%   ORIGINAL: h4/quantHeuristics/LIST__LENGTH__10_c139
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/list/LENGTH__EQ__NUM__compute_c0: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/arithmetic/SUB__EQUAL__0: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm: h4/list/LENGTH__EQ__NUM__compute_c1: !n l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) <=> (?h l_27. h4/list/LENGTH l_27 = h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ l = h4/list/CONS h l_27)
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% 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/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/list/LENGTH__EQ__NUM_c2: !n2 n1 l. h4/list/LENGTH l = h4/arithmetic/_2B n1 n2 <=> (?l1 l2. h4/list/LENGTH l1 = n1 /\ h4/list/LENGTH l2 = n2 /\ l = h4/list/APPEND l1 l2)
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c55: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c27: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c13: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c69: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c97: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c41: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 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/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c8: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c135: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c92: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c37: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c54: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c36: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c50: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c65: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__3_c40: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c64: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c22: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c26: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c134: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__2_c23: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c12: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c96: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__10_c138: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__1_c9: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__4_c51: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__5_c68: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 l_27)
% Assm: h4/quantHeuristics/LIST__LENGTH__7_c93: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = h4/list/CONS e1 l_27)
% Assm: h4/list/LEN__DEF_c1: !t n h. h4/list/LEN (h4/list/CONS h t) n = h4/list/LEN t (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/numpair/invtri0__def: !n a. h4/numpair/invtri0 n a = h4/bool/COND (h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a) (h4/numpair/invtri0 (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/numpair/invtri__unique: !y n. h4/arithmetic/_3C_3D (h4/numpair/tri y) n /\ h4/prim__rec/_3C n (h4/numpair/tri (h4/arithmetic/_2B y (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) ==> h4/numpair/invtri n = y
% 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/pred__set/count__add1: !n. h4/pred__set/count (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/pred__set/INSERT n (h4/pred__set/count n)
% Assm: h4/bool/TRUTH: 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% 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/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/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/pred__set/COUNT__SUC: !n. h4/pred__set/count (h4/num/SUC n) = h4/pred__set/INSERT n (h4/pred__set/count n)
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/arithmetic/ADD1: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/numpair/invtri__upper: !n. h4/prim__rec/_3C n (h4/numpair/tri (h4/arithmetic/_2B (h4/numpair/invtri n) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/numpair/invtri__lower: !n. h4/arithmetic/_3C_3D (h4/numpair/tri (h4/numpair/invtri n)) n
% Assm: h4/numpair/tri__LE: !n m. h4/arithmetic/_3C_3D (h4/numpair/tri m) (h4/numpair/tri n) <=> h4/arithmetic/_3C_3D m n
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/numpair/invtri0__curried__def: !x1 x. h4/numpair/invtri0 x x1 = h4/numpair/invtri0__tupled (h4/pair/_2C x x1)
% Assm: h4/numpair/invtri0__tupled__primitive__def: h4/numpair/invtri0__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!a n. ~h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> R (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a)))) (\invtri0__tupled a_27. h4/pair/pair__CASE a_27 (\n a. h4/combin/I (h4/bool/COND (h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a) (invtri0__tupled (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/SUB__RIGHT__LESS: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Goal: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = h4/list/CONS e1 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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c0]: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_arithmetics_SUBu_u_EQUALu_u_0]: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c1]: !n l. h4/list/LENGTH l = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) <=> (?h l_27. h4/list/LENGTH l_27 = h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ l = happ (happ h4/list/CONS h) l_27)
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_lists_LENGTHu_u_EQu_u_NUMu_c2]: !n2 n1 l. h4/list/LENGTH l = h4/arithmetic/_2B n1 n2 <=> (?l1 l2. h4/list/LENGTH l1 = n1 /\ h4/list/LENGTH l2 = n2 /\ l = h4/list/APPEND l1 l2)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c55]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c27]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c13]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c69]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c97]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c41]: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) 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_GREATERu_u_EQ]: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c8]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c135]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c92]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c37]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c54]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c36]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c50]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c65]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c40]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c64]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c22]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c26]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c134]: !x l. h4/arithmetic/_3C_3D (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/list/LENGTH l) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c23]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c12]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c96]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c138]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c9]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_c51]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c68]: !x l. h4/list/LENGTH l = h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c93]: !x l. h4/arithmetic/_3E_3D (h4/list/LENGTH l) (h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?l_27 e1. h4/arithmetic/_3C_3D x (h4/list/LENGTH l_27) /\ l = happ (happ h4/list/CONS e1) l_27)
% Assm [h4s_lists_LENu_u_DEFu_c1]: !t n h. h4/list/LEN (happ (happ h4/list/CONS h) t) n = h4/list/LEN t (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_numpairs_invtri0u_u_def]: !n a. h4/numpair/invtri0 n a = h4/bool/COND (happ (happ h4/prim__rec/_3C n) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a) (h4/numpair/invtri0 (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_numpairs_invtriu_u_unique]: !y n. h4/arithmetic/_3C_3D (h4/numpair/tri y) n /\ happ (happ h4/prim__rec/_3C n) (h4/numpair/tri (h4/arithmetic/_2B y (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) ==> h4/numpair/invtri n = y
% 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_predu_u_sets_countu_u_add1]: !n. h4/pred__set/count (h4/arithmetic/_2B n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/pred__set/INSERT n (h4/pred__set/count n)
% Assm [h4s_bools_TRUTH]: 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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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_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_MULTu_u_COMM]: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_predu_u_sets_COUNTu_u_SUC]: !n. h4/pred__set/count (h4/num/SUC n) = h4/pred__set/INSERT n (h4/pred__set/count n)
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_arithmetics_ADD1]: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_numpairs_invtriu_u_upper]: !n. happ (happ h4/prim__rec/_3C n) (h4/numpair/tri (h4/arithmetic/_2B (h4/numpair/invtri n) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_numpairs_invtriu_u_lower]: !n. h4/arithmetic/_3C_3D (h4/numpair/tri (h4/numpair/invtri n)) n
% Assm [h4s_numpairs_triu_u_LE]: !n m. h4/arithmetic/_3C_3D (h4/numpair/tri m) (h4/numpair/tri n) <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_numpairs_invtri0u_u_curriedu_u_def]: !x1 x. h4/numpair/invtri0 x x1 = happ h4/numpair/invtri0__tupled (h4/pair/_2C x x1)
% Assm [h4s_numpairs_invtri0u_u_tupledu_u_primitiveu_u_def]: !_4. (!invtri0__tupled n a. happ (happ (happ _4 invtri0__tupled) n) a = h4/combin/I (h4/bool/COND (happ (happ h4/prim__rec/_3C n) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a) (happ invtri0__tupled (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) ==> (!_3. (!invtri0__tupled n. happ (happ _3 invtri0__tupled) n = happ (happ _4 invtri0__tupled) n) ==> (!_2. (!invtri0__tupled a_27. happ (happ _2 invtri0__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 invtri0__tupled)) ==> (!_1. (!invtri0__tupled. happ _1 invtri0__tupled = happ _2 invtri0__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!a n. ~happ (happ h4/prim__rec/_3C n) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> happ (happ R (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/pair/_2C n a))) ==> h4/numpair/invtri0__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESS]: !p n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/_2D m n)) p <=> happ (happ h4/prim__rec/_3C m) (h4/arithmetic/_2B n p) /\ happ (happ h4/prim__rec/_3C h4/num/0) p
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Goal: !x l. h4/arithmetic/_2B x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/list/LENGTH l <=> (?l_27 e1. h4/list/LENGTH l_27 = x /\ l = happ (happ h4/list/CONS e1) 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_Q1111881,TV_Q1111877]: ![V_f, V_g]: (![V_x]: s(TV_Q1111877,happ(s(t_fun(TV_Q1111881,TV_Q1111877),V_f),s(TV_Q1111881,V_x))) = s(TV_Q1111877,happ(s(t_fun(TV_Q1111881,TV_Q1111877),V_g),s(TV_Q1111881,V_x))) => s(t_fun(TV_Q1111881,TV_Q1111877),V_f) = s(t_fun(TV_Q1111881,TV_Q1111877),V_g))).
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_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_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c0, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_arithmetics_SUBu_u_EQUALu_u_0, axiom, ![V_c]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_c),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_LENGTHu_u_EQu_u_NUMu_u_computeu_c1, axiom, ![TV_u_27a]: ![V_n, V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) <=> ?[V_h, V_lu_27]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_lists_LENGTHu_u_EQu_u_NUMu_c2, axiom, ![TV_u_27a]: ![V_n2, V_n1, V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n1),s(t_h4s_nums_num,V_n2))) <=> ?[V_l1, V_l2]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,V_n1) & (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_nums_num,V_n2) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c69, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c97, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_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_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_1u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c135, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c92, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_c37, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c65, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_3u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c64, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c134, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_2u_c23, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c96, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c138, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_1u_c9, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_4u_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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_5u_c68, 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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_quantHeuristicss_LISTu_u_LENGTHu_u_7u_c93, axiom, ![TV_u_27a]: ![V_x, V_l]: (p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_lu_27, V_e1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))) & s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
fof(ah4s_lists_LENu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_n, V_h]: s(t_h4s_nums_num,h4s_lists_len(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_t))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_lists_len(s(t_h4s_lists_list(TV_u_27a),V_t),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_numpairs_invtri0u_u_def, axiom, ![V_n, V_a]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),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_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),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_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)))))))))))).
fof(ah4s_numpairs_invtriu_u_unique, axiom, ![V_y, V_n]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_y),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))) => s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_y))).
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_predu_u_sets_countu_u_add1, axiom, ![V_n]: s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_count(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))))))))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,V_n),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_count(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_bools_TRUTH, axiom, 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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_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_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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_lists_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => 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,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
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_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_predu_u_sets_COUNTu_u_SUC, axiom, ![V_n]: s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_count(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,V_n),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_count(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_arithmetics_ADD1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_numpairs_invtriu_u_upper, axiom, ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numpairs_invtri(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_numpairs_invtriu_u_lower, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_n))))).
fof(ah4s_numpairs_triu_u_LE, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_numpairs_invtri0u_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_x1))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_numpairs_invtri0u_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_x1)))))).
fof(ah4s_numpairs_invtri0u_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_4]: (![V_invtri0u_u_tupled, V_n, V_a]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_a))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_combins_i(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),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_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),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_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))))))))))))))) => ![V_uu_3]: (![V_invtri0u_u_tupled, V_n]: s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_nums_num,V_n))) => ![V_uu_2]: (![V_invtri0u_u_tupled, V_au_27]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_au_27))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_au_27),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))))) => ![V_uu_1]: (![V_invtri0u_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),V_R)))) & ![V_a, V_n]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),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))))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),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_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_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_numpairs_invtri0u_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_1))))))))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESS, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_p)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_p))))))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ch4s_quantHeuristicss_LISTu_u_LENGTHu_u_10u_c139, conjecture, ![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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ?[V_lu_27, V_e1]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e1))),s(t_h4s_lists_list(TV_u_27a),V_lu_27)))))).
