%   ORIGINAL: h4/quantHeuristics/LIST__LENGTH__4_c33
% 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__2_c5: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c19: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% 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/list/LENGTH__EQ__NUM__compute_c0: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% 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/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/arithmetic/SUB__EQUAL__0: !c. h4/arithmetic/_2D c c = h4/num/0
% 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/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/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/arithmetic/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% 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/quantHeuristics/LENGTH__LE__PLUS: !n m l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B n m) (h4/list/LENGTH l) <=> (?l1 l2. h4/list/LENGTH l1 = n /\ h4/arithmetic/_3C_3D m (h4/list/LENGTH l2) /\ l = h4/list/APPEND l1 l2)
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/list/LENGTH__EQ__NUM_c2: !n2 n1 l. h4/list/LENGTH l = h4/arithmetic/_2B n1 n2 <=> (?l1 l2. h4/list/LENGTH l1 = n1 /\ h4/list/LENGTH l2 = n2 /\ l = h4/list/APPEND l1 l2)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c23: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c21: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c9: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c7: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/numeral/iDUB__removal_c0: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% 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_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% 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__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/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% 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/quantHeuristics/LIST__LENGTH__4_c16: !l. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?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__3_c27: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c11: !x l. h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c22: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c32: !l. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c26: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c25: !x l. h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c8: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c10: !x l. h4/list/LENGTH l = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c20: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c12: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c13: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c18: !l. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c4: !l. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 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__3_c2: !l. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?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__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__2_c6: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c24: !x l. h4/list/LENGTH l = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c5: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (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_c9: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ 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_c7: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) <=> (?l_27 e1 e2 e3 e4. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ 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_c19: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 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__3_c7: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c5: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 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__3_c9: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c21: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c23: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c28: !l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c0: !l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c1: !l. h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/list/LENGTH l <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c14: !l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c15: !l. h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/list/LENGTH l <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c29: !l. h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/list/LENGTH l <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm: h4/numeral/numeral__distrib_c14: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm: h4/numeral/numeral__suc_c2: !n. h4/num/SUC (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 (h4/num/SUC n)
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c33: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c35: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c21: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c5: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c19: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c7: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c9: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c23: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c37: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/arithmetic/TWO: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/bool/TRUTH: T
% Assm: h4/numpair/twotri__formula: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/numpair/tri n) = h4/arithmetic/_2A n (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/ind__type/NUMPAIR0: !y x. h4/ind__type/NUMPAIR x y = h4/arithmetic/_2A (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) y) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/arithmetic/EVEN__EXISTS: !n. h4/arithmetic/EVEN n <=> (?m. n = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m)
% Assm: h4/arithmetic/GREATER__DEF: !n m. h4/arithmetic/_3E m n <=> h4/prim__rec/_3C n m
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/EVEN__DOUBLE: !n. h4/arithmetic/EVEN (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)
% Assm: h4/arithmetic/EVEN__ODD__EXISTS_c0: !n. h4/arithmetic/EVEN n ==> (?m. n = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/arithmetic/BIT20: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm: h4/arithmetic/ADD_c0: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/arithmetic/ALT__ZERO: h4/arithmetic/ZERO = h4/num/0
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c7: !n. h4/num/SUC (h4/arithmetic/_2B n h4/arithmetic/ZERO) = h4/num/SUC n
% Assm: h4/numeral/numeral__add_c6: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm: h4/numpair/tri__def_c0: h4/numpair/tri h4/num/0 = h4/num/0
% Assm: h4/numeral/numeral__add_c3: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% 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/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% 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__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% 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/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/EXP__1_c1: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = 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/numpair/tri__def_c1: !n. h4/numpair/tri (h4/num/SUC n) = h4/arithmetic/_2B (h4/num/SUC n) (h4/numpair/tri n)
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% 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/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/EXP__ADD: !q p n. h4/arithmetic/EXP n (h4/arithmetic/_2B p q) = h4/arithmetic/_2A (h4/arithmetic/EXP n p) (h4/arithmetic/EXP n q)
% Assm: h4/arithmetic/RIGHT__ADD__DISTRIB: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm: h4/arithmetic/LEFT__ADD__DISTRIB: !p n m. h4/arithmetic/_2A p (h4/arithmetic/_2B m n) = h4/arithmetic/_2B (h4/arithmetic/_2A p m) (h4/arithmetic/_2A p n)
% Assm: h4/arithmetic/MULT__CLAUSES_c5: !n m. h4/arithmetic/_2A m (h4/num/SUC n) = h4/arithmetic/_2B m (h4/arithmetic/_2A 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/MULT__CLAUSES_c3: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm: h4/arithmetic/MULT__CLAUSES_c1: !m. h4/arithmetic/_2A m h4/num/0 = h4/num/0
% Assm: h4/arithmetic/MULT__LEFT__1: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/MULT__CLAUSES_c4: !n m. h4/arithmetic/_2A (h4/num/SUC m) n = h4/arithmetic/_2B (h4/arithmetic/_2A m n) n
% Assm: h4/arithmetic/MULT__CLAUSES_c0: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Goal: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 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_2u_c5]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 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_c19]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% 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_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c0]: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% 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_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_arithmetics_SUBu_u_EQUALu_u_0]: !c. h4/arithmetic/_2D c c = h4/num/0
% 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_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_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_arithmetics_GREATERu_u_EQ]: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% 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_quantHeuristicss_LENGTHu_u_LEu_u_PLUS]: !n m l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B n m) (h4/list/LENGTH l) <=> (?l1 l2. h4/list/LENGTH l1 = n /\ h4/arithmetic/_3C_3D m (h4/list/LENGTH l2) /\ l = h4/list/APPEND l1 l2)
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_c2]: !n2 n1 l. h4/list/LENGTH l = h4/arithmetic/_2B n1 n2 <=> (?l1 l2. h4/list/LENGTH l1 = n1 /\ h4/list/LENGTH l2 = n2 /\ l = h4/list/APPEND l1 l2)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c23]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c21]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c9]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c7]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% 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_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% 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_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% 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_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_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% 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_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c16]: !l. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?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_3u_c27]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c11]: !x l. h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c22]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c32]: !l. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c26]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c25]: !x l. h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c8]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c10]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c20]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c12]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c13]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c18]: !l. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c4]: !l. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 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_3u_c2]: !l. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/LENGTH l) <=> (?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_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_2u_c6]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) (h4/list/LENGTH l) <=> (?l_27 e1 e2. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c24]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x <=> (?l_27 e1 e2. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 (h4/list/CONS e2 l_27))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c5]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (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_c9]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3 e4. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ 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_c7]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) <=> (?l_27 e1 e2 e3 e4. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ 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_c19]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 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_3u_c7]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c5]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 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_3u_c9]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c21]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c23]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) <=> (?l_27 e1 e2 e3. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c28]: !l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c0]: !l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c1]: !l. h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/list/LENGTH l <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c14]: !l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c15]: !l. h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/list/LENGTH l <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c29]: !l. h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/list/LENGTH l <=> (?e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 h4/list/NIL))
% 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_numeralu_u_sucu_c2]: !n. h4/num/SUC (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 (h4/num/SUC n)
% 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_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c33]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c35]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c21]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c5]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c19]: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c7]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c9]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c23]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c37]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm [h4s_arithmetics_TWO]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_numpairs_twotriu_u_formula]: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/numpair/tri n) = h4/arithmetic/_2A n (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_indu_u_types_NUMPAIR0]: !y x. h4/ind__type/NUMPAIR x y = h4/arithmetic/_2A (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) y) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_arithmetics_EVENu_u_EXISTS]: !n. h4/arithmetic/EVEN n <=> (?m. n = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m)
% Assm [h4s_arithmetics_GREATERu_u_DEF]: !n m. h4/arithmetic/_3E m n <=> h4/prim__rec/_3C n m
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_EVENu_u_DOUBLE]: !n. h4/arithmetic/EVEN (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)
% Assm [h4s_arithmetics_EVENu_u_ODDu_u_EXISTSu_c0]: !n. h4/arithmetic/EVEN n ==> (?m. n = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_arithmetics_BIT20]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm [h4s_arithmetics_ADDu_c0]: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_arithmetics_ALTu_u_ZERO]: h4/arithmetic/ZERO = h4/num/0
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% 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_addu_c7]: !n. h4/num/SUC (h4/arithmetic/_2B n h4/arithmetic/ZERO) = h4/num/SUC n
% Assm [h4s_numerals_numeralu_u_addu_c6]: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm [h4s_numpairs_triu_u_defu_c0]: h4/numpair/tri h4/num/0 = h4/num/0
% Assm [h4s_numerals_numeralu_u_addu_c3]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% 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_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% 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_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% 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_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_EXPu_u_1u_c1]: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = 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_numpairs_triu_u_defu_c1]: !n. h4/numpair/tri (h4/num/SUC n) = h4/arithmetic/_2B (h4/num/SUC n) (h4/numpair/tri n)
% Assm [h4s_numerals_numeralu_u_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% 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_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_EXPu_u_ADD]: !q p n. h4/arithmetic/EXP n (h4/arithmetic/_2B p q) = h4/arithmetic/_2A (h4/arithmetic/EXP n p) (h4/arithmetic/EXP n q)
% Assm [h4s_arithmetics_RIGHTu_u_ADDu_u_DISTRIB]: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm [h4s_arithmetics_LEFTu_u_ADDu_u_DISTRIB]: !p n m. h4/arithmetic/_2A p (h4/arithmetic/_2B m n) = h4/arithmetic/_2B (h4/arithmetic/_2A p m) (h4/arithmetic/_2A p n)
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c5]: !n m. h4/arithmetic/_2A m (h4/num/SUC n) = h4/arithmetic/_2B m (h4/arithmetic/_2A 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_MULTu_u_CLAUSESu_c3]: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2A m h4/num/0 = h4/num/0
% Assm [h4s_arithmetics_MULTu_u_LEFTu_u_1]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c4]: !n m. h4/arithmetic/_2A (h4/num/SUC m) n = h4/arithmetic/_2B (h4/arithmetic/_2A m n) n
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Goal: !l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2. l = h4/list/CONS e1 (h4/list/CONS e2 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_Q1103127,TV_Q1103123]: ![V_f, V_g]: (![V_x]: s(TV_Q1103123,happ(s(t_fun(TV_Q1103127,TV_Q1103123),V_f),s(TV_Q1103127,V_x))) = s(TV_Q1103123,happ(s(t_fun(TV_Q1103127,TV_Q1103123),V_g),s(TV_Q1103127,V_x))) => s(t_fun(TV_Q1103127,TV_Q1103123),V_f) = s(t_fun(TV_Q1103127,TV_Q1103123),V_g))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c5, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_c19, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_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_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_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_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_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_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_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_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_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_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_quantHeuristicss_LENGTHu_u_LEu_u_PLUS, axiom, ![TV_u_27a]: ![V_n, V_m, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),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) & (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2)))))) & 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_arithmetics_ADDu_u_SYM, 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,V_n))) = 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_lists_LENGTHu_u_EQu_u_NUMu_c2, axiom, ![TV_u_27a]: ![V_n2, V_n1, 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_u_2b(s(t_h4s_nums_num,V_n1),s(t_h4s_nums_num,V_n2))) <=> ?[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_n1) & (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_nums_num,V_n2) & 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_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c23, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c21, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(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_x)))))) <=> ?[V_lu_27, V_e1, V_e2]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c9, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c7, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(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_x)))))) <=> ?[V_lu_27, V_e1, V_e2]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_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_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_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_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_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_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_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_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_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c16, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_primu_u_recs_u_3c(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[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_3u_c27, axiom, ![TV_u_27a]: ![V_x, V_l]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1, V_e2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c11, axiom, ![TV_u_27a]: ![V_x, V_l]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_x))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1, V_e2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c22, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1, V_e2]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c32, axiom, ![TV_u_27a]: ![V_l]: (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_zero))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[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_c26, axiom, ![TV_u_27a]: ![V_x, 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_u_2b(s(t_h4s_nums_num,V_x),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]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c25, axiom, ![TV_u_27a]: ![V_x, V_l]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_x))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1, V_e2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c8, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1, V_e2]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c10, axiom, ![TV_u_27a]: ![V_x, 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_u_2b(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_x))) <=> ?[V_lu_27, V_e1, V_e2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c20, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_x))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1, V_e2]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c12, axiom, ![TV_u_27a]: ![V_x, 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_u_2b(s(t_h4s_nums_num,V_x),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]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c13, axiom, ![TV_u_27a]: ![V_x, V_l]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1, V_e2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c18, axiom, ![TV_u_27a]: ![V_l]: (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_zero))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[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_c4, axiom, ![TV_u_27a]: ![V_l]: (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_zero))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[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_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_3u_c2, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_primu_u_recs_u_3c(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_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[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_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_2u_c6, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_x))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1, V_e2]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c24, axiom, ![TV_u_27a]: ![V_x, 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_u_2b(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_x))) <=> ?[V_lu_27, V_e1, V_e2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,V_x) & 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_c5, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_c9, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c7, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(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,V_x)))))) <=> ?[V_lu_27, V_e1, V_e2, V_e3, V_e4]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c19, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_3u_c7, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_x)))))) <=> ?[V_lu_27, V_e1, V_e2, V_e3]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_3u_c5, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_3u_c9, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c21, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_x)))))) <=> ?[V_lu_27, V_e1, V_e2, V_e3]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c23, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c28, 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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))) <=> ?[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),h4s_lists_nil))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))) <=> ?[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),h4s_lists_nil))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c1, axiom, ![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))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[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),h4s_lists_nil))))))).
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_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c14, 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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))) <=> ?[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),h4s_lists_nil))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c15, axiom, ![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))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[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),h4s_lists_nil))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c29, axiom, ![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))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[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),h4s_lists_nil))))))).
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_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c33, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_c35, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_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_x)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c21, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_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_x)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c5, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_c19, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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_c7, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_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_x)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c9, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c23, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_c37, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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_u_2b(s(t_h4s_nums_num,V_x),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]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & 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_arithmetics_TWO, axiom, 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_nums_suc(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_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_numpairs_twotriu_u_formula, 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,h4s_numpairs_tri(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_indu_u_types_NUMPAIR0, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_indu_u_types_numpair(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,V_x))),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,V_y))),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_EVENu_u_EXISTS, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,V_n)))) <=> ?[V_m]: s(t_h4s_nums_num,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_m))))).
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_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_arithmetics_EVENu_u_DOUBLE, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_even(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))))))).
fof(ah4s_arithmetics_EVENu_u_ODDu_u_EXISTSu_c0, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,V_n)))) => ?[V_m]: s(t_h4s_nums_num,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_m))))).
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_arithmetics_ONE, axiom, 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_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_BIT20, 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_u_2b(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,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))))).
fof(ah4s_arithmetics_ADDu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_arithmetics_ALTu_u_ZERO, axiom, s(t_h4s_nums_num,h4s_arithmetics_zero) = s(t_h4s_nums_num,h4s_nums_0)).
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_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_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_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_numerals_numeralu_u_addu_c6, 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,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numpairs_triu_u_defu_c0, axiom, s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numerals_numeralu_u_addu_c3, 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_bit1(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,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_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_numeralu_u_addu_c2, 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_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_arithmetics_bit2(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_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_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
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_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_arithmetics_EXPu_u_1u_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(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_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_numpairs_triu_u_defu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numpairs_tri(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_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_addu_c1, axiom, ![V_n]: 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,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,V_n)).
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_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_EXPu_u_ADD, axiom, ![V_q, V_p, V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_q))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_q)))))).
fof(ah4s_arithmetics_RIGHTu_u_ADDu_u_DISTRIB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_LEFTu_u_ADDu_u_DISTRIB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_p),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,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c5, axiom, ![V_n, 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_suc(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,h4s_arithmetics_u_2a(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_MULTu_u_CLAUSESu_c3, 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_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)).
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_MULTu_u_LEFTu_u_1, 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_MULTu_u_CLAUSESu_c4, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(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,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n)))).
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_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_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, 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_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,V_p)))).
fof(ah4s_arithmetics_ADDu_u_COMM, 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,V_n))) = 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_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_nums_INDUCTION, 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)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ch4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c33, conjecture, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(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]: 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))))))).
