/0
% Assm [h4s_arithmetics_SUBu_u_0u_c1]: !m. h4/arithmetic/_2D m h4/num/0 = m
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_arithmetics_LESSu_u_0u_u_CASES]: !m. h4/num/0 = m \/ h4/prim__rec/_3C h4/num/0 m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c3]: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_GREATERu_u_ORu_u_EQ]: !n m. h4/arithmetic/_3E_3D m n <=> h4/arithmetic/_3E m n \/ m = n
% Goal: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
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_Q1110926,TV_Q1110922]: ![V_f, V_g]: (![V_x]: s(TV_Q1110922,happ(s(t_fun(TV_Q1110926,TV_Q1110922),V_f),s(TV_Q1110926,V_x))) = s(TV_Q1110922,happ(s(t_fun(TV_Q1110926,TV_Q1110922),V_g),s(TV_Q1110926,V_x))) => s(t_fun(TV_Q1110926,TV_Q1110922),V_f) = s(t_fun(TV_Q1110926,TV_Q1110922),V_g))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c59, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_COMPAREu_u_1u_c1, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_arithmetics_GREATERu_u_DEF, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = 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_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: 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_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
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_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_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_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c0, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_arithmetics_SUBu_u_EQUALu_u_0, axiom, ![V_c]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_c),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c1, axiom, ![TV_u_27a]: ![V_n, V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) <=> ?[V_h, V_lu_27]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LENGTHu_u_LEu_u_NUM, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_l1, V_l2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,V_n) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & 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,V_a)))))).
fof(ah4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c2, axiom, ![TV_u_27a]: ![V_n, V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) <=> ?[V_h, V_lu_27]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = 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_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_numerals_numeralu_u_distribu_c14, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),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,h4s_numerals_idub(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)))))).
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_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_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_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_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_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(ah4s_numerals_iSUBu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,V_n)).
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_distribu_c8, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
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_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6, V_e7]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e7),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c59, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c45, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6, V_e7]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e7),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))).
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_ltu_c1, 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_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6, V_e7, V_e8, V_e9, V_e10]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e7),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e8),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e9),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e10),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6, V_e7, V_e8, V_e9]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e7),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e8),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e9),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c73, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c45, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c87, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))).
fof(ah4s_numerals_numeralu_u_distribu_c13, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))) = 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_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4, V_e5, V_e6, V_e7, V_e8]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e5),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e6),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e7),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e8),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3, V_e4]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e4),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c45, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c73, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c87, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_nums_0)))) <=> ?[V_lu_27, V_e1]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c45, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_nums_0)))) <=> ?[V_lu_27, V_e1]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_nums_0)))) <=> ?[V_lu_27, V_e1]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c59, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_nums_0)))) <=> ?[V_lu_27, V_e1]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_nums_0)))) <=> ?[V_lu_27, V_e1]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_nums_0)))) <=> ?[V_lu_27, V_e1]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_0u_c3, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c17, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c59, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c73, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c101, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c45, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_numerals_numeralu_u_distribu_c24, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3e(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_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
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_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_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_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_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_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_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
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_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
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_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
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_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_lists_LENGTHu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(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_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_arithmetics_NOTu_u_GREATERu_u_EQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,V_n)))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_NOTu_u_GREATER, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_0, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_nums_0))).
fof(ah4s_arithmetics_GREATERu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, 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))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
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_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_numerals_iZ0, axiom, ![V_x]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_bools_NOTu_u_FORALLu_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_EXISTSu_u_ORu_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,happ(s(t_fun(TV_u_27a,t_bool),V_Q),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)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_0)).
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_arithmetics_SUBu_u_0u_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_arithmetics_SUBu_u_0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
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_arithmetics_LESSu_u_0u_u_CASES, axiom, ![V_m]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,V_m) | p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,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_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_GREATERu_u_ORu_u_EQ, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) <=> (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) | s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)))).
fof(ch4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c101, conjecture, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
