%   ORIGINAL: h4/quantHeuristics/LIST__LENGTH__15_c186
% 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/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% 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/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/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/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/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_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__7_c74: !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__10_c116: !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__5_c46: !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/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/arithmetic/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c78: !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__10_c121: !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__4_c37: !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__5_c49: !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__10_c118: !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__10_c120: !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__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__10_c119: !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__7_c79: !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__7_c77: !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_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/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__4_c36: !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__5_c48: !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_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__5_c50: !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__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__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_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__4_c35: !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/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c34: !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/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/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/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__distrib_c14: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/numeral/iSUB__THM_c3: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm: h4/numeral/numeral__suc_c2: !n. h4/num/SUC (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 (h4/num/SUC n)
% 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__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c76: !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__5_c51: !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_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__7_c83: !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__10_c100: !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__4_c39: !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__5_c54: !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_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__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_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__10_c101: !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__10_c124: !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__10_c125: !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__5_c30: !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_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__10_c122: !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/arithmetic/GREATER__DEF: !n m. h4/arithmetic/_3E m n <=> h4/prim__rec/_3C n m
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c58: !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__4_c33: !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__5_c53: !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__7_c81: !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__10_c117: !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__4_c40: !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__7_c82: !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_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__5_c31: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c52: !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_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__5_c47: !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__7_c80: !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__15_c171: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__4_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_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__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__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/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__7_c59: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c55: !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_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__15_c170: !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__4_c38: !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__10_c123: !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_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__7_c75: !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__4_c41: !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__15_c182: !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__10_c112: !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__5_c42: !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__10_c113: !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__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__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__5_c43: !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__7_c70: !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/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__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/quantHeuristics/LIST__LENGTH__15_c183: !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__7_c71: !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/texp__help0: !n. h4/numeral/texp__help n h4/num/0 = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/arithmetic/findq__thm: !n m a. h4/arithmetic/findq (h4/pair/_2C a (h4/pair/_2C m n)) = h4/bool/COND (n = h4/num/0) a (h4/bool/LET (\d. h4/bool/COND (h4/prim__rec/_3C m d) a (h4/arithmetic/findq (h4/pair/_2C (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) a) (h4/pair/_2C m d)))) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n))
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/bool/TRUTH: T
% Assm: h4/numeral/texp__help__thm: !n a. h4/numeral/texp__help n a = h4/arithmetic/_2A (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/arithmetic/EXP__1_c1: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% 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/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Goal: !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))
%   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_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% 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_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_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_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_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_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_7u_c74]: !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_10u_c116]: !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_5u_c46]: !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_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_arithmetics_GREATERu_u_EQ]: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c78]: !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_10u_c121]: !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_4u_c37]: !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_5u_c49]: !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_10u_c118]: !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_10u_c120]: !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_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_10u_c119]: !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_7u_c79]: !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_7u_c77]: !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_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_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_4u_c36]: !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_5u_c48]: !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_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_5u_c50]: !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_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_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_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_4u_c35]: !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_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c34]: !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_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_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_numeralu_u_ltu_c3]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_distribu_c14]: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_numerals_iSUBu_u_THMu_c3]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm [h4s_numerals_numeralu_u_sucu_c2]: !n. h4/num/SUC (h4/arithmetic/BIT2 n) = h4/arithmetic/BIT1 (h4/num/SUC n)
% 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_ltu_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c76]: !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_5u_c51]: !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_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_7u_c83]: !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_10u_c100]: !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_4u_c39]: !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_5u_c54]: !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_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_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_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_10u_c101]: !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_10u_c124]: !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_10u_c125]: !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_5u_c30]: !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_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_10u_c122]: !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_arithmetics_GREATERu_u_DEF]: !n m. h4/arithmetic/_3E m n <=> h4/prim__rec/_3C n m
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c58]: !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_4u_c33]: !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_5u_c53]: !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_7u_c81]: !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_10u_c117]: !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_4u_c40]: !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_7u_c82]: !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_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_5u_c31]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c52]: !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_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_5u_c47]: !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_7u_c80]: !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_15u_c171]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_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_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_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_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_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_7u_c59]: !l. h4/arithmetic/_3E (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) <=> (?l_27 e1 e2 e3. l = h4/list/CONS e1 (h4/list/CONS e2 (h4/list/CONS e3 l_27)))
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c55]: !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_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_15u_c170]: !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_4u_c38]: !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_10u_c123]: !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_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_7u_c75]: !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_4u_c41]: !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_15u_c182]: !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_10u_c112]: !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_5u_c42]: !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_10u_c113]: !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_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_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_5u_c43]: !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_7u_c70]: !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_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_15u_c183]: !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_7u_c71]: !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_texpu_u_help0]: !n. h4/numeral/texp__help n h4/num/0 = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_arithmetics_findqu_u_thm]: !_0. (!a m d. happ (happ (happ _0 a) m) d = h4/bool/COND (h4/prim__rec/_3C m d) a (h4/arithmetic/findq (h4/pair/_2C (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) a) (h4/pair/_2C m d)))) ==> (!n m a. ?v. (v <=> n = h4/num/0) /\ h4/arithmetic/findq (h4/pair/_2C a (h4/pair/_2C m n)) = h4/bool/COND v a (h4/bool/LET (happ (happ _0 a) m) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)))
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_numerals_texpu_u_helpu_u_thm]: !n a. h4/numeral/texp__help n a = h4/arithmetic/_2A (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% 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_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_MULTu_u_COMM]: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Goal: !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))
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_Q1116712,TV_Q1116708]: ![V_f, V_g]: (![V_x]: s(TV_Q1116708,happ(s(t_fun(TV_Q1116712,TV_Q1116708),V_f),s(TV_Q1116712,V_x))) = s(TV_Q1116708,happ(s(t_fun(TV_Q1116712,TV_Q1116708),V_g),s(TV_Q1116712,V_x))) => s(t_fun(TV_Q1116712,TV_Q1116708),V_f) = s(t_fun(TV_Q1116712,TV_Q1116708),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_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_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_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_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_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_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_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_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_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_7u_c74, 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_10u_c116, 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_5u_c46, 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_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_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_LISTu_u_LENGTHu_u_7u_c78, 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_10u_c121, 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_4u_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_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_5u_c49, 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_10u_c118, 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_10u_c120, 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_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_10u_c119, 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_7u_c79, 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_7u_c77, 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_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_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_4u_c36, 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_5u_c48, 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_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_5u_c50, 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_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_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_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_4u_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_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c34, 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_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_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_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_distribu_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_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_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_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_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_numerals_numeralu_u_sucu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c76, 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_5u_c51, 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_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_7u_c83, 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_10u_c100, 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_4u_c39, 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_5u_c54, 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_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_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_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_10u_c101, 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_10u_c124, 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_10u_c125, 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_5u_c30, 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_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_10u_c122, 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_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_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c58, 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_4u_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_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_5u_c53, 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_7u_c81, 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_10u_c117, 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_4u_c40, 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_7u_c82, 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_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_5u_c31, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) <=> ?[V_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c52, 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_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_5u_c47, 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_7u_c80, 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_15u_c171, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) <=> ?[V_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_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_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_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_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_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_7u_c59, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) <=> ?[V_lu_27, V_e1, V_e2, V_e3]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_e3),s(t_h4s_lists_list(TV_u_27a),V_lu_27))))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c55, 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_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_15u_c170, 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_4u_c38, 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_10u_c123, 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_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_7u_c75, 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_4u_c41, 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_15u_c182, 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_10u_c112, 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_5u_c42, 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_10u_c113, 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_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_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_5u_c43, 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_7u_c70, 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_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_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_quantHeuristicss_LISTu_u_LENGTHu_u_15u_c183, 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_7u_c71, 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_texpu_u_help0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_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_arithmetics_findqu_u_thm, axiom, ![V_uu_0]: (![V_a, V_m, V_d]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_0),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_d))) = 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_d))),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_findq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(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_a))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_d))))))))) => ![V_n, V_m, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_nums_num,h4s_arithmetics_findq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_a),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_0),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,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_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))))))))).
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_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_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_numerals_texpu_u_helpu_u_thm, axiom, ![V_n, V_a]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_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_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_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_MULTu_u_COMM, 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,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ch4s_quantHeuristicss_LISTu_u_LENGTHu_u_15u_c186, conjecture, ![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))))))).
