%   ORIGINAL: h4/int__arith/NOT__INT__DIVIDES
% 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/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/prim__rec/NOT__LESS__0: !n. ~h4/prim__rec/_3C n h4/num/0
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/LESS__EQ__0: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__ADD__ASSOC: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm: h4/integer/int__sub0: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/INT__ADD__LID: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm: h4/integer/INT__ADD__RID: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/integer/INT__MUL__LID: !x. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/integer/INT__RDISTRIB: !z y x. h4/integer/int__mul (h4/integer/int__add x y) z = h4/integer/int__add (h4/integer/int__mul x z) (h4/integer/int__mul y z)
% Assm: h4/integer/INT__LT__GT: !y x. h4/integer/int__lt x y ==> ~h4/integer/int__lt y x
% Assm: h4/integer/INT__LE__LT: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm: h4/integer/INT__LT__IMP__LE: !y x. h4/integer/int__lt x y ==> h4/integer/int__le x y
% Assm: h4/integer/INT__LE__TRANS: !z y x. h4/integer/int__le x y /\ h4/integer/int__le y z ==> h4/integer/int__le x z
% Assm: h4/integer/INT__LE__01: h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/integer/INT__LE__LADD: !z y x. h4/integer/int__le (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__le y z
% Assm: h4/integer/INT__SUB__ADD2: !y x. h4/integer/int__add y (h4/integer/int__sub x y) = x
% Assm: h4/integer/INT__NEG__EQ0: !x. h4/integer/int__neg x = h4/integer/int__of__num h4/num/0 <=> x = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__LE: !n m. h4/integer/int__le (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm: h4/integer/INT__LT: !n m. h4/integer/int__lt (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/prim__rec/_3C m n
% Assm: h4/integer/INT__INJ: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm: h4/integer/INT__LE__SUB__LADD: !z y x. h4/integer/int__le x (h4/integer/int__sub y z) <=> h4/integer/int__le (h4/integer/int__add x z) y
% Assm: h4/integer/INT__LE__SUB__RADD: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm: h4/integer/INT__LT__CALCULATE_c0: !n m. h4/integer/int__lt (h4/integer/int__of__num n) (h4/integer/int__of__num m) <=> h4/prim__rec/_3C n m
% Assm: h4/integer/INT__NUM__CASES: !p. (?n. p = h4/integer/int__of__num n /\ ~(n = h4/num/0)) \/ (?n. p = h4/integer/int__neg (h4/integer/int__of__num n) /\ ~(n = h4/num/0)) \/ p = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__DIVISION: !q. ~(q = h4/integer/int__of__num h4/num/0) ==> (!p. p = h4/integer/int__add (h4/integer/int__mul (h4/integer/int__div p q) q) (h4/integer/int__mod p q) /\ h4/bool/COND (h4/integer/int__lt q (h4/integer/int__of__num h4/num/0)) (h4/integer/int__lt q (h4/integer/int__mod p q) /\ h4/integer/int__le (h4/integer/int__mod p q) (h4/integer/int__of__num h4/num/0)) (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__mod p q) /\ h4/integer/int__lt (h4/integer/int__mod p q) q))
% Assm: h4/integer/INT__MOD__UNIQUE: !m j i. (?q. i = h4/integer/int__add (h4/integer/int__mul q j) m /\ h4/bool/COND (h4/integer/int__lt j (h4/integer/int__of__num h4/num/0)) (h4/integer/int__lt j m /\ h4/integer/int__le m (h4/integer/int__of__num h4/num/0)) (h4/integer/int__le (h4/integer/int__of__num h4/num/0) m /\ h4/integer/int__lt m j)) ==> h4/integer/int__mod i j = m
% Assm: h4/integer/INT__MOD__COMMON__FACTOR: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> (!q. h4/integer/int__mod (h4/integer/int__mul q p) p = h4/integer/int__of__num h4/num/0)
% Assm: h4/integer/INT__ABS__NUM: !n. h4/integer/ABS (h4/integer/int__of__num n) = h4/integer/int__of__num n
% Assm: h4/integer/INT__ABS__NEG: !p. h4/integer/ABS (h4/integer/int__neg p) = h4/integer/ABS p
% Assm: h4/integer/INT__DIVIDES__MOD0: !q p. h4/integer/int__divides p q <=> h4/integer/int__mod q p = h4/integer/int__of__num h4/num/0 /\ ~(p = h4/integer/int__of__num h4/num/0) \/ p = h4/integer/int__of__num h4/num/0 /\ q = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__DIVIDES__NEG_c1: !q p. h4/integer/int__divides (h4/integer/int__neg p) q <=> h4/integer/int__divides p q
% Assm: h4/int__arith/less__to__leq__samel: !y x. h4/integer/int__lt x y <=> h4/integer/int__le x (h4/integer/int__add y (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/int__arith/less__to__leq__samer: !y x. h4/integer/int__lt x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y
% Assm: h4/int__arith/move__sub: !c b a. h4/integer/int__add (h4/integer/int__sub a c) b = h4/integer/int__sub (h4/integer/int__add a b) c
% Goal: !d c. ~(c = h4/integer/int__of__num h4/num/0) ==> (~h4/integer/int__divides c d <=> (?i. h4/integer/int__le (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i /\ h4/integer/int__le i (h4/integer/int__sub (h4/integer/ABS c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ h4/integer/int__divides c (h4/integer/int__add d 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_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% 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_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_markers_Abbrevu_u_def]: !x. h4/marker/Abbrev x <=> x
% Assm [h4s_primu_u_recs_NOTu_u_LESSu_u_0]: !n. ~h4/prim__rec/_3C n h4/num/0
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_0]: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_ADDu_u_ASSOC]: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm [h4s_integers_intu_u_sub0]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_ADDu_u_LID]: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm [h4s_integers_INTu_u_ADDu_u_RID]: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_integers_INTu_u_MULu_u_LID]: !x. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_integers_INTu_u_RDISTRIB]: !z y x. h4/integer/int__mul (h4/integer/int__add x y) z = h4/integer/int__add (h4/integer/int__mul x z) (h4/integer/int__mul y z)
% Assm [h4s_integers_INTu_u_LTu_u_GT]: !y x. h4/integer/int__lt x y ==> ~h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_LEu_u_LT]: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm [h4s_integers_INTu_u_LTu_u_IMPu_u_LE]: !y x. h4/integer/int__lt x y ==> h4/integer/int__le x y
% Assm [h4s_integers_INTu_u_LEu_u_TRANS]: !z y x. h4/integer/int__le x y /\ h4/integer/int__le y z ==> h4/integer/int__le x z
% Assm [h4s_integers_INTu_u_LEu_u_01]: h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_integers_INTu_u_LEu_u_LADD]: !z y x. h4/integer/int__le (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__le y z
% Assm [h4s_integers_INTu_u_SUBu_u_ADD2]: !y x. h4/integer/int__add y (h4/integer/int__sub x y) = x
% Assm [h4s_integers_INTu_u_NEGu_u_EQ0]: !x. h4/integer/int__neg x = h4/integer/int__of__num h4/num/0 <=> x = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_LE]: !n m. h4/integer/int__le (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_integers_INTu_u_LT]: !n m. h4/integer/int__lt (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/prim__rec/_3C m n
% Assm [h4s_integers_INTu_u_INJ]: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_LADD]: !z y x. h4/integer/int__le x (h4/integer/int__sub y z) <=> h4/integer/int__le (h4/integer/int__add x z) y
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_RADD]: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm [h4s_integers_INTu_u_LTu_u_CALCULATEu_c0]: !n m. h4/integer/int__lt (h4/integer/int__of__num n) (h4/integer/int__of__num m) <=> h4/prim__rec/_3C n m
% Assm [h4s_integers_INTu_u_NUMu_u_CASES]: !p. (?n. p = h4/integer/int__of__num n /\ ~(n = h4/num/0)) \/ (?n. p = h4/integer/int__neg (h4/integer/int__of__num n) /\ ~(n = h4/num/0)) \/ p = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_DIVISION]: !q. ~(q = h4/integer/int__of__num h4/num/0) ==> (!p. p = h4/integer/int__add (h4/integer/int__mul (h4/integer/int__div p q) q) (h4/integer/int__mod p q) /\ (?v. (v <=> h4/integer/int__lt q (h4/integer/int__mod p q) /\ h4/integer/int__le (h4/integer/int__mod p q) (h4/integer/int__of__num h4/num/0)) /\ (?v'. (v' <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__mod p q) /\ h4/integer/int__lt (h4/integer/int__mod p q) q) /\ h4/bool/COND (h4/integer/int__lt q (h4/integer/int__of__num h4/num/0)) v v')))
% Assm [h4s_integers_INTu_u_MODu_u_UNIQUE]: !m j i. (?q. i = h4/integer/int__add (h4/integer/int__mul q j) m /\ (?v. (v <=> h4/integer/int__lt j m /\ h4/integer/int__le m (h4/integer/int__of__num h4/num/0)) /\ (?v'. (v' <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) m /\ h4/integer/int__lt m j) /\ h4/bool/COND (h4/integer/int__lt j (h4/integer/int__of__num h4/num/0)) v v'))) ==> h4/integer/int__mod i j = m
% Assm [h4s_integers_INTu_u_MODu_u_COMMONu_u_FACTOR]: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> (!q. h4/integer/int__mod (h4/integer/int__mul q p) p = h4/integer/int__of__num h4/num/0)
% Assm [h4s_integers_INTu_u_ABSu_u_NUM]: !n. h4/integer/ABS (h4/integer/int__of__num n) = h4/integer/int__of__num n
% Assm [h4s_integers_INTu_u_ABSu_u_NEG]: !p. h4/integer/ABS (h4/integer/int__neg p) = h4/integer/ABS p
% Assm [h4s_integers_INTu_u_DIVIDESu_u_MOD0]: !q p. h4/integer/int__divides p q <=> h4/integer/int__mod q p = h4/integer/int__of__num h4/num/0 /\ ~(p = h4/integer/int__of__num h4/num/0) \/ p = h4/integer/int__of__num h4/num/0 /\ q = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_DIVIDESu_u_NEGu_c1]: !q p. h4/integer/int__divides (h4/integer/int__neg p) q <=> h4/integer/int__divides p q
% Assm [h4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samel]: !y x. h4/integer/int__lt x y <=> h4/integer/int__le x (h4/integer/int__add y (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samer]: !y x. h4/integer/int__lt x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y
% Assm [h4s_intu_u_ariths_moveu_u_sub]: !c b a. h4/integer/int__add (h4/integer/int__sub a c) b = h4/integer/int__sub (h4/integer/int__add a b) c
% Goal: !d c. ~(c = h4/integer/int__of__num h4/num/0) ==> (~h4/integer/int__divides c d <=> (?i. h4/integer/int__le (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i /\ h4/integer/int__le i (h4/integer/int__sub (h4/integer/ABS c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ h4/integer/int__divides c (h4/integer/int__add d 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_Q209447,TV_Q209443]: ![V_f, V_g]: (![V_x]: s(TV_Q209443,happ(s(t_fun(TV_Q209447,TV_Q209443),V_f),s(TV_Q209447,V_x))) = s(TV_Q209443,happ(s(t_fun(TV_Q209447,TV_Q209443),V_g),s(TV_Q209447,V_x))) => s(t_fun(TV_Q209447,TV_Q209443),V_f) = s(t_fun(TV_Q209447,TV_Q209443),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,f))).
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,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
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,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(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,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
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_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_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_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_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_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,f))))).
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_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_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_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_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_abbrev(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_primu_u_recs_NOTu_u_LESSu_u_0, axiom, ![V_n]: ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_0, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0)))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c17, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_ADDu_u_COMM, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_intu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_ADDu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_RID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(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_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_RDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(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))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_LTu_u_GT, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) => ~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_integers_INTu_u_LEu_u_LT, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) | s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LTu_u_IMPu_u_LE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_LEu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_LEu_u_01, axiom, p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))).
fof(ah4s_integers_INTu_u_LEu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_SUBu_u_ADD2, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_NEGu_u_EQ0, axiom, ![V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_integers_INTu_u_LE, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_integers_INTu_u_LT, axiom, ![V_n, V_m]: 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,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_integers_INTu_u_INJ, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0, axiom, ![V_n, V_m]: 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,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_integers_INTu_u_NUMu_u_CASES, axiom, ![V_p]: (?[V_n]: (s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) & ~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))) | (?[V_n]: (s(t_h4s_integers_int,V_p) = 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,V_n))))) & ~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_integers_INTu_u_DIVISION, axiom, ![V_q]: (~ (s(t_h4s_integers_int,V_q) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => ![V_p]: (s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))))) & ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,V_q)))))) & p(s(t_bool,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_bool,V_v),s(t_bool,V_vi_))))))))).
fof(ah4s_integers_INTu_u_MODu_u_UNIQUE, axiom, ![V_m, V_j, V_i]: (?[V_q]: (s(t_h4s_integers_int,V_i) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_j))),s(t_h4s_integers_int,V_m))) & ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_m)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_m),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> (p(s(t_bool,h4s_integers_intu_u_le(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_m)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_m),s(t_h4s_integers_int,V_j)))))) & p(s(t_bool,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_bool,V_v),s(t_bool,V_vi_))))))) => s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_j))) = s(t_h4s_integers_int,V_m))).
fof(ah4s_integers_INTu_u_MODu_u_COMMONu_u_FACTOR, axiom, ![V_p]: (~ (s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => ![V_q]: s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_p))),s(t_h4s_integers_int,V_p))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_integers_INTu_u_ABSu_u_NUM, axiom, ![V_n]: s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n)))).
fof(ah4s_integers_INTu_u_ABSu_u_NEG, axiom, ![V_p]: s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_p))))) = s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,V_p)))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_MOD0, axiom, ![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_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_p))) = 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_p) = 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_p) = 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_q) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_NEGu_c1, axiom, ![V_q, V_p]: s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,h4s_integers_intu_u_neg(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,V_q)))).
fof(ah4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samel, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_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_intu_u_ariths_lessu_u_tou_u_lequ_u_samer, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_intu_u_ariths_moveu_u_sub, axiom, ![V_c, V_b, V_a]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,V_c))),s(t_h4s_integers_int,V_b))) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,V_b))),s(t_h4s_integers_int,V_c)))).
fof(ch4s_intu_u_ariths_NOTu_u_INTu_u_DIVIDES, conjecture, ![V_d, V_c]: (~ (s(t_h4s_integers_int,V_c) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => (~ (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))) <=> ?[V_i]: (p(s(t_bool,h4s_integers_intu_u_le(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_i)))) & (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,V_c))),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)))))))))))) & p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_d),s(t_h4s_integers_int,V_i))))))))))).
