%   ORIGINAL: h4/DeepSyntax/in__aset_c10
% 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/TRUTH: T
% Assm: h4/DeepSyntax/xEQ0: h4/DeepSyntax/xEQ = h4/DeepSyntax/_20_40ind__typeDeepSyntax6
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/DeepSyntax/in__aset_c9: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (h4/DeepSyntax/xEQ i)) /\ P a) <=> P (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/DeepSyntax/xLT0: h4/DeepSyntax/xLT = h4/DeepSyntax/_20_40ind__typeDeepSyntax4
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% 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____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/deep__form__repfns_c0: !a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a) = a
% 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/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/DeepSyntax/LTx0: h4/DeepSyntax/LTx = h4/DeepSyntax/_20_40ind__typeDeepSyntax5
% 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/xDivided0: h4/DeepSyntax/xDivided = h4/DeepSyntax/_20_40ind__typeDeepSyntax7
% 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/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/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/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/UnrelatedBool0: h4/DeepSyntax/UnrelatedBool = h4/DeepSyntax/_20_40ind__typeDeepSyntax3
% 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/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/DeepSyntax/in__bset_c10: !i P. (?b. h4/bool/IN b (h4/DeepSyntax/Bset F (h4/DeepSyntax/xEQ i)) /\ P b) <=> P i
% Assm: h4/DeepSyntax/in__bset_c9: !i P. (?b. h4/bool/IN b (h4/DeepSyntax/Bset T (h4/DeepSyntax/xEQ i)) /\ P b) <=> P (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/DeepSyntax/Bset__def_c6: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xEQ i) = h4/bool/COND pos (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (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/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/DeepSyntax/in__aset_c2: !f P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (h4/DeepSyntax/Negn f)) /\ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset F f) /\ P a)
% Assm: h4/DeepSyntax/in__aset_c4: !pos a0 P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos (h4/DeepSyntax/UnrelatedBool a0)) /\ P a) <=> F
% Assm: h4/DeepSyntax/in__aset_c7: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (h4/DeepSyntax/LTx i)) /\ P a) <=> F
% Assm: h4/DeepSyntax/in__aset_c8: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (h4/DeepSyntax/LTx i)) /\ P a) <=> P (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/DeepSyntax/in__aset_c3: !f P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (h4/DeepSyntax/Negn f)) /\ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset T f) /\ P a)
% Assm: h4/DeepSyntax/deep__form__case__def_c6: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/xEQ a) f f1 f2 f3 f4 f5 f6 f7 = f6 a
% Assm: h4/DeepSyntax/in__aset_c6: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (h4/DeepSyntax/xLT i)) /\ P a) <=> F
% Assm: h4/DeepSyntax/posinf__def_c6: !i. h4/DeepSyntax/posinf (h4/DeepSyntax/xEQ i) = h4/DeepSyntax/UnrelatedBool F
% Assm: h4/DeepSyntax/neginf__def_c6: !i. h4/DeepSyntax/neginf (h4/DeepSyntax/xEQ i) = h4/DeepSyntax/UnrelatedBool F
% Assm: h4/DeepSyntax/in__aset_c5: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (h4/DeepSyntax/xLT i)) /\ P a) <=> P i
% Assm: h4/DeepSyntax/in__aset_c1: !pos f2 f1 P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos (h4/DeepSyntax/Disjn f1 f2)) /\ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f1) /\ P a) \/ (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f2) /\ P a)
% Assm: h4/DeepSyntax/in__aset_c0: !pos f2 f1 P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos (h4/DeepSyntax/Conjn f1 f2)) /\ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f1) /\ P a) \/ (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f2) /\ P a)
% Assm: h4/DeepSyntax/deep__form__11_c6: !a_27 a. h4/DeepSyntax/xEQ a = h4/DeepSyntax/xEQ a_27 <=> a = a_27
% Assm: h4/DeepSyntax/deep__form__nchotomy: !dd. (?d d0. dd = h4/DeepSyntax/Conjn d d0) \/ (?d d0. dd = h4/DeepSyntax/Disjn d d0) \/ (?d. dd = h4/DeepSyntax/Negn d) \/ (?b. dd = h4/DeepSyntax/UnrelatedBool b) \/ (?i. dd = h4/DeepSyntax/xLT i) \/ (?i. dd = h4/DeepSyntax/LTx i) \/ (?i. dd = h4/DeepSyntax/xEQ i) \/ (?i i0. dd = h4/DeepSyntax/xDivided i i0)
% Assm: h4/DeepSyntax/deep__form__size__def_c6: !a. h4/DeepSyntax/deep__form__size (h4/DeepSyntax/xEQ a) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/DeepSyntax/deep__form__distinct_c25: !a_27 a. ~(h4/DeepSyntax/LTx a = h4/DeepSyntax/xEQ a_27)
% Assm: h4/DeepSyntax/deep__form__distinct_c5: !a1 a0 a. ~(h4/DeepSyntax/Conjn a0 a1 = h4/DeepSyntax/xEQ a)
% Assm: h4/DeepSyntax/deep__form__distinct_c11: !a1 a0 a. ~(h4/DeepSyntax/Disjn a0 a1 = h4/DeepSyntax/xEQ a)
% Assm: h4/DeepSyntax/deep__form__distinct_c23: !a_27 a. ~(h4/DeepSyntax/xLT a = h4/DeepSyntax/xEQ a_27)
% Assm: h4/DeepSyntax/deep__form__distinct_c27: !a1 a0 a. ~(h4/DeepSyntax/xEQ a = h4/DeepSyntax/xDivided a0 a1)
% Assm: h4/DeepSyntax/deep__form__case__cong: !f7_27 f7 f6_27 f6 f5_27 f5 f4_27 f4 f3_27 f3 f2_27 f2 f1_27 f1 f_27 f M_27 M. M = M_27 /\ (!a0 a1. M_27 = h4/DeepSyntax/Conjn a0 a1 ==> f a0 a1 = f_27 a0 a1) /\ (!a0 a1. M_27 = h4/DeepSyntax/Disjn a0 a1 ==> f1 a0 a1 = f1_27 a0 a1) /\ (!a. M_27 = h4/DeepSyntax/Negn a ==> f2 a = f2_27 a) /\ (!a. M_27 = h4/DeepSyntax/UnrelatedBool a ==> f3 a = f3_27 a) /\ (!a. M_27 = h4/DeepSyntax/xLT a ==> f4 a = f4_27 a) /\ (!a. M_27 = h4/DeepSyntax/LTx a ==> f5 a = f5_27 a) /\ (!a. M_27 = h4/DeepSyntax/xEQ a ==> f6 a = f6_27 a) /\ (!a0 a1. M_27 = h4/DeepSyntax/xDivided a0 a1 ==> f7 a0 a1 = f7_27 a0 a1) ==> h4/DeepSyntax/deep__form__CASE M f f1 f2 f3 f4 f5 f6 f7 = h4/DeepSyntax/deep__form__CASE M_27 f_27 f1_27 f2_27 f3_27 f4_27 f5_27 f6_27 f7_27
% Assm: h4/DeepSyntax/eval__form__def_c6: !x i. h4/DeepSyntax/eval__form (h4/DeepSyntax/xEQ i) x <=> x = i
% Assm: h4/DeepSyntax/deep__form__distinct_c20: !a_27 a. ~(h4/DeepSyntax/UnrelatedBool a = h4/DeepSyntax/xEQ a_27)
% Assm: h4/DeepSyntax/deep__form__Axiom: !f7 f6 f5 f4 f3 f2 f1 f0. ?fn. (!a0 a1. fn (h4/DeepSyntax/Conjn a0 a1) = f0 a0 a1 (fn a0) (fn a1)) /\ (!a0 a1. fn (h4/DeepSyntax/Disjn a0 a1) = f1 a0 a1 (fn a0) (fn a1)) /\ (!a. fn (h4/DeepSyntax/Negn a) = f2 a (fn a)) /\ (!a. fn (h4/DeepSyntax/UnrelatedBool a) = f3 a) /\ (!a. fn (h4/DeepSyntax/xLT a) = f4 a) /\ (!a. fn (h4/DeepSyntax/LTx a) = f5 a) /\ (!a. fn (h4/DeepSyntax/xEQ a) = f6 a) /\ (!a0 a1. fn (h4/DeepSyntax/xDivided a0 a1) = f7 a0 a1)
% Assm: h4/DeepSyntax/alldivide__def_c6: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xEQ i) d <=> T
% Assm: h4/DeepSyntax/deep__form__distinct_c16: !a_27 a. ~(h4/DeepSyntax/Negn a = h4/DeepSyntax/xEQ a_27)
% Assm: h4/DeepSyntax/deep__form__induction: !P. (!d d0. P d /\ P d0 ==> P (h4/DeepSyntax/Conjn d d0)) /\ (!d d0. P d /\ P d0 ==> P (h4/DeepSyntax/Disjn d d0)) /\ (!d. P d ==> P (h4/DeepSyntax/Negn d)) /\ (!b. P (h4/DeepSyntax/UnrelatedBool b)) /\ (!i. P (h4/DeepSyntax/xLT i)) /\ (!i. P (h4/DeepSyntax/LTx i)) /\ (!i. P (h4/DeepSyntax/xEQ i)) /\ (!i i0. P (h4/DeepSyntax/xDivided i i0)) ==> (!d. P d)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% 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/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/DeepSyntax/datatype__deep__form: !deep__form. h4/bool/DATATYPE (deep__form h4/DeepSyntax/Conjn h4/DeepSyntax/Disjn h4/DeepSyntax/Negn h4/DeepSyntax/UnrelatedBool h4/DeepSyntax/xLT h4/DeepSyntax/LTx h4/DeepSyntax/xEQ h4/DeepSyntax/xDivided)
% Assm: h4/bool/FALSITY: !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/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% 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/IN__SING: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% 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_c7: !pos i2 i1. h4/DeepSyntax/Aset pos (h4/DeepSyntax/xDivided i1 i2) = h4/pred__set/EMPTY
% 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_c3: !pos b. h4/DeepSyntax/Aset pos (h4/DeepSyntax/UnrelatedBool b) = h4/pred__set/EMPTY
% 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_c2: !pos f. h4/DeepSyntax/Aset pos (h4/DeepSyntax/Negn f) = h4/DeepSyntax/Aset (~pos) f
% 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/posinf__exoriginal__eq__rhs: !f d. h4/DeepSyntax/alldivide f d /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> ((?x. h4/DeepSyntax/eval__form f x) <=> (?i. h4/combin/K (h4/integer/int__lt (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i d) i /\ h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) i) \/ (?b j. (h4/bool/IN b (h4/DeepSyntax/Aset T f) /\ h4/combin/K (h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d) j) /\ h4/DeepSyntax/eval__form f (h4/integer/int__add b (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) j))))
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/DeepSyntax/Bset__def_c7: !pos i2 i1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xDivided i1 i2) = h4/pred__set/EMPTY
% Assm: h4/DeepSyntax/Bset__def_c5: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/LTx i) = h4/bool/COND pos (h4/pred__set/INSERT i h4/pred__set/EMPTY) h4/pred__set/EMPTY
% Assm: h4/DeepSyntax/Bset__def_c3: !pos b. h4/DeepSyntax/Bset pos (h4/DeepSyntax/UnrelatedBool b) = h4/pred__set/EMPTY
% Assm: h4/DeepSyntax/Bset__def_c4: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xLT i) = h4/bool/COND pos h4/pred__set/EMPTY (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/pred__set/EMPTY)
% Assm: h4/DeepSyntax/Bset__def_c2: !pos f. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Negn f) = h4/DeepSyntax/Bset (~pos) f
% Assm: h4/DeepSyntax/Bset__def_c1: !pos f2 f1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Disjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm: h4/DeepSyntax/Bset__def_c0: !pos f2 f1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Conjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm: h4/DeepSyntax/deep__form__case__def_c7: !f7 f6 f5 f4 f3 f2 f1 f a1 a0. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/xDivided a0 a1) f f1 f2 f3 f4 f5 f6 f7 = f7 a0 a1
% Assm: h4/DeepSyntax/deep__form__case__def_c5: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/LTx a) f f1 f2 f3 f4 f5 f6 f7 = f5 a
% Assm: h4/DeepSyntax/deep__form__case__def_c3: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/UnrelatedBool a) f f1 f2 f3 f4 f5 f6 f7 = f3 a
% Assm: h4/DeepSyntax/deep__form__case__def_c2: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/Negn a) f f1 f2 f3 f4 f5 f6 f7 = f2 a
% Assm: h4/DeepSyntax/deep__form__case__def_c4: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/xLT a) f f1 f2 f3 f4 f5 f6 f7 = f4 a
% Assm: h4/DeepSyntax/deep__form__case__def_c1: !f7 f6 f5 f4 f3 f2 f1 f a1 a0. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/Disjn a0 a1) f f1 f2 f3 f4 f5 f6 f7 = f1 a0 a1
% Assm: h4/DeepSyntax/deep__form__case__def_c0: !f7 f6 f5 f4 f3 f2 f1 f a1 a0. h4/DeepSyntax/deep__form__CASE (h4/DeepSyntax/Conjn a0 a1) f f1 f2 f3 f4 f5 f6 f7 = f a0 a1
% Goal: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (h4/DeepSyntax/xEQ i)) /\ P a) <=> P i
%   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_TRUTH]: T
% Assm [h4s_DeepSyntaxs_xEQ0]: h4/DeepSyntax/xEQ = h4/DeepSyntax/_20_40ind__typeDeepSyntax6
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c9]: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (happ h4/DeepSyntax/xEQ i)) /\ happ P a) <=> happ P (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_DeepSyntaxs_xLT0]: h4/DeepSyntax/xLT = h4/DeepSyntax/_20_40ind__typeDeepSyntax4
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% 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_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_deepu_u_formu_u_repfnsu_c0]: !a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a) = a
% 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_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_DeepSyntaxs_LTx0]: h4/DeepSyntax/LTx = h4/DeepSyntax/_20_40ind__typeDeepSyntax5
% 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_xDivided0]: h4/DeepSyntax/xDivided = h4/DeepSyntax/_20_40ind__typeDeepSyntax7
% 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_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_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_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_UnrelatedBool0]: h4/DeepSyntax/UnrelatedBool = h4/DeepSyntax/_20_40ind__typeDeepSyntax3
% 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_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_DeepSyntaxs_inu_u_bsetu_c10]: !i P. (?b. h4/bool/IN b (h4/DeepSyntax/Bset F (happ h4/DeepSyntax/xEQ i)) /\ happ P b) <=> happ P i
% Assm [h4s_DeepSyntaxs_inu_u_bsetu_c9]: !i P. (?b. h4/bool/IN b (h4/DeepSyntax/Bset T (happ h4/DeepSyntax/xEQ i)) /\ happ P b) <=> happ P (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c6]: !pos i. h4/DeepSyntax/Bset pos (happ h4/DeepSyntax/xEQ i) = h4/bool/COND pos (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (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_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c2]: !f P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (happ h4/DeepSyntax/Negn f)) /\ happ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset F f) /\ happ P a)
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c4]: !pos a0 P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos (happ h4/DeepSyntax/UnrelatedBool a0)) /\ happ P a) <=> F
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c7]: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (happ h4/DeepSyntax/LTx i)) /\ happ P a) <=> F
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c8]: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (happ h4/DeepSyntax/LTx i)) /\ happ P a) <=> happ P (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c3]: !f P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (happ h4/DeepSyntax/Negn f)) /\ happ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset T f) /\ happ P a)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c6]: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (happ h4/DeepSyntax/xEQ a) f f1 f2 f3 f4 f5 f6 f7 = happ f6 a
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c6]: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (happ h4/DeepSyntax/xLT i)) /\ happ P a) <=> F
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c6]: !i. h4/DeepSyntax/posinf (happ h4/DeepSyntax/xEQ i) = happ h4/DeepSyntax/UnrelatedBool F
% Assm [h4s_DeepSyntaxs_neginfu_u_defu_c6]: !i. h4/DeepSyntax/neginf (happ h4/DeepSyntax/xEQ i) = happ h4/DeepSyntax/UnrelatedBool F
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c5]: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset T (happ h4/DeepSyntax/xLT i)) /\ happ P a) <=> happ P i
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c1]: !pos f2 f1 P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos (happ (happ h4/DeepSyntax/Disjn f1) f2)) /\ happ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f1) /\ happ P a) \/ (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f2) /\ happ P a)
% Assm [h4s_DeepSyntaxs_inu_u_asetu_c0]: !pos f2 f1 P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos (happ (happ h4/DeepSyntax/Conjn f1) f2)) /\ happ P a) <=> (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f1) /\ happ P a) \/ (?a. h4/bool/IN a (h4/DeepSyntax/Aset pos f2) /\ happ P a)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_11u_c6]: !a_27 a. happ h4/DeepSyntax/xEQ a = happ h4/DeepSyntax/xEQ a_27 <=> a = a_27
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_nchotomy]: !dd. (?d d0. dd = happ (happ h4/DeepSyntax/Conjn d) d0) \/ (?d d0. dd = happ (happ h4/DeepSyntax/Disjn d) d0) \/ (?d. dd = happ h4/DeepSyntax/Negn d) \/ (?b. dd = happ h4/DeepSyntax/UnrelatedBool b) \/ (?i. dd = happ h4/DeepSyntax/xLT i) \/ (?i. dd = happ h4/DeepSyntax/LTx i) \/ (?i. dd = happ h4/DeepSyntax/xEQ i) \/ (?i i0. dd = happ (happ h4/DeepSyntax/xDivided i) i0)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_sizeu_u_defu_c6]: !a. h4/DeepSyntax/deep__form__size (happ h4/DeepSyntax/xEQ a) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c25]: !a_27 a. ~(happ h4/DeepSyntax/LTx a = happ h4/DeepSyntax/xEQ a_27)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c5]: !a1 a0 a. ~(happ (happ h4/DeepSyntax/Conjn a0) a1 = happ h4/DeepSyntax/xEQ a)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c11]: !a1 a0 a. ~(happ (happ h4/DeepSyntax/Disjn a0) a1 = happ h4/DeepSyntax/xEQ a)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c23]: !a_27 a. ~(happ h4/DeepSyntax/xLT a = happ h4/DeepSyntax/xEQ a_27)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c27]: !a1 a0 a. ~(happ h4/DeepSyntax/xEQ a = happ (happ h4/DeepSyntax/xDivided a0) a1)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_cong]: !f7_27 f7 f6_27 f6 f5_27 f5 f4_27 f4 f3_27 f3 f2_27 f2 f1_27 f1 f_27 f M_27 M. M = M_27 /\ (!a0 a1. M_27 = happ (happ h4/DeepSyntax/Conjn a0) a1 ==> happ (happ f a0) a1 = happ (happ f_27 a0) a1) /\ (!a0 a1. M_27 = happ (happ h4/DeepSyntax/Disjn a0) a1 ==> happ (happ f1 a0) a1 = happ (happ f1_27 a0) a1) /\ (!a. M_27 = happ h4/DeepSyntax/Negn a ==> happ f2 a = happ f2_27 a) /\ (!a. M_27 = happ h4/DeepSyntax/UnrelatedBool a ==> happ f3 a = happ f3_27 a) /\ (!a. M_27 = happ h4/DeepSyntax/xLT a ==> happ f4 a = happ f4_27 a) /\ (!a. M_27 = happ h4/DeepSyntax/LTx a ==> happ f5 a = happ f5_27 a) /\ (!a. M_27 = happ h4/DeepSyntax/xEQ a ==> happ f6 a = happ f6_27 a) /\ (!a0 a1. M_27 = happ (happ h4/DeepSyntax/xDivided a0) a1 ==> happ (happ f7 a0) a1 = happ (happ f7_27 a0) a1) ==> h4/DeepSyntax/deep__form__CASE M f f1 f2 f3 f4 f5 f6 f7 = h4/DeepSyntax/deep__form__CASE M_27 f_27 f1_27 f2_27 f3_27 f4_27 f5_27 f6_27 f7_27
% 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_deepu_u_formu_u_distinctu_c20]: !a_27 a. ~(happ h4/DeepSyntax/UnrelatedBool a = happ h4/DeepSyntax/xEQ a_27)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_Axiom]: !f7 f6 f5 f4 f3 f2 f1 f0. ?fn. (!a0 a1. happ fn (happ (happ h4/DeepSyntax/Conjn a0) a1) = happ (happ (happ (happ f0 a0) a1) (happ fn a0)) (happ fn a1)) /\ (!a0 a1. happ fn (happ (happ h4/DeepSyntax/Disjn a0) a1) = happ (happ (happ (happ f1 a0) a1) (happ fn a0)) (happ fn a1)) /\ (!a. happ fn (happ h4/DeepSyntax/Negn a) = happ (happ f2 a) (happ fn a)) /\ (!a. happ fn (happ h4/DeepSyntax/UnrelatedBool a) = happ f3 a) /\ (!a. happ fn (happ h4/DeepSyntax/xLT a) = happ f4 a) /\ (!a. happ fn (happ h4/DeepSyntax/LTx a) = happ f5 a) /\ (!a. happ fn (happ h4/DeepSyntax/xEQ a) = happ f6 a) /\ (!a0 a1. happ fn (happ (happ h4/DeepSyntax/xDivided a0) a1) = happ (happ f7 a0) a1)
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c6]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/xEQ i) d <=> T
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c16]: !a_27 a. ~(happ h4/DeepSyntax/Negn a = happ h4/DeepSyntax/xEQ a_27)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_induction]: !P. (!d d0. happ P d /\ happ P d0 ==> happ P (happ (happ h4/DeepSyntax/Conjn d) d0)) /\ (!d d0. happ P d /\ happ P d0 ==> happ P (happ (happ h4/DeepSyntax/Disjn d) d0)) /\ (!d. happ P d ==> happ P (happ h4/DeepSyntax/Negn d)) /\ (!b. happ P (happ h4/DeepSyntax/UnrelatedBool b)) /\ (!i. happ P (happ h4/DeepSyntax/xLT i)) /\ (!i. happ P (happ h4/DeepSyntax/LTx i)) /\ (!i. happ P (happ h4/DeepSyntax/xEQ i)) /\ (!i i0. happ P (happ (happ h4/DeepSyntax/xDivided i) i0)) ==> (!d. happ P d)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% 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_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_DeepSyntaxs_datatypeu_u_deepu_u_form]: !deep__form. h4/bool/DATATYPE (happ (happ (happ (happ (happ (happ (happ (happ deep__form h4/DeepSyntax/Conjn) h4/DeepSyntax/Disjn) h4/DeepSyntax/Negn) h4/DeepSyntax/UnrelatedBool) h4/DeepSyntax/xLT) h4/DeepSyntax/LTx) h4/DeepSyntax/xEQ) h4/DeepSyntax/xDivided)
% Assm [h4s_bools_FALSITY]: !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_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% 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_INu_u_SING]: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% 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_c7]: !pos i2 i1. h4/DeepSyntax/Aset pos (happ (happ h4/DeepSyntax/xDivided i1) i2) = h4/pred__set/EMPTY
% 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_c3]: !pos b. h4/DeepSyntax/Aset pos (happ h4/DeepSyntax/UnrelatedBool b) = h4/pred__set/EMPTY
% 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_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_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_posinfu_u_exoriginalu_u_equ_u_rhs]: !f d. h4/DeepSyntax/alldivide f d /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> ((?x. h4/DeepSyntax/eval__form f x) <=> (?i. (?v. (v <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i d) /\ h4/combin/K v i) /\ h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) i) \/ (?b j. (h4/bool/IN b (h4/DeepSyntax/Aset T f) /\ (?v. (v <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d) /\ h4/combin/K v j)) /\ h4/DeepSyntax/eval__form f (h4/integer/int__add b (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) j))))
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c7]: !pos i2 i1. h4/DeepSyntax/Bset pos (happ (happ h4/DeepSyntax/xDivided i1) i2) = h4/pred__set/EMPTY
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c5]: !pos i. h4/DeepSyntax/Bset pos (happ h4/DeepSyntax/LTx i) = h4/bool/COND pos (h4/pred__set/INSERT i h4/pred__set/EMPTY) h4/pred__set/EMPTY
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c3]: !pos b. h4/DeepSyntax/Bset pos (happ h4/DeepSyntax/UnrelatedBool b) = h4/pred__set/EMPTY
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c4]: !pos i. h4/DeepSyntax/Bset pos (happ h4/DeepSyntax/xLT i) = h4/bool/COND pos h4/pred__set/EMPTY (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/pred__set/EMPTY)
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c2]: !pos f. ?v. (v <=> ~pos) /\ h4/DeepSyntax/Bset pos (happ h4/DeepSyntax/Negn f) = h4/DeepSyntax/Bset v f
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c1]: !pos f2 f1. h4/DeepSyntax/Bset pos (happ (happ h4/DeepSyntax/Disjn f1) f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c0]: !pos f2 f1. h4/DeepSyntax/Bset pos (happ (happ h4/DeepSyntax/Conjn f1) f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c7]: !f7 f6 f5 f4 f3 f2 f1 f a1 a0. h4/DeepSyntax/deep__form__CASE (happ (happ h4/DeepSyntax/xDivided a0) a1) f f1 f2 f3 f4 f5 f6 f7 = happ (happ f7 a0) a1
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c5]: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (happ h4/DeepSyntax/LTx a) f f1 f2 f3 f4 f5 f6 f7 = happ f5 a
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c3]: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (happ h4/DeepSyntax/UnrelatedBool a) f f1 f2 f3 f4 f5 f6 f7 = happ f3 a
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c2]: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (happ h4/DeepSyntax/Negn a) f f1 f2 f3 f4 f5 f6 f7 = happ f2 a
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c4]: !f7 f6 f5 f4 f3 f2 f1 f a. h4/DeepSyntax/deep__form__CASE (happ h4/DeepSyntax/xLT a) f f1 f2 f3 f4 f5 f6 f7 = happ f4 a
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c1]: !f7 f6 f5 f4 f3 f2 f1 f a1 a0. h4/DeepSyntax/deep__form__CASE (happ (happ h4/DeepSyntax/Disjn a0) a1) f f1 f2 f3 f4 f5 f6 f7 = happ (happ f1 a0) a1
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c0]: !f7 f6 f5 f4 f3 f2 f1 f a1 a0. h4/DeepSyntax/deep__form__CASE (happ (happ h4/DeepSyntax/Conjn a0) a1) f f1 f2 f3 f4 f5 f6 f7 = happ (happ f a0) a1
% Goal: !i P. (?a. h4/bool/IN a (h4/DeepSyntax/Aset F (happ h4/DeepSyntax/xEQ i)) /\ happ P a) <=> happ P i
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1447588,TV_Q1447584]: ![V_f, V_g]: (![V_x]: s(TV_Q1447584,happ(s(t_fun(TV_Q1447588,TV_Q1447584),V_f),s(TV_Q1447588,V_x))) = s(TV_Q1447584,happ(s(t_fun(TV_Q1447588,TV_Q1447584),V_g),s(TV_Q1447588,V_x))) => s(t_fun(TV_Q1447588,TV_Q1447584),V_f) = s(t_fun(TV_Q1447588,TV_Q1447584),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_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_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_DeepSyntaxs_inu_u_asetu_c9, axiom, ![V_i, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,t),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> 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_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)))))))))))))).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_DeepSyntaxs_inu_u_bsetu_c10, axiom, ![V_i, V_P]: (?[V_b]: (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_bset(s(t_bool,f),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_b))))) <=> p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_i)))))).
fof(ah4s_DeepSyntaxs_inu_u_bsetu_c9, axiom, ![V_i, V_P]: (?[V_b]: (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_bset(s(t_bool,t),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_b))))) <=> 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_i),s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_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_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_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_DeepSyntaxs_Bsetu_u_defu_c6, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(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_neg(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_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c2, axiom, ![V_f, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,t),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> ?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,f),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c4, axiom, ![V_pos, V_a0, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_a0)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> p(s(t_bool,f)))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c7, axiom, ![V_i, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,t),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> p(s(t_bool,f)))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c8, axiom, ![V_i, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,f),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> 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_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)))))))))))))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c3, axiom, ![V_f, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,f),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> ?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c6, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_h4s_integers_int,V_a)))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c6, axiom, ![V_i, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,f),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> p(s(t_bool,f)))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c6, axiom, ![V_i]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(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_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,f)))).
fof(ah4s_DeepSyntaxs_neginfu_u_defu_c6, axiom, ![V_i]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_neginf(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_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,f)))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c5, axiom, ![V_i, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,t),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_i)))))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c1, axiom, ![V_pos, V_f2, V_f1, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) | ?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a)))))))).
fof(ah4s_DeepSyntaxs_inu_u_asetu_c0, axiom, ![V_pos, V_f2, V_f1, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) | ?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),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)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a)))))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_11u_c6, axiom, ![V_au_27, V_a]: (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_a))) = 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_au_27))) <=> s(t_h4s_integers_int,V_a) = s(t_h4s_integers_int,V_au_27))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_nchotomy, axiom, ![V_dd]: (?[V_d, V_d0]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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_d))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d0))) | (?[V_d, V_d0]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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_d))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d0))) | (?[V_d]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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_d))) | (?[V_b]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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))) | (?[V_i]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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))) | (?[V_i]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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))) | (?[V_i]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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))) | ?[V_i, V_i0]: s(t_h4s_DeepSyntaxs_deepu_u_form,V_dd) = 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_i))),s(t_h4s_integers_int,V_i0))))))))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_sizeu_u_defu_c6, axiom, ![V_a]: s(t_h4s_nums_num,h4s_deepsyntaxs_deepu_u_formu_u_size(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_a))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c25, axiom, ![V_au_27, V_a]: ~ (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_a))) = 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_au_27))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c5, axiom, ![V_a1, V_a0, V_a]: ~ (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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))) = 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_a))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c11, axiom, ![V_a1, V_a0, V_a]: ~ (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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))) = 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_a))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c23, axiom, ![V_au_27, V_a]: ~ (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_a))) = 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_au_27))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_distinctu_c27, axiom, ![V_a1, V_a0, V_a]: ~ (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_a))) = 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_a0))),s(t_h4s_integers_int,V_a1))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_cong, axiom, ![TV_u_27a]: ![V_f7u_27, V_f7, V_f6u_27, V_f6, V_f5u_27, V_f5, V_f4u_27, V_f4, V_f3u_27, V_f3, V_f2u_27, V_f2, V_f1u_27, V_f1, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_DeepSyntaxs_deepu_u_form,V_M) = s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) & (![V_a0, V_a1]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))) => s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_fu_27),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1)))) & (![V_a0, V_a1]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))) => s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1u_27),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1)))) & (![V_a]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2u_27),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a)))) & (![V_a]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a))) => s(TV_u_27a,happ(s(t_fun(t_bool,TV_u_27a),V_f3),s(t_bool,V_a))) = s(TV_u_27a,happ(s(t_fun(t_bool,TV_u_27a),V_f3u_27),s(t_bool,V_a)))) & (![V_a]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_h4s_integers_int,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4u_27),s(t_h4s_integers_int,V_a)))) & (![V_a]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_h4s_integers_int,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5u_27),s(t_h4s_integers_int,V_a)))) & (![V_a]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_h4s_integers_int,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6u_27),s(t_h4s_integers_int,V_a)))) & ![V_a0, V_a1]: (s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27) = 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_a0))),s(t_h4s_integers_int,V_a1))) => s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7),s(t_h4s_integers_int,V_a0))),s(t_h4s_integers_int,V_a1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7u_27),s(t_h4s_integers_int,V_a0))),s(t_h4s_integers_int,V_a1)))))))))))) => s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(s(t_h4s_DeepSyntaxs_deepu_u_form,V_M),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(s(t_h4s_DeepSyntaxs_deepu_u_form,V_Mu_27),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_fu_27),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1u_27),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2u_27),s(t_fun(t_bool,TV_u_27a),V_f3u_27),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4u_27),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5u_27),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6u_27),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7u_27))))).
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_deepu_u_formu_u_distinctu_c20, axiom, ![V_au_27, V_a]: ~ (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_a))) = 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_au_27))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_Axiom, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f0]: ?[V_fn]: (![V_a0, V_a1]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)))),V_f0),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))),s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))))),s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))))) & (![V_a0, V_a1]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)))),V_f1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))),s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))))),s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))))) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(TV_u_27a,TV_u_27a)),V_f2),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a))))) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a))))) = s(TV_u_27a,happ(s(t_fun(t_bool,TV_u_27a),V_f3),s(t_bool,V_a))) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_h4s_integers_int,V_a))) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_h4s_integers_int,V_a))) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_h4s_integers_int,V_a))) & ![V_a0, V_a1]: s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_fn),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_a0))),s(t_h4s_integers_int,V_a1))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7),s(t_h4s_integers_int,V_a0))),s(t_h4s_integers_int,V_a1))))))))))).
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_deepu_u_formu_u_distinctu_c16, axiom, ![V_au_27, V_a]: ~ (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_a))) = 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_au_27))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_induction, axiom, ![V_P]: ((![V_d, V_d0]: ((p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d)))) & p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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_d))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d0))))))) & (![V_d, V_d0]: ((p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d)))) & p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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_d))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d0))))))) & (![V_d]: (p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d)))) => p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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_d))))))) & (![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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)))))) & (![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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)))))) & (![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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)))))) & (![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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)))))) & ![V_i, V_i0]: p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),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_i))),s(t_h4s_integers_int,V_i0))))))))))))) => ![V_d]: p(s(t_bool,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_bool),V_P),s(t_h4s_DeepSyntaxs_deepu_u_form,V_d)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_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_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_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_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_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_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_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_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_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_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_DeepSyntaxs_datatypeu_u_deepu_u_form, axiom, ![V_deepu_u_form]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool),happ(s(t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)),happ(s(t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool))),happ(s(t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)))),happ(s(t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool))))),happ(s(t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)))))),happ(s(t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool))))))),happ(s(t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),t_fun(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),t_fun(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),t_bool)))))))),V_deepu_u_form),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_disjn))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn))),s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool))),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_ltx))),s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq))),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => 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,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_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_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_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
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_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_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_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_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_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_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(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_c3, axiom, ![V_pos, V_b]: 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_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_b))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)).
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_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_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_posinfu_u_exoriginalu_u_equ_u_rhs, axiom, ![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))))) => (?[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)))) <=> (?[V_i]: (?[V_v]: ((p(s(t_bool,V_v)) <=> (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_combins_k(s(t_bool,V_v),s(t_h4s_integers_int,V_i))))) & 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_b, V_j]: ((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)))))) & ?[V_v]: ((p(s(t_bool,V_v)) <=> (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_combins_k(s(t_bool,V_v),s(t_h4s_integers_int,V_j)))))) & 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_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_j))))))))))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c7, axiom, ![V_pos, V_i2, V_i1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(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(ah4s_DeepSyntaxs_Bsetu_u_defu_c5, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(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_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_Bsetu_u_defu_c3, axiom, ![V_pos, V_b]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),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_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c4, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(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_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_neg(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_Bsetu_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_bset(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_bset(s(t_bool,V_v),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c1, axiom, ![V_pos, V_f2, V_f1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(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_bset(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_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c0, axiom, ![V_pos, V_f2, V_f1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(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_bset(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_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c7, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a0))),s(t_h4s_integers_int,V_a1))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7),s(t_h4s_integers_int,V_a0))),s(t_h4s_integers_int,V_a1)))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c5, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_h4s_integers_int,V_a)))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c3, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_bool,TV_u_27a),V_f3),s(t_bool,V_a)))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a)))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c4, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_h4s_integers_int,V_a)))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1)))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f7, V_f6, V_f5, V_f4, V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27a,h4s_deepsyntaxs_deepu_u_formu_u_case(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_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1))),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f1),s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),V_f2),s(t_fun(t_bool,TV_u_27a),V_f3),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f4),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f5),s(t_fun(t_h4s_integers_int,TV_u_27a),V_f6),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,TV_u_27a)),V_f7))) = s(TV_u_27a,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,TV_u_27a)),V_f),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a0))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_a1)))).
fof(ch4s_DeepSyntaxs_inu_u_asetu_c10, conjecture, ![V_i, V_P]: (?[V_a]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_a),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_aset(s(t_bool,f),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)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_a))))) <=> p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_i)))))).
