%   ORIGINAL: h4/int__bitwise/int__bit__not
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/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_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/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/COND__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/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% 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__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/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lte_c0: !n. h4/arithmetic/_3C_3D h4/arithmetic/ZERO n <=> T
% Assm: h4/numeral/numeral__lte_c3: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/arithmetic/_3C_3D n m
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/enumeral__mult_c2: !y x. h4/arithmetic/_2A (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y) = h4/numeral/internal__mult (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y)
% Assm: h4/numeral/internal__mult__characterisation_c0: !n. h4/numeral/internal__mult h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm: h4/numeral/internal__mult__characterisation_c2: !n m. h4/numeral/internal__mult (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/numeral/internal__mult n m)) m)
% Assm: h4/list/MEM_c0: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% 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__RID: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/integer/INT__ADD__RINV: !x. h4/integer/int__add x (h4/integer/int__neg x) = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__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__NEG__LMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm: h4/integer/INT__NEGNEG: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integer/INT__NOT__LT: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm: h4/integer/INT__LT__GT: !y x. h4/integer/int__lt x y ==> ~h4/integer/int__lt y x
% Assm: h4/integer/INT__NEG__LT0: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm: h4/integer/INT__LT__ADD2: !z y x w. h4/integer/int__lt w x /\ h4/integer/int__lt y z ==> h4/integer/int__lt (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm: h4/integer/INT__NEG__SUB: !y x. h4/integer/int__neg (h4/integer/int__sub x y) = h4/integer/int__sub y x
% Assm: h4/integer/INT__ADD__SUB: !y x. h4/integer/int__sub (h4/integer/int__add x y) x = y
% Assm: h4/integer/INT__NEG__MINUS1: !x. h4/integer/int__neg x = h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x
% 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__SUB__LZERO: !x. h4/integer/int__sub (h4/integer/int__of__num h4/num/0) x = h4/integer/int__neg x
% Assm: h4/integer/INT__SUB__RNEG: !y x. h4/integer/int__sub x (h4/integer/int__neg y) = h4/integer/int__add x y
% Assm: h4/integer/INT__DIVIDES__1_c0: !x. h4/integer/int__divides (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x
% Assm: h4/integer/INT__MAX__LT: !z y x. h4/integer/int__lt (h4/integer/int__max x y) z ==> h4/integer/int__lt x z /\ h4/integer/int__lt y z
% Assm: h4/integer/INT__ADD__REDUCE_c0: !p. h4/integer/int__add (h4/integer/int__of__num h4/num/0) p = p
% Assm: h4/integer/INT__ADD__REDUCE_c1: !p. h4/integer/int__add p (h4/integer/int__of__num h4/num/0) = p
% Assm: h4/integer/INT__ADD__REDUCE_c2: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__ADD__REDUCE_c5: !n m. h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))))
% Assm: h4/integer/INT__ADD__REDUCE_c6: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))))
% Assm: h4/integer/INT__SUB__CALCULATE: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/INT__SUB__REDUCE_c2: !n m. h4/integer/int__sub (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)))
% Assm: h4/integer/INT__MUL__REDUCE_c3: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2A m n)))
% Assm: h4/integer/INT__LT__REDUCE_c0: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c2: h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num h4/num/0) <=> F
% Assm: h4/integer/INT__LT__REDUCE_c5: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c11: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> h4/prim__rec/_3C m n
% Assm: h4/int__arith/not__less: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/int__arith/less__to__leq__samer: !y x. h4/integer/int__lt x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y
% Assm: h4/int__arith/lt__move__left__left: !z y x. h4/integer/int__lt x (h4/integer/int__add y z) <=> h4/integer/int__lt (h4/integer/int__add x (h4/integer/int__neg y)) z
% Assm: h4/int__arith/lt__move__left__right: !z y x. h4/integer/int__lt (h4/integer/int__add x y) z <=> h4/integer/int__lt y (h4/integer/int__add z (h4/integer/int__neg x))
% Assm: h4/int__arith/lcm__eliminate: !c P. (?x. P (h4/integer/int__mul c x)) <=> (?x. P x /\ h4/integer/int__divides c x)
% Assm: h4/int__arith/can__get__big: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__mul c d)))
% Assm: h4/int__arith/restricted__quantification__simp: !x low high. h4/integer/int__lt low x /\ h4/integer/int__le x high <=> h4/integer/int__lt low high /\ (x = high \/ h4/integer/int__lt low x /\ h4/integer/int__le x (h4/integer/int__sub high (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/int__arith/bot__and__greaters: !x0 d P. (!x. P x ==> P (h4/integer/int__add x d)) /\ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> P (h4/integer/int__add x0 (h4/integer/int__mul c d)))
% Assm: h4/int__arith/in__subtractive__range: !x high d. h4/integer/int__le (h4/integer/int__sub high d) x /\ h4/integer/int__lt x high <=> (?j. x = h4/integer/int__sub high j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm: h4/int__arith/add__to__great: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__add x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul k d)) d)
% Assm: h4/int__bitwise/int__not__def: !i. h4/int__bitwise/int__not i = h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/int__bitwise/int__bit__def: !i b. h4/int__bitwise/int__bit b i <=> h4/bool/COND (h4/integer/int__lt i (h4/integer/int__of__num h4/num/0)) (~h4/bit/BIT b (h4/integer/Num (h4/int__bitwise/int__not i))) (h4/bit/BIT b (h4/integer/Num i))
% Goal: !i b. h4/int__bitwise/int__bit b (h4/int__bitwise/int__not i) <=> ~h4/int__bitwise/int__bit b 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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_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_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_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_CONDu_u_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_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% 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_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_combins_Ku_u_THM]: !y x. h4/combin/K x y = x
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_lteu_c0]: !n. h4/arithmetic/_3C_3D h4/arithmetic/ZERO n <=> T
% Assm [h4s_numerals_numeralu_u_lteu_c3]: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_enumeralu_u_multu_c2]: !y x. h4/arithmetic/_2A (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y) = h4/numeral/internal__mult (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y)
% Assm [h4s_numerals_internalu_u_multu_u_characterisationu_c0]: !n. h4/numeral/internal__mult h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm [h4s_numerals_internalu_u_multu_u_characterisationu_c2]: !n m. h4/numeral/internal__mult (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/numeral/internal__mult n m)) m)
% Assm [h4s_lists_MEMu_c0]: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% 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_RID]: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_integers_INTu_u_ADDu_u_RINV]: !x. h4/integer/int__add x (h4/integer/int__neg x) = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_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_NEGu_u_LMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm [h4s_integers_INTu_u_NEGNEG]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integers_INTu_u_NOTu_u_LT]: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm [h4s_integers_INTu_u_LTu_u_GT]: !y x. h4/integer/int__lt x y ==> ~h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_NEGu_u_LT0]: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm [h4s_integers_INTu_u_LTu_u_ADD2]: !z y x w. h4/integer/int__lt w x /\ h4/integer/int__lt y z ==> h4/integer/int__lt (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm [h4s_integers_INTu_u_NEGu_u_SUB]: !y x. h4/integer/int__neg (h4/integer/int__sub x y) = h4/integer/int__sub y x
% Assm [h4s_integers_INTu_u_ADDu_u_SUB]: !y x. h4/integer/int__sub (h4/integer/int__add x y) x = y
% Assm [h4s_integers_INTu_u_NEGu_u_MINUS1]: !x. h4/integer/int__neg x = h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x
% 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_SUBu_u_LZERO]: !x. h4/integer/int__sub (h4/integer/int__of__num h4/num/0) x = h4/integer/int__neg x
% Assm [h4s_integers_INTu_u_SUBu_u_RNEG]: !y x. h4/integer/int__sub x (h4/integer/int__neg y) = h4/integer/int__add x y
% Assm [h4s_integers_INTu_u_DIVIDESu_u_1u_c0]: !x. h4/integer/int__divides (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x
% Assm [h4s_integers_INTu_u_MAXu_u_LT]: !z y x. h4/integer/int__lt (h4/integer/int__max x y) z ==> h4/integer/int__lt x z /\ h4/integer/int__lt y z
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c0]: !p. h4/integer/int__add (h4/integer/int__of__num h4/num/0) p = p
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c1]: !p. h4/integer/int__add p (h4/integer/int__of__num h4/num/0) = p
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c2]: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c5]: !n m. h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))))
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c6]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))))
% Assm [h4s_integers_INTu_u_SUBu_u_CALCULATE]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_SUBu_u_REDUCEu_c2]: !n m. h4/integer/int__sub (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)))
% Assm [h4s_integers_INTu_u_MULu_u_REDUCEu_c3]: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2A m n)))
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c0]: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c2]: h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num h4/num/0) <=> F
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c5]: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c11]: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> h4/prim__rec/_3C m n
% Assm [h4s_intu_u_ariths_notu_u_less]: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samer]: !y x. h4/integer/int__lt x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y
% Assm [h4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_left]: !z y x. h4/integer/int__lt x (h4/integer/int__add y z) <=> h4/integer/int__lt (h4/integer/int__add x (h4/integer/int__neg y)) z
% Assm [h4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_right]: !z y x. h4/integer/int__lt (h4/integer/int__add x y) z <=> h4/integer/int__lt y (h4/integer/int__add z (h4/integer/int__neg x))
% Assm [h4s_intu_u_ariths_lcmu_u_eliminate]: !c P. (?x. happ P (h4/integer/int__mul c x)) <=> (?x. happ P x /\ h4/integer/int__divides c x)
% Assm [h4s_intu_u_ariths_canu_u_getu_u_big]: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_restrictedu_u_quantificationu_u_simp]: !x low high. h4/integer/int__lt low x /\ h4/integer/int__le x high <=> h4/integer/int__lt low high /\ (x = high \/ h4/integer/int__lt low x /\ h4/integer/int__le x (h4/integer/int__sub high (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_intu_u_ariths_botu_u_andu_u_greaters]: !x0 d P. (!x. happ P x ==> happ P (h4/integer/int__add x d)) /\ happ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> happ P (h4/integer/int__add x0 (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_inu_u_subtractiveu_u_range]: !x high d. h4/integer/int__le (h4/integer/int__sub high d) x /\ h4/integer/int__lt x high <=> (?j. x = h4/integer/int__sub high j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm [h4s_intu_u_ariths_addu_u_tou_u_great]: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__add x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul k d)) d)
% Assm [h4s_intu_u_bitwises_intu_u_notu_u_def]: !i. h4/int__bitwise/int__not i = h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_intu_u_bitwises_intu_u_bitu_u_def]: !i b. ?v. (v <=> ~h4/bit/BIT b (h4/integer/Num (h4/int__bitwise/int__not i))) /\ (h4/int__bitwise/int__bit b i <=> h4/bool/COND (h4/integer/int__lt i (h4/integer/int__of__num h4/num/0)) v (h4/bit/BIT b (h4/integer/Num i)))
% Goal: !i b. h4/int__bitwise/int__bit b (h4/int__bitwise/int__not i) <=> ~h4/int__bitwise/int__bit b 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_Q78892,TV_Q78888]: ![V_f, V_g]: (![V_x]: s(TV_Q78888,happ(s(t_fun(TV_Q78892,TV_Q78888),V_f),s(TV_Q78892,V_x))) = s(TV_Q78888,happ(s(t_fun(TV_Q78892,TV_Q78888),V_g),s(TV_Q78892,V_x))) => s(t_fun(TV_Q78892,TV_Q78888),V_f) = s(t_fun(TV_Q78892,TV_Q78888),V_g))).
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,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_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_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_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_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_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_CONDu_u_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_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_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_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_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_combins_k(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(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_numerals_numeralu_u_lteu_c0, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_lteu_c3, axiom, ![V_n, V_m]: 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_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_enumeralu_u_multu_c2, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_y))))) = s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numerals_internalu_u_multu_u_characterisationu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_internalu_u_multu_u_characterisationu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_lists_MEMu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(t_bool,f)).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
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_RID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_RINV, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_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_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_NEGNEG, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_NOTu_u_LT, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_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_NEGu_u_LT0, axiom, ![V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_ADD2, axiom, ![V_z, V_y, V_x, V_w]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))))).
fof(ah4s_integers_INTu_u_NEGu_u_SUB, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_SUB, axiom, ![V_y, V_x]: 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_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_NEGu_u_MINUS1, 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_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,V_x)))).
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_SUBu_u_LZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(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_neg(s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_SUBu_u_RNEG, 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,h4s_integers_intu_u_neg(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_y)))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_1u_c0, axiom, ![V_x]: p(s(t_bool,h4s_integers_intu_u_divides(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))))).
fof(ah4s_integers_INTu_u_MAXu_u_LT, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_max(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))) => (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c0, axiom, ![V_p]: 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_p))) = s(t_h4s_integers_int,V_p)).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c1, axiom, ![V_p]: s(t_h4s_integers_int,h4s_integers_intu_u_add(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)).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c2, axiom, 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_nums_0))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c5, axiom, ![V_n, V_m]: 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_arithmetics_numeral(s(t_h4s_nums_num,V_n))))),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,V_m))))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),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_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))),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_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c6, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(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,V_n))))))),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,V_m))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),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_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))),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_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))))))).
fof(ah4s_integers_INTu_u_SUBu_u_CALCULATE, 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_SUBu_u_REDUCEu_c2, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(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,V_m))))),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,V_n))))))) = 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_arithmetics_numeral(s(t_h4s_nums_num,V_m))))),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,V_n)))))))))).
fof(ah4s_integers_INTu_u_MULu_u_REDUCEu_c3, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))))),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,V_n))))))) = 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_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c0, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c2, axiom, s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c5, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(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,V_n))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c11, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(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,V_n))))))),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,V_m))))))))) = 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_intu_u_ariths_notu_u_less, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))).
fof(ah4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samer, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_left, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_lt(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))))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_right, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(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_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))))))).
fof(ah4s_intu_u_ariths_lcmu_u_eliminate, axiom, ![V_c, V_P]: (?[V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_x)))))) <=> ?[V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_intu_u_ariths_canu_u_getu_u_big, axiom, ![V_y, V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_restrictedu_u_quantificationu_u_simp, axiom, ![V_x, V_low, V_high]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_high))))) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_high)))) & (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_high) | (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_x)))) & p(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_high),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_botu_u_andu_u_greaters, axiom, ![V_x0, V_d, V_P]: ((![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_d))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x0))))) => ![V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x0),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_inu_u_subtractiveu_u_range, axiom, ![V_x, V_high, V_d]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,V_d))),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_high))))) <=> ?[V_j]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,V_j))) & (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_j)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_d)))))))).
fof(ah4s_intu_u_ariths_addu_u_tou_u_great, axiom, ![V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_k]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d)))))))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d))))),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_intu_u_bitwises_intu_u_notu_u_def, axiom, ![V_i]: s(t_h4s_integers_int,h4s_intu_u_bitwises_intu_u_not(s(t_h4s_integers_int,V_i))) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i))),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_bitwises_intu_u_bitu_u_def, axiom, ![V_i, V_b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ~ (p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_intu_u_bitwises_intu_u_not(s(t_h4s_integers_int,V_i)))))))))) & s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_integers_int,V_i))) = s(t_bool,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_bool,V_v),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_i))))))))).
fof(ch4s_intu_u_bitwises_intu_u_bitu_u_not, conjecture, ![V_i, V_b]: (p(s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_integers_int,h4s_intu_u_bitwises_intu_u_not(s(t_h4s_integers_int,V_i)))))) <=> ~ (p(s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_integers_int,V_i))))))).
