%   ORIGINAL: h4/DeepSyntax/posinf__exoriginal__implies__rhs
% 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/T__DEF: T <=> (\x. x) = (\x. x)
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/bool/LEFT__OR__EXISTS__THM: !Q P. (?x. P x) \/ Q <=> (?x. P x \/ Q)
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DISJ__COMM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/COND__EXPAND: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__OR: !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/bool/UNWIND__FORALL__THM2: !v f. (!x. x = v ==> f x) <=> f v
% Assm: h4/bool/SKOLEM__THM: !P. (!x. ?y. P x y) <=> (?f. !x. P x (f x))
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% 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/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/pred__set/SUBSET__DEF: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm: h4/pred__set/SUBSET__REFL: !s. h4/pred__set/SUBSET s s
% Assm: h4/pred__set/EMPTY__SUBSET: !s. h4/pred__set/SUBSET h4/pred__set/EMPTY s
% Assm: h4/pred__set/IN__UNION: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm: h4/pred__set/UNION__SUBSET: !u t s. h4/pred__set/SUBSET (h4/pred__set/UNION s t) u <=> h4/pred__set/SUBSET s u /\ h4/pred__set/SUBSET t u
% Assm: h4/pred__set/INSERT__SUBSET: !x t s. h4/pred__set/SUBSET (h4/pred__set/INSERT x s) t <=> h4/bool/IN x t /\ h4/pred__set/SUBSET s t
% Assm: h4/pred__set/IN__SING: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm: h4/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__ADD__ASSOC: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm: h4/integer/int__sub0: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/INT__ADD__LID: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm: h4/integer/INT__ADD__RID: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/integer/INT__ADD__RINV: !x. h4/integer/int__add x (h4/integer/int__neg x) = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__ADD__RID__UNIQ: !y x. h4/integer/int__add x y = x <=> y = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__NEG__LMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm: h4/integer/INT__NOT__LT: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm: h4/integer/INT__NOT__LE: !y x. ~h4/integer/int__le x y <=> h4/integer/int__lt y x
% Assm: h4/integer/INT__LE__REFL: !x. h4/integer/int__le x x
% Assm: h4/integer/INT__NEG__LT0: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm: h4/integer/INT__LT__ADD2: !z y x w. h4/integer/int__lt w x /\ h4/integer/int__lt y z ==> h4/integer/int__lt (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm: h4/integer/INT__LE__SUB__RADD: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm: h4/integer/INT__DISCRETE: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/integer/INT__DIVIDES__LADD: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add q r) <=> h4/integer/int__divides p r)
% Assm: h4/integer/INT__DIVIDES__RADD: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add r q) <=> h4/integer/int__divides p r)
% Assm: h4/integer/INT__LT__REDUCE_c0: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm: h4/int__arith/not__less: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/int__arith/less__to__leq__samer: !y x. h4/integer/int__lt x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y
% Assm: h4/int__arith/can__get__big: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__mul c d)))
% Assm: h4/int__arith/bot__and__greaters: !x0 d P. (!x. P x ==> P (h4/integer/int__add x d)) /\ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> P (h4/integer/int__add x0 (h4/integer/int__mul c d)))
% Assm: h4/int__arith/in__subtractive__range: !x high d. h4/integer/int__le (h4/integer/int__sub high d) x /\ h4/integer/int__lt x high <=> (?j. x = h4/integer/int__sub high j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm: h4/int__arith/subtract__to__small: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__sub x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__sub x (h4/integer/int__mul k d)) d)
% Assm: h4/DeepSyntax/deep__form__repfns_c0: !a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a) = a
% Assm: h4/DeepSyntax/deep__form__repfns_c1: !r. (\a0_27. !_27deep__form_27. (!a0_270. (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27deep__form_27 a0 /\ _27deep__form_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27deep__form_27 a0 /\ _27deep__form_27 a1) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27deep__form_27 a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C a0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a00 a10)) (\n. h4/ind__type/BOTTOM)) a0 a1) ==> _27deep__form_27 a0_270) ==> _27deep__form_27 a0_27) r <=> h4/DeepSyntax/_20_40ind__typeDeepSyntax9 (h4/DeepSyntax/_20_40ind__typeDeepSyntax8 r) = r
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax0____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax0 = (\a0 a1. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a0) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a1)))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax1____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax1 = (\a0 a1. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a0) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a1)))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax2____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax2 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a)))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax3____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax3 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C a0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax4____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax4 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax5____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax5 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax6____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax6 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax7____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax7 = (\a0 a1. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a00 a10)) (\n. h4/ind__type/BOTTOM)) a0 a1))
% Assm: h4/DeepSyntax/Conjn0: h4/DeepSyntax/Conjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax0
% Assm: h4/DeepSyntax/Disjn0: h4/DeepSyntax/Disjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax1
% Assm: h4/DeepSyntax/Negn0: h4/DeepSyntax/Negn = h4/DeepSyntax/_20_40ind__typeDeepSyntax2
% Assm: h4/DeepSyntax/UnrelatedBool0: h4/DeepSyntax/UnrelatedBool = h4/DeepSyntax/_20_40ind__typeDeepSyntax3
% Assm: h4/DeepSyntax/xLT0: h4/DeepSyntax/xLT = h4/DeepSyntax/_20_40ind__typeDeepSyntax4
% Assm: h4/DeepSyntax/LTx0: h4/DeepSyntax/LTx = h4/DeepSyntax/_20_40ind__typeDeepSyntax5
% Assm: h4/DeepSyntax/xEQ0: h4/DeepSyntax/xEQ = h4/DeepSyntax/_20_40ind__typeDeepSyntax6
% Assm: h4/DeepSyntax/xDivided0: h4/DeepSyntax/xDivided = h4/DeepSyntax/_20_40ind__typeDeepSyntax7
% Assm: h4/DeepSyntax/eval__form__def_c0: !x f2 f1. h4/DeepSyntax/eval__form (h4/DeepSyntax/Conjn f1 f2) x <=> h4/DeepSyntax/eval__form f1 x /\ h4/DeepSyntax/eval__form f2 x
% Assm: h4/DeepSyntax/eval__form__def_c1: !x f2 f1. h4/DeepSyntax/eval__form (h4/DeepSyntax/Disjn f1 f2) x <=> h4/DeepSyntax/eval__form f1 x \/ h4/DeepSyntax/eval__form f2 x
% Assm: h4/DeepSyntax/eval__form__def_c2: !x f. h4/DeepSyntax/eval__form (h4/DeepSyntax/Negn f) x <=> ~h4/DeepSyntax/eval__form f x
% Assm: h4/DeepSyntax/eval__form__def_c3: !x b. h4/DeepSyntax/eval__form (h4/DeepSyntax/UnrelatedBool b) x <=> b
% Assm: h4/DeepSyntax/eval__form__def_c4: !x i. h4/DeepSyntax/eval__form (h4/DeepSyntax/xLT i) x <=> h4/integer/int__lt x i
% Assm: h4/DeepSyntax/eval__form__def_c5: !x i. h4/DeepSyntax/eval__form (h4/DeepSyntax/LTx i) x <=> h4/integer/int__lt i x
% Assm: h4/DeepSyntax/eval__form__def_c6: !x i. h4/DeepSyntax/eval__form (h4/DeepSyntax/xEQ i) x <=> x = i
% Assm: h4/DeepSyntax/eval__form__def_c7: !x i2 i1. h4/DeepSyntax/eval__form (h4/DeepSyntax/xDivided i1 i2) x <=> h4/integer/int__divides i1 (h4/integer/int__add x i2)
% Assm: h4/DeepSyntax/posinf__ok: !f. ?y. !x. h4/integer/int__lt y x ==> (h4/DeepSyntax/eval__form f x <=> h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) x)
% Assm: h4/DeepSyntax/alldivide__def_c0: !f2 f1 d. h4/DeepSyntax/alldivide (h4/DeepSyntax/Conjn f1 f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm: h4/DeepSyntax/alldivide__def_c1: !f2 f1 d. h4/DeepSyntax/alldivide (h4/DeepSyntax/Disjn f1 f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm: h4/DeepSyntax/alldivide__def_c2: !f d. h4/DeepSyntax/alldivide (h4/DeepSyntax/Negn f) d <=> h4/DeepSyntax/alldivide f d
% Assm: h4/DeepSyntax/alldivide__def_c4: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xLT i) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c5: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/LTx i) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c6: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xEQ i) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c7: !i2 i1 d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xDivided i1 i2) d <=> h4/integer/int__divides i1 d
% Assm: h4/DeepSyntax/add__d__posinf: !y x f d. h4/DeepSyntax/alldivide f d ==> (h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) x <=> h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) (h4/integer/int__add x (h4/integer/int__mul y d)))
% Assm: h4/DeepSyntax/Aset__def_c0: !pos f2 f1. h4/DeepSyntax/Aset pos (h4/DeepSyntax/Conjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Aset pos f1) (h4/DeepSyntax/Aset pos f2)
% Assm: h4/DeepSyntax/Aset__def_c1: !pos f2 f1. h4/DeepSyntax/Aset pos (h4/DeepSyntax/Disjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Aset pos f1) (h4/DeepSyntax/Aset pos f2)
% Assm: h4/DeepSyntax/Aset__def_c2: !pos f. h4/DeepSyntax/Aset pos (h4/DeepSyntax/Negn f) = h4/DeepSyntax/Aset (~pos) f
% Assm: h4/DeepSyntax/Aset__def_c4: !pos i. h4/DeepSyntax/Aset pos (h4/DeepSyntax/xLT i) = h4/bool/COND pos (h4/pred__set/INSERT i h4/pred__set/EMPTY) h4/pred__set/EMPTY
% Assm: h4/DeepSyntax/Aset__def_c5: !pos i. h4/DeepSyntax/Aset pos (h4/DeepSyntax/LTx i) = h4/bool/COND pos h4/pred__set/EMPTY (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/pred__set/EMPTY)
% Assm: h4/DeepSyntax/Aset__def_c6: !pos i. h4/DeepSyntax/Aset pos (h4/DeepSyntax/xEQ i) = h4/bool/COND pos (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/pred__set/EMPTY) (h4/pred__set/INSERT i h4/pred__set/EMPTY)
% Assm: h4/DeepSyntax/Aset__def_c7: !pos i2 i1. h4/DeepSyntax/Aset pos (h4/DeepSyntax/xDivided i1 i2) = h4/pred__set/EMPTY
% Goal: !x f d. h4/DeepSyntax/alldivide f d /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> h4/DeepSyntax/eval__form f x ==> (?i. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i d /\ h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) i) \/ (?j b. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d /\ h4/bool/IN b (h4/DeepSyntax/Aset T f) /\ h4/DeepSyntax/eval__form f (h4/integer/int__add b (h4/integer/int__neg j)))
%   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_Tu_u_DEF]: T <=> (!x. x <=> x)
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% Assm [h4s_bools_LEFTu_u_ORu_u_EXISTSu_u_THM]: !Q P. (?x. happ P x) \/ Q <=> (?x. happ P x \/ Q)
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DISJu_u_COMM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_CONDu_u_EXPAND]: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_OR]: !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_bools_UNWINDu_u_FORALLu_u_THM2]: !v f. (!x. x = v ==> happ f x) <=> happ f v
% Assm [h4s_bools_SKOLEMu_u_THM]: !P. (!x. ?y. happ (happ P x) y) <=> (?f. !x. happ (happ P x) (happ f x))
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% 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_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_SUBSETu_u_DEF]: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm [h4s_predu_u_sets_SUBSETu_u_REFL]: !s. h4/pred__set/SUBSET s s
% Assm [h4s_predu_u_sets_EMPTYu_u_SUBSET]: !s. h4/pred__set/SUBSET h4/pred__set/EMPTY s
% Assm [h4s_predu_u_sets_INu_u_UNION]: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm [h4s_predu_u_sets_UNIONu_u_SUBSET]: !u t s. h4/pred__set/SUBSET (h4/pred__set/UNION s t) u <=> h4/pred__set/SUBSET s u /\ h4/pred__set/SUBSET t u
% Assm [h4s_predu_u_sets_INSERTu_u_SUBSET]: !x t s. h4/pred__set/SUBSET (h4/pred__set/INSERT x s) t <=> h4/bool/IN x t /\ h4/pred__set/SUBSET s t
% Assm [h4s_predu_u_sets_INu_u_SING]: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm [h4s_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_ADDu_u_ASSOC]: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm [h4s_integers_intu_u_sub0]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_ADDu_u_LID]: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm [h4s_integers_INTu_u_ADDu_u_RID]: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_integers_INTu_u_ADDu_u_RINV]: !x. h4/integer/int__add x (h4/integer/int__neg x) = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_ADDu_u_RIDu_u_UNIQ]: !y x. h4/integer/int__add x y = x <=> y = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_NEGu_u_LMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm [h4s_integers_INTu_u_NOTu_u_LT]: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm [h4s_integers_INTu_u_NOTu_u_LE]: !y x. ~h4/integer/int__le x y <=> h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_LEu_u_REFL]: !x. h4/integer/int__le x x
% Assm [h4s_integers_INTu_u_NEGu_u_LT0]: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm [h4s_integers_INTu_u_LTu_u_ADD2]: !z y x w. h4/integer/int__lt w x /\ h4/integer/int__lt y z ==> h4/integer/int__lt (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_RADD]: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm [h4s_integers_INTu_u_DISCRETE]: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_integers_INTu_u_DIVIDESu_u_LADD]: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add q r) <=> h4/integer/int__divides p r)
% Assm [h4s_integers_INTu_u_DIVIDESu_u_RADD]: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add r q) <=> h4/integer/int__divides p r)
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c0]: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm [h4s_intu_u_ariths_notu_u_less]: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samer]: !y x. h4/integer/int__lt x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y
% Assm [h4s_intu_u_ariths_canu_u_getu_u_big]: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_botu_u_andu_u_greaters]: !x0 d P. (!x. happ P x ==> happ P (h4/integer/int__add x d)) /\ happ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> happ P (h4/integer/int__add x0 (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_inu_u_subtractiveu_u_range]: !x high d. h4/integer/int__le (h4/integer/int__sub high d) x /\ h4/integer/int__lt x high <=> (?j. x = h4/integer/int__sub high j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm [h4s_intu_u_ariths_subtractu_u_tou_u_small]: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__sub x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__sub x (h4/integer/int__mul k d)) d)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c0]: !a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a) = a
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27deep__form_27. (!a0_270. (?a0 a1. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27deep__form_27 a0 /\ happ _27deep__form_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27deep__form_27 a0 /\ happ _27deep__form_27 a1) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a _0) /\ happ _27deep__form_27 a) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C a (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a h4/bool/ARB)) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a h4/bool/ARB)) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a h4/bool/ARB)) _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 a1)) _0) ==> happ _27deep__form_27 a0_270) ==> happ _27deep__form_27 r) <=> h4/DeepSyntax/_20_40ind__typeDeepSyntax9 (h4/DeepSyntax/_20_40ind__typeDeepSyntax8 r) = r)
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/DeepSyntax/_20_40ind__typeDeepSyntax0 x) x' = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x') _0))))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/DeepSyntax/_20_40ind__typeDeepSyntax1 x) x' = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x') _0))))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax2 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x) _0)))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax3u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax3 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C x (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax4 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax5 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax6 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax7u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/DeepSyntax/_20_40ind__typeDeepSyntax7 x) x' = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x x')) _0))
% Assm [h4s_DeepSyntaxs_Conjn0]: h4/DeepSyntax/Conjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax0
% Assm [h4s_DeepSyntaxs_Disjn0]: h4/DeepSyntax/Disjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax1
% Assm [h4s_DeepSyntaxs_Negn0]: h4/DeepSyntax/Negn = h4/DeepSyntax/_20_40ind__typeDeepSyntax2
% Assm [h4s_DeepSyntaxs_UnrelatedBool0]: h4/DeepSyntax/UnrelatedBool = h4/DeepSyntax/_20_40ind__typeDeepSyntax3
% Assm [h4s_DeepSyntaxs_xLT0]: h4/DeepSyntax/xLT = h4/DeepSyntax/_20_40ind__typeDeepSyntax4
% Assm [h4s_DeepSyntaxs_LTx0]: h4/DeepSyntax/LTx = h4/DeepSyntax/_20_40ind__typeDeepSyntax5
% Assm [h4s_DeepSyntaxs_xEQ0]: h4/DeepSyntax/xEQ = h4/DeepSyntax/_20_40ind__typeDeepSyntax6
% Assm [h4s_DeepSyntaxs_xDivided0]: h4/DeepSyntax/xDivided = h4/DeepSyntax/_20_40ind__typeDeepSyntax7
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c0]: !x f2 f1. h4/DeepSyntax/eval__form (happ (happ h4/DeepSyntax/Conjn f1) f2) x <=> h4/DeepSyntax/eval__form f1 x /\ h4/DeepSyntax/eval__form f2 x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c1]: !x f2 f1. h4/DeepSyntax/eval__form (happ (happ h4/DeepSyntax/Disjn f1) f2) x <=> h4/DeepSyntax/eval__form f1 x \/ h4/DeepSyntax/eval__form f2 x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c2]: !x f. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/Negn f) x <=> ~h4/DeepSyntax/eval__form f x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c3]: !x b. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/UnrelatedBool b) x <=> b
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c4]: !x i. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/xLT i) x <=> h4/integer/int__lt x i
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c5]: !x i. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/LTx i) x <=> h4/integer/int__lt i x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c6]: !x i. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/xEQ i) x <=> x = i
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c7]: !x i2 i1. h4/DeepSyntax/eval__form (happ (happ h4/DeepSyntax/xDivided i1) i2) x <=> h4/integer/int__divides i1 (h4/integer/int__add x i2)
% Assm [h4s_DeepSyntaxs_posinfu_u_ok]: !f. ?y. !x. h4/integer/int__lt y x ==> (h4/DeepSyntax/eval__form f x <=> h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) x)
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c0]: !f2 f1 d. h4/DeepSyntax/alldivide (happ (happ h4/DeepSyntax/Conjn f1) f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c1]: !f2 f1 d. h4/DeepSyntax/alldivide (happ (happ h4/DeepSyntax/Disjn f1) f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c2]: !f d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/Negn f) d <=> h4/DeepSyntax/alldivide f d
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c4]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/xLT i) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c5]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/LTx i) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c6]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/xEQ i) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c7]: !i2 i1 d. h4/DeepSyntax/alldivide (happ (happ h4/DeepSyntax/xDivided i1) i2) d <=> h4/integer/int__divides i1 d
% Assm [h4s_DeepSyntaxs_addu_u_du_u_posinf]: !y x f d. h4/DeepSyntax/alldivide f d ==> (h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) x <=> h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) (h4/integer/int__add x (h4/integer/int__mul y d)))
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c0]: !pos f2 f1. h4/DeepSyntax/Aset pos (happ (happ h4/DeepSyntax/Conjn f1) f2) = h4/pred__set/UNION (h4/DeepSyntax/Aset pos f1) (h4/DeepSyntax/Aset pos f2)
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c1]: !pos f2 f1. h4/DeepSyntax/Aset pos (happ (happ h4/DeepSyntax/Disjn f1) f2) = h4/pred__set/UNION (h4/DeepSyntax/Aset pos f1) (h4/DeepSyntax/Aset pos f2)
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c2]: !pos f. ?v. (v <=> ~pos) /\ h4/DeepSyntax/Aset pos (happ h4/DeepSyntax/Negn f) = h4/DeepSyntax/Aset v f
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c4]: !pos i. h4/DeepSyntax/Aset pos (happ h4/DeepSyntax/xLT i) = h4/bool/COND pos (h4/pred__set/INSERT i h4/pred__set/EMPTY) h4/pred__set/EMPTY
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c5]: !pos i. h4/DeepSyntax/Aset pos (happ h4/DeepSyntax/LTx i) = h4/bool/COND pos h4/pred__set/EMPTY (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/pred__set/EMPTY)
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c6]: !pos i. h4/DeepSyntax/Aset pos (happ h4/DeepSyntax/xEQ i) = h4/bool/COND pos (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/pred__set/EMPTY) (h4/pred__set/INSERT i h4/pred__set/EMPTY)
% Assm [h4s_DeepSyntaxs_Asetu_u_defu_c7]: !pos i2 i1. h4/DeepSyntax/Aset pos (happ (happ h4/DeepSyntax/xDivided i1) i2) = h4/pred__set/EMPTY
% Goal: !x f d. h4/DeepSyntax/alldivide f d /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> h4/DeepSyntax/eval__form f x ==> (?i. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i d /\ h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) i) \/ (?j b. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d /\ h4/bool/IN b (h4/DeepSyntax/Aset T f) /\ h4/DeepSyntax/eval__form f (h4/integer/int__add b (h4/integer/int__neg j)))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q350294,TV_Q350290]: ![V_f, V_g]: (![V_x]: s(TV_Q350290,happ(s(t_fun(TV_Q350294,TV_Q350290),V_f),s(TV_Q350294,V_x))) = s(TV_Q350290,happ(s(t_fun(TV_Q350294,TV_Q350290),V_g),s(TV_Q350294,V_x))) => s(t_fun(TV_Q350294,TV_Q350290),V_f) = s(t_fun(TV_Q350294,TV_Q350290),V_g))).
fof(ah4s_bools_Tu_u_DEF, axiom, (p(s(t_bool,t)) <=> ![V_x]: s(t_bool,V_x) = s(t_bool,V_x))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
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_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_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_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f0))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f0))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
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_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f0))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f0) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_ANDu_u_FORALLu_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_bools_LEFTu_u_ORu_u_EXISTSu_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_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ?[V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) & ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) | ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_DISJu_u_COMM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_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_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_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_CONDu_u_EXPAND, axiom, ![V_t2, V_t1, V_b]: (p(s(t_bool,h4s_bools_cond(s(t_bool,V_b),s(t_bool,V_t1),s(t_bool,V_t2)))) <=> ((~ (p(s(t_bool,V_b))) | p(s(t_bool,V_t1))) & (p(s(t_bool,V_b)) | p(s(t_bool,V_t2)))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
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_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_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_bools_UNWINDu_u_FORALLu_u_THM2, axiom, ![TV_u_27a]: ![V_v, V_f]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_v) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_v)))))).
fof(ah4s_bools_SKOLEMu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (![V_x]: ?[V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))) <=> ?[V_f]: ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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,f0))))).
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,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
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,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
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_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_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_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_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_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_predu_u_sets_SUBSETu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_SUBSETu_u_REFL, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_predu_u_sets_EMPTYu_u_SUBSET, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_predu_u_sets_INu_u_UNION, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_UNIONu_u_SUBSET, axiom, ![TV_u_27a]: ![V_u, V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))),s(t_fun(TV_u_27a,t_bool),V_u)))) <=> (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_u)))) & p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_u))))))).
fof(ah4s_predu_u_sets_INSERTu_u_SUBSET, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t)))) & p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_INu_u_SING, axiom, ![TV_u_27a]: ![V_y, V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_integers_INTu_u_ADDu_u_COMM, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_intu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_ADDu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_RID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_RINV, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_ADDu_u_RIDu_u_UNIQ, axiom, ![V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,V_x) <=> s(t_h4s_integers_int,V_y) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_integers_INTu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_NOTu_u_LT, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_NOTu_u_LE, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_x))))).
fof(ah4s_integers_INTu_u_NEGu_u_LT0, axiom, ![V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_ADD2, axiom, ![V_z, V_y, V_x, V_w]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))))).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_DISCRETE, axiom, ![V_y, V_x]: ~ ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_INTu_u_DIVIDESu_u_LADD, axiom, ![V_r, V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) => s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_r))))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_r))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_RADD, axiom, ![V_r, V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) => s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_r),s(t_h4s_integers_int,V_q))))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_r))))).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c0, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_bool,t)).
fof(ah4s_intu_u_ariths_notu_u_less, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_intu_u_ariths_lessu_u_tou_u_lequ_u_samer, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,V_y)))).
fof(ah4s_intu_u_ariths_canu_u_getu_u_big, axiom, ![V_y, V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_botu_u_andu_u_greaters, axiom, ![V_x0, V_d, V_P]: ((![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_d))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x0))))) => ![V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x0),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_inu_u_subtractiveu_u_range, axiom, ![V_x, V_high, V_d]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,V_d))),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_high))))) <=> ?[V_j]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,V_j))) & (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_j)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_d)))))))).
fof(ah4s_intu_u_ariths_subtractu_u_tou_u_small, axiom, ![V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_k]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d)))))))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d))))),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c0, axiom, ![V_a]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_a))))) = s(t_h4s_DeepSyntaxs_deepu_u_form,V_a)).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27deepu_u_formu_27]: (![V_a0u_270]: ((?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1)))))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1)))))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a))))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,V_a),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | ?[V_a0, V_a1]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a0),s(t_h4s_integers_int,V_a1))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0)))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_r)))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax0u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax0),s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax1u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax2u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax2),s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax3u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax3),s(t_bool,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,V_x),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax4u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax4),s(t_h4s_integers_int,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax5u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax5),s(t_h4s_integers_int,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax6u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax6),s(t_h4s_integers_int,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax7u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax7),s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_xi_))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_xi_))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_Conjn0, axiom, s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn) = s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax0)).
fof(ah4s_DeepSyntaxs_Disjn0, axiom, s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn) = s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax1)).
fof(ah4s_DeepSyntaxs_Negn0, axiom, s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn) = s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax2)).
fof(ah4s_DeepSyntaxs_UnrelatedBool0, axiom, s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool) = s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax3)).
fof(ah4s_DeepSyntaxs_xLT0, axiom, s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt) = s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax4)).
fof(ah4s_DeepSyntaxs_LTx0, axiom, s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx) = s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax5)).
fof(ah4s_DeepSyntaxs_xEQ0, axiom, s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq) = s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax6)).
fof(ah4s_DeepSyntaxs_xDivided0, axiom, s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax7)).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c0, axiom, ![V_x, V_f2, V_f1]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_x)))) <=> (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c1, axiom, ![V_x, V_f2, V_f1]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_x)))) <=> (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_x)))) | p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c2, axiom, ![V_x, V_f]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_x)))) <=> ~ (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c3, axiom, ![V_x, V_b]: s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_b))),s(t_h4s_integers_int,V_x))) = s(t_bool,V_b)).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c4, axiom, ![V_x, V_i]: s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_i)))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c5, axiom, ![V_x, V_i]: s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_x)))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c6, axiom, ![V_x, V_i]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_x)))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_i))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c7, axiom, ![V_x, V_i2, V_i1]: s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided),s(t_h4s_integers_int,V_i1))),s(t_h4s_integers_int,V_i2))),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_i1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_i2)))))).
fof(ah4s_DeepSyntaxs_posinfu_u_ok, axiom, ![V_f]: ?[V_y]: ![V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))) => s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_x))))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c0, axiom, ![V_f2, V_f1, V_d]: (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_d)))) <=> (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_d)))) & p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c1, axiom, ![V_f2, V_f1, V_d]: (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_d)))) <=> (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_d)))) & p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c2, axiom, ![V_f, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_d))) = s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_d)))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c4, axiom, ![V_i, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c5, axiom, ![V_i, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c6, axiom, ![V_i, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c7, axiom, ![V_i2, V_i1, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided),s(t_h4s_integers_int,V_i1))),s(t_h4s_integers_int,V_i2))),s(t_h4s_integers_int,V_d))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_i1),s(t_h4s_integers_int,V_d)))).
fof(ah4s_DeepSyntaxs_addu_u_du_u_posinf, axiom, ![V_y, V_x, V_f, V_d]: (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_d)))) => s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_d))))))))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c0, axiom, ![V_pos, V_f2, V_f1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c1, axiom, ![V_pos, V_f2, V_f1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c2, axiom, ![V_pos, V_f]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ~ (p(s(t_bool,V_pos)))) & s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_v),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c4, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt),s(t_h4s_integers_int,V_i))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,V_pos),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,V_i),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c5, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx),s(t_h4s_integers_int,V_i))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,V_pos),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c6, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq),s(t_h4s_integers_int,V_i))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,V_pos),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,V_i),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_DeepSyntaxs_Asetu_u_defu_c7, axiom, ![V_pos, V_i2, V_i1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided),s(t_h4s_integers_int,V_i1))),s(t_h4s_integers_int,V_i2))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)).
fof(ch4s_DeepSyntaxs_posinfu_u_exoriginalu_u_impliesu_u_rhs, conjecture, ![V_x, V_f, V_d]: ((p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_d)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d))))) => (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_x)))) => (?[V_i]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i)))) & (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_d)))) & p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_i)))))) | ?[V_j, V_b]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_j)))) & (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_d)))) & (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_b),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,t),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f)))))) & p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_b),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_j))))))))))))))).
