%   ORIGINAL: h4/DeepSyntax/add__d__posinf
% 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/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__ADD__ASSOC: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm: h4/integer/INT__DIVIDES__RMUL: !r q p. h4/integer/int__divides p q ==> h4/integer/int__divides p (h4/integer/int__mul r q)
% Assm: h4/integer/INT__DIVIDES__LADD: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add q r) <=> h4/integer/int__divides p r)
% Assm: h4/DeepSyntax/deep__form__repfns_c0: !a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a) = a
% Assm: h4/DeepSyntax/deep__form__repfns_c1: !r. (\a0_27. !_27deep__form_27. (!a0_270. (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27deep__form_27 a0 /\ _27deep__form_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27deep__form_27 a0 /\ _27deep__form_27 a1) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27deep__form_27 a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C a0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a00 a10)) (\n. h4/ind__type/BOTTOM)) a0 a1) ==> _27deep__form_27 a0_270) ==> _27deep__form_27 a0_27) r <=> h4/DeepSyntax/_20_40ind__typeDeepSyntax9 (h4/DeepSyntax/_20_40ind__typeDeepSyntax8 r) = r
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax0____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax0 = (\a0 a1. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a0) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a1)))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax1____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax1 = (\a0 a1. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a0) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a1)))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax2____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax2 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a)))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax3____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax3 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C a0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax4____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax4 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax5____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax5 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax6____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax6 = (\a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/DeepSyntax/hidden____20__40ind____typeDeepSyntax7____def: h4/DeepSyntax/_20_40ind__typeDeepSyntax7 = (\a0 a1. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a00 a10)) (\n. h4/ind__type/BOTTOM)) a0 a1))
% Assm: h4/DeepSyntax/Conjn0: h4/DeepSyntax/Conjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax0
% Assm: h4/DeepSyntax/Disjn0: h4/DeepSyntax/Disjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax1
% Assm: h4/DeepSyntax/Negn0: h4/DeepSyntax/Negn = h4/DeepSyntax/_20_40ind__typeDeepSyntax2
% Assm: h4/DeepSyntax/UnrelatedBool0: h4/DeepSyntax/UnrelatedBool = h4/DeepSyntax/_20_40ind__typeDeepSyntax3
% Assm: h4/DeepSyntax/xLT0: h4/DeepSyntax/xLT = h4/DeepSyntax/_20_40ind__typeDeepSyntax4
% Assm: h4/DeepSyntax/LTx0: h4/DeepSyntax/LTx = h4/DeepSyntax/_20_40ind__typeDeepSyntax5
% Assm: h4/DeepSyntax/xEQ0: h4/DeepSyntax/xEQ = h4/DeepSyntax/_20_40ind__typeDeepSyntax6
% Assm: h4/DeepSyntax/xDivided0: h4/DeepSyntax/xDivided = h4/DeepSyntax/_20_40ind__typeDeepSyntax7
% Assm: h4/DeepSyntax/eval__form__def_c0: !x f2 f1. h4/DeepSyntax/eval__form (h4/DeepSyntax/Conjn f1 f2) x <=> h4/DeepSyntax/eval__form f1 x /\ h4/DeepSyntax/eval__form f2 x
% Assm: h4/DeepSyntax/eval__form__def_c1: !x f2 f1. h4/DeepSyntax/eval__form (h4/DeepSyntax/Disjn f1 f2) x <=> h4/DeepSyntax/eval__form f1 x \/ h4/DeepSyntax/eval__form f2 x
% Assm: h4/DeepSyntax/eval__form__def_c2: !x f. h4/DeepSyntax/eval__form (h4/DeepSyntax/Negn f) x <=> ~h4/DeepSyntax/eval__form f x
% Assm: h4/DeepSyntax/eval__form__def_c3: !x b. h4/DeepSyntax/eval__form (h4/DeepSyntax/UnrelatedBool b) x <=> b
% Assm: h4/DeepSyntax/eval__form__def_c7: !x i2 i1. h4/DeepSyntax/eval__form (h4/DeepSyntax/xDivided i1 i2) x <=> h4/integer/int__divides i1 (h4/integer/int__add x i2)
% Assm: h4/DeepSyntax/posinf__def_c0: !f2 f1. h4/DeepSyntax/posinf (h4/DeepSyntax/Conjn f1 f2) = h4/DeepSyntax/Conjn (h4/DeepSyntax/posinf f1) (h4/DeepSyntax/posinf f2)
% Assm: h4/DeepSyntax/posinf__def_c1: !f2 f1. h4/DeepSyntax/posinf (h4/DeepSyntax/Disjn f1 f2) = h4/DeepSyntax/Disjn (h4/DeepSyntax/posinf f1) (h4/DeepSyntax/posinf f2)
% Assm: h4/DeepSyntax/posinf__def_c2: !f. h4/DeepSyntax/posinf (h4/DeepSyntax/Negn f) = h4/DeepSyntax/Negn (h4/DeepSyntax/posinf f)
% Assm: h4/DeepSyntax/posinf__def_c3: !b. h4/DeepSyntax/posinf (h4/DeepSyntax/UnrelatedBool b) = h4/DeepSyntax/UnrelatedBool b
% Assm: h4/DeepSyntax/posinf__def_c4: !i. h4/DeepSyntax/posinf (h4/DeepSyntax/xLT i) = h4/DeepSyntax/UnrelatedBool F
% Assm: h4/DeepSyntax/posinf__def_c5: !i. h4/DeepSyntax/posinf (h4/DeepSyntax/LTx i) = h4/DeepSyntax/UnrelatedBool T
% Assm: h4/DeepSyntax/posinf__def_c6: !i. h4/DeepSyntax/posinf (h4/DeepSyntax/xEQ i) = h4/DeepSyntax/UnrelatedBool F
% Assm: h4/DeepSyntax/posinf__def_c7: !i2 i1. h4/DeepSyntax/posinf (h4/DeepSyntax/xDivided i1 i2) = h4/DeepSyntax/xDivided i1 i2
% Assm: h4/DeepSyntax/alldivide__def_c0: !f2 f1 d. h4/DeepSyntax/alldivide (h4/DeepSyntax/Conjn f1 f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm: h4/DeepSyntax/alldivide__def_c1: !f2 f1 d. h4/DeepSyntax/alldivide (h4/DeepSyntax/Disjn f1 f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm: h4/DeepSyntax/alldivide__def_c2: !f d. h4/DeepSyntax/alldivide (h4/DeepSyntax/Negn f) d <=> h4/DeepSyntax/alldivide f d
% Assm: h4/DeepSyntax/alldivide__def_c3: !d b. h4/DeepSyntax/alldivide (h4/DeepSyntax/UnrelatedBool b) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c4: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xLT i) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c5: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/LTx i) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c6: !i d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xEQ i) d <=> T
% Assm: h4/DeepSyntax/alldivide__def_c7: !i2 i1 d. h4/DeepSyntax/alldivide (h4/DeepSyntax/xDivided i1 i2) d <=> h4/integer/int__divides i1 d
% Goal: !y x f d. h4/DeepSyntax/alldivide f d ==> (h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) x <=> h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) (h4/integer/int__add x (h4/integer/int__mul y d)))
%   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_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_ADDu_u_ASSOC]: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm [h4s_integers_INTu_u_DIVIDESu_u_RMUL]: !r q p. h4/integer/int__divides p q ==> h4/integer/int__divides p (h4/integer/int__mul r q)
% Assm [h4s_integers_INTu_u_DIVIDESu_u_LADD]: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add q r) <=> h4/integer/int__divides p r)
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c0]: !a. h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 a) = a
% Assm [h4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27deep__form_27. (!a0_270. (?a0 a1. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27deep__form_27 a0 /\ happ _27deep__form_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27deep__form_27 a0 /\ happ _27deep__form_27 a1) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS a _0) /\ happ _27deep__form_27 a) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C a (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a h4/bool/ARB)) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a h4/bool/ARB)) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a h4/bool/ARB)) _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C a0 a1)) _0) ==> happ _27deep__form_27 a0_270) ==> happ _27deep__form_27 r) <=> h4/DeepSyntax/_20_40ind__typeDeepSyntax9 (h4/DeepSyntax/_20_40ind__typeDeepSyntax8 r) = r)
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/DeepSyntax/_20_40ind__typeDeepSyntax0 x) x' = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x') _0))))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/DeepSyntax/_20_40ind__typeDeepSyntax1 x) x' = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x') _0))))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax2 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (h4/ind__type/FCONS (h4/DeepSyntax/_20_40ind__typeDeepSyntax9 x) _0)))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax3u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax3 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C x (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax4 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax5 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/DeepSyntax/_20_40ind__typeDeepSyntax6 x = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax7u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/DeepSyntax/_20_40ind__typeDeepSyntax7 x) x' = h4/DeepSyntax/_20_40ind__typeDeepSyntax8 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))))))) (h4/pair/_2C h4/bool/ARB (h4/pair/_2C x x')) _0))
% Assm [h4s_DeepSyntaxs_Conjn0]: h4/DeepSyntax/Conjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax0
% Assm [h4s_DeepSyntaxs_Disjn0]: h4/DeepSyntax/Disjn = h4/DeepSyntax/_20_40ind__typeDeepSyntax1
% Assm [h4s_DeepSyntaxs_Negn0]: h4/DeepSyntax/Negn = h4/DeepSyntax/_20_40ind__typeDeepSyntax2
% Assm [h4s_DeepSyntaxs_UnrelatedBool0]: h4/DeepSyntax/UnrelatedBool = h4/DeepSyntax/_20_40ind__typeDeepSyntax3
% Assm [h4s_DeepSyntaxs_xLT0]: h4/DeepSyntax/xLT = h4/DeepSyntax/_20_40ind__typeDeepSyntax4
% Assm [h4s_DeepSyntaxs_LTx0]: h4/DeepSyntax/LTx = h4/DeepSyntax/_20_40ind__typeDeepSyntax5
% Assm [h4s_DeepSyntaxs_xEQ0]: h4/DeepSyntax/xEQ = h4/DeepSyntax/_20_40ind__typeDeepSyntax6
% Assm [h4s_DeepSyntaxs_xDivided0]: h4/DeepSyntax/xDivided = h4/DeepSyntax/_20_40ind__typeDeepSyntax7
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c0]: !x f2 f1. h4/DeepSyntax/eval__form (happ (happ h4/DeepSyntax/Conjn f1) f2) x <=> h4/DeepSyntax/eval__form f1 x /\ h4/DeepSyntax/eval__form f2 x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c1]: !x f2 f1. h4/DeepSyntax/eval__form (happ (happ h4/DeepSyntax/Disjn f1) f2) x <=> h4/DeepSyntax/eval__form f1 x \/ h4/DeepSyntax/eval__form f2 x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c2]: !x f. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/Negn f) x <=> ~h4/DeepSyntax/eval__form f x
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c3]: !x b. h4/DeepSyntax/eval__form (happ h4/DeepSyntax/UnrelatedBool b) x <=> b
% Assm [h4s_DeepSyntaxs_evalu_u_formu_u_defu_c7]: !x i2 i1. h4/DeepSyntax/eval__form (happ (happ h4/DeepSyntax/xDivided i1) i2) x <=> h4/integer/int__divides i1 (h4/integer/int__add x i2)
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c0]: !f2 f1. h4/DeepSyntax/posinf (happ (happ h4/DeepSyntax/Conjn f1) f2) = happ (happ h4/DeepSyntax/Conjn (h4/DeepSyntax/posinf f1)) (h4/DeepSyntax/posinf f2)
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c1]: !f2 f1. h4/DeepSyntax/posinf (happ (happ h4/DeepSyntax/Disjn f1) f2) = happ (happ h4/DeepSyntax/Disjn (h4/DeepSyntax/posinf f1)) (h4/DeepSyntax/posinf f2)
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c2]: !f. h4/DeepSyntax/posinf (happ h4/DeepSyntax/Negn f) = happ h4/DeepSyntax/Negn (h4/DeepSyntax/posinf f)
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c3]: !b. h4/DeepSyntax/posinf (happ h4/DeepSyntax/UnrelatedBool b) = happ h4/DeepSyntax/UnrelatedBool b
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c4]: !i. h4/DeepSyntax/posinf (happ h4/DeepSyntax/xLT i) = happ h4/DeepSyntax/UnrelatedBool F
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c5]: !i. h4/DeepSyntax/posinf (happ h4/DeepSyntax/LTx i) = happ h4/DeepSyntax/UnrelatedBool T
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c6]: !i. h4/DeepSyntax/posinf (happ h4/DeepSyntax/xEQ i) = happ h4/DeepSyntax/UnrelatedBool F
% Assm [h4s_DeepSyntaxs_posinfu_u_defu_c7]: !i2 i1. h4/DeepSyntax/posinf (happ (happ h4/DeepSyntax/xDivided i1) i2) = happ (happ h4/DeepSyntax/xDivided i1) i2
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c0]: !f2 f1 d. h4/DeepSyntax/alldivide (happ (happ h4/DeepSyntax/Conjn f1) f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c1]: !f2 f1 d. h4/DeepSyntax/alldivide (happ (happ h4/DeepSyntax/Disjn f1) f2) d <=> h4/DeepSyntax/alldivide f1 d /\ h4/DeepSyntax/alldivide f2 d
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c2]: !f d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/Negn f) d <=> h4/DeepSyntax/alldivide f d
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c3]: !d b. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/UnrelatedBool b) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c4]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/xLT i) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c5]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/LTx i) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c6]: !i d. h4/DeepSyntax/alldivide (happ h4/DeepSyntax/xEQ i) d <=> T
% Assm [h4s_DeepSyntaxs_alldivideu_u_defu_c7]: !i2 i1 d. h4/DeepSyntax/alldivide (happ (happ h4/DeepSyntax/xDivided i1) i2) d <=> h4/integer/int__divides i1 d
% Goal: !y x f d. h4/DeepSyntax/alldivide f d ==> (h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) x <=> h4/DeepSyntax/eval__form (h4/DeepSyntax/posinf f) (h4/integer/int__add x (h4/integer/int__mul y d)))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q350193,TV_Q350189]: ![V_f, V_g]: (![V_x]: s(TV_Q350189,happ(s(t_fun(TV_Q350193,TV_Q350189),V_f),s(TV_Q350193,V_x))) = s(TV_Q350189,happ(s(t_fun(TV_Q350193,TV_Q350189),V_g),s(TV_Q350193,V_x))) => s(t_fun(TV_Q350193,TV_Q350189),V_f) = s(t_fun(TV_Q350193,TV_Q350189),V_g))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f0))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f0))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_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_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f0) = 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,f0) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_integers_INTu_u_ADDu_u_COMM, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_RMUL, axiom, ![V_r, V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) => p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_r),s(t_h4s_integers_int,V_q)))))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_LADD, axiom, ![V_r, V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) => s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_r))))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_r))))).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c0, axiom, ![V_a]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_a))))) = s(t_h4s_DeepSyntaxs_deepu_u_form,V_a)).
fof(ah4s_DeepSyntaxs_deepu_u_formu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27deepu_u_formu_27]: (![V_a0u_270]: ((?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1)))))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a1)))))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a))))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,V_a),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))) | ?[V_a0, V_a1]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_a0),s(t_h4s_integers_int,V_a1))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0)))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),t_bool),V_uu_27deepu_u_formu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),V_r)))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax0u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax0),s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax1u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax2u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax2),s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax9(s(t_h4s_DeepSyntaxs_deepu_u_form,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax3u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax3),s(t_bool,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,V_x),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_bools_arb),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax4u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax4),s(t_h4s_integers_int,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax5u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax5),s(t_h4s_integers_int,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax6u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax6),s(t_h4s_integers_int,V_x))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeDeepSyntax7u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax7),s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_xi_))) = s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax8(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))))))))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)),h4s_pairs_u_2c(s(t_bool,h4s_bools_arb),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_xi_))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int)))),V_uu_0))))))).
fof(ah4s_DeepSyntaxs_Conjn0, axiom, s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn) = s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax0)).
fof(ah4s_DeepSyntaxs_Disjn0, axiom, s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn) = s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax1)).
fof(ah4s_DeepSyntaxs_Negn0, axiom, s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn) = s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax2)).
fof(ah4s_DeepSyntaxs_UnrelatedBool0, axiom, s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool) = s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax3)).
fof(ah4s_DeepSyntaxs_xLT0, axiom, s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt) = s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax4)).
fof(ah4s_DeepSyntaxs_LTx0, axiom, s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx) = s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax5)).
fof(ah4s_DeepSyntaxs_xEQ0, axiom, s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq) = s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax6)).
fof(ah4s_DeepSyntaxs_xDivided0, axiom, s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_u_20u_40indu_u_typedeepsyntax7)).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c0, axiom, ![V_x, V_f2, V_f1]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_x)))) <=> (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c1, axiom, ![V_x, V_f2, V_f1]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_x)))) <=> (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_x)))) | p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c2, axiom, ![V_x, V_f]: (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_x)))) <=> ~ (p(s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c3, axiom, ![V_x, V_b]: s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_b))),s(t_h4s_integers_int,V_x))) = s(t_bool,V_b)).
fof(ah4s_DeepSyntaxs_evalu_u_formu_u_defu_c7, axiom, ![V_x, V_i2, V_i1]: s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided),s(t_h4s_integers_int,V_i1))),s(t_h4s_integers_int,V_i2))),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_i1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_i2)))))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c0, axiom, ![V_f2, V_f1]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))))) = s(t_h4s_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,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))))),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c1, axiom, ![V_f2, V_f1]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))))) = s(t_h4s_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,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))))),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c2, axiom, ![V_f]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))))) = s(t_h4s_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,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f)))))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c3, axiom, ![V_b]: s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_b))))) = s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_b)))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c4, 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_xlt),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,f0)))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c5, 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_ltx),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,t)))).
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,f0)))).
fof(ah4s_DeepSyntaxs_posinfu_u_defu_c7, axiom, ![V_i2, V_i1]: 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),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided),s(t_h4s_integers_int,V_i1))),s(t_h4s_integers_int,V_i2))))) = s(t_h4s_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)))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c0, axiom, ![V_f2, V_f1, V_d]: (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_conjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_d)))) <=> (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_d)))) & p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c1, axiom, ![V_f2, V_f1, V_d]: (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_disjn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))),s(t_h4s_integers_int,V_d)))) <=> (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_integers_int,V_d)))) & p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c2, axiom, ![V_f, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_DeepSyntaxs_deepu_u_form,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_negn),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_d))) = s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_d)))).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c3, axiom, ![V_d, V_b]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_bool,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_unrelatedbool),s(t_bool,V_b))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c4, axiom, ![V_i, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xlt),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c5, axiom, ![V_i, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_ltx),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c6, axiom, ![V_i, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),h4s_deepsyntaxs_xeq),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_d))) = s(t_bool,t)).
fof(ah4s_DeepSyntaxs_alldivideu_u_defu_c7, axiom, ![V_i2, V_i1, V_d]: s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,happ(s(t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_DeepSyntaxs_deepu_u_form)),h4s_deepsyntaxs_xdivided),s(t_h4s_integers_int,V_i1))),s(t_h4s_integers_int,V_i2))),s(t_h4s_integers_int,V_d))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_i1),s(t_h4s_integers_int,V_d)))).
fof(ch4s_DeepSyntaxs_addu_u_du_u_posinf, conjecture, ![V_y, V_x, V_f, V_d]: (p(s(t_bool,h4s_deepsyntaxs_alldivide(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f),s(t_h4s_integers_int,V_d)))) => s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,V_x))) = s(t_bool,h4s_deepsyntaxs_evalu_u_form(s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_posinf(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_d))))))))).
