%   ORIGINAL: h4/HolSmt/r107
% 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/HolSmt/r095: !y x. h4/integer/int__ge (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__le y x
% Assm: h4/HolSmt/r089: !y x. h4/integer/int__ge x y <=> h4/integer/int__ge (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r099: !y x. h4/integer/int__gt x y <=> ~h4/integer/int__ge (h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__of__num h4/num/0)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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__ADD__RID: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> 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/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% 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/NOT__NOT: !t. ~ ~t <=> t
% 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/integer/INT__ADD__REDUCE_c1: !p. h4/integer/int__add p (h4/integer/int__of__num h4/num/0) = p
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/integer/INT__NOT__LE: !y x. ~h4/integer/int__le x y <=> h4/integer/int__lt y x
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/integer/INT__NEGNEG: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integer/INT__NEG__ADD: !y x. h4/integer/int__neg (h4/integer/int__add x y) = h4/integer/int__add (h4/integer/int__neg x) (h4/integer/int__neg y)
% Assm: h4/integer/INT__NEG__RMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul x (h4/integer/int__neg y)
% Assm: h4/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__ADD__REDUCE_c0: !p. h4/integer/int__add (h4/integer/int__of__num h4/num/0) p = p
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/integer/INT__NEG__0: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/int__arith/le__move__all__right: !y x. h4/integer/int__le x y <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add y (h4/integer/int__neg x))
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/integer/int__ge0: !y x. h4/integer/int__ge x y <=> h4/integer/int__le y x
% Assm: h4/HolSmt/r091: !z y x. h4/integer/int__ge x (h4/integer/int__add y z) <=> h4/integer/int__le (h4/integer/int__add y (h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x))) (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r094: !y x. h4/integer/int__ge (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) y) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r090: !y x. h4/integer/int__ge x y <=> h4/integer/int__le (h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r100: !z y x. h4/integer/int__gt x (h4/integer/int__add y z) <=> ~h4/integer/int__ge (h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__neg y)
% Assm: h4/HolSmt/r106: !y x. h4/integer/int__le x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm: h4/int__arith/le__context__rwt2: !y x c. h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add c x) ==> h4/integer/int__lt y (h4/integer/int__neg x) ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add (h4/integer/int__neg c) y) <=> F)
% 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_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/HolSmt/r098: !y x. h4/integer/int__gt x y <=> ~h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r067: !z y x. x = h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) <=> h4/integer/int__add x (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) z) = h4/integer/int__of__num h4/num/0
% Assm: h4/HolSmt/r065: !y x. x = y <=> h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) = h4/integer/int__of__num h4/num/0
% Assm: h4/HolSmt/r070: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add y (h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) = h4/integer/int__of__num h4/num/0
% Assm: h4/HolSmt/r073: !z y x. x = h4/integer/int__add (h4/integer/int__neg y) z <=> h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) = y
% Assm: h4/HolSmt/r066: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) = y
% Assm: h4/HolSmt/r077: !z y x. h4/integer/int__add x y = z <=> h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) = h4/integer/int__neg x
% Assm: h4/HolSmt/r072: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) = h4/integer/int__neg y
% Assm: h4/HolSmt/r075: !z y x. h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) y = z <=> h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) = h4/integer/int__neg z
% Assm: h4/HolSmt/r093: !y x. h4/integer/int__ge (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__neg y) <=> h4/integer/int__le x y
% Assm: h4/HolSmt/r092: !x. h4/integer/int__ge (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__le x (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r105: !x. h4/integer/int__le (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__ge x (h4/integer/int__of__num h4/num/0)
% Assm: h4/HolSmt/r069: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add x (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z)) = h4/integer/int__of__num h4/num/0
% Assm: h4/HolSmt/r068: !z y x. x = h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) z <=> h4/integer/int__add y (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) x) = h4/integer/int__of__num h4/num/0
% Assm: h4/HolSmt/r071: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add y (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) z) = h4/integer/int__of__num h4/num/0
% Assm: h4/HolSmt/r078: !z y x w v a. h4/integer/int__add a (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__add (h4/integer/int__mul v y) (h4/integer/int__mul w z))) = h4/integer/int__of__num h4/num/0 <=> h4/integer/int__add x (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg v) y) (h4/integer/int__mul (h4/integer/int__neg w) z)) = a
% Assm: h4/int__arith/eq__move__all__right: !y x. x = y <=> h4/integer/int__of__num h4/num/0 = h4/integer/int__add y (h4/integer/int__neg x)
% Assm: h4/int__arith/eq__context__rwt1: !y x c. h4/integer/int__of__num h4/num/0 = h4/integer/int__add c x ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add c y) <=> h4/integer/int__le x y)
% Assm: h4/integer/INT__LE__REDUCE_c2: !n. h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) <=> F
% Assm: h4/int__arith/eq__context__rwt2: !y x c. h4/integer/int__of__num h4/num/0 = h4/integer/int__add c x ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add (h4/integer/int__neg c) y) <=> h4/integer/int__le (h4/integer/int__neg x) y)
% Assm: h4/integer/INT__LE__ANTISYM: !y x. h4/integer/int__le x y /\ h4/integer/int__le y x <=> x = y
% Assm: h4/bool/CONJ__COMM: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm: h4/integer/INT__EQ__NEG: !y x. h4/integer/int__neg x = h4/integer/int__neg y <=> x = y
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/OR__CLAUSES_c4: !t. t \/ t <=> t
% Assm: h4/HolSmt/r074: !y x. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x = h4/integer/int__neg 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/HolSmt/r103: !y x. h4/integer/int__le x y <=> h4/integer/int__ge y x
% Assm: h4/integer/INT__GE__CALCULATE: !y x. h4/integer/int__ge x y <=> h4/integer/int__le y x
% Assm: h4/Omega/dark__shadow__row__tupled__primitive__def: h4/Omega/dark__shadow__row__tupled = h4/relation/WFREC (h4/min/_40 (\R_27. h4/relation/WF R_27 /\ (!R d rs L c. R_27 (h4/pair/_2C c (h4/pair/_2C L rs)) (h4/pair/_2C c (h4/pair/_2C L (h4/list/CONS (h4/pair/_2C d R) rs)))))) (\dark__shadow__row__tupled a. h4/pair/pair__CASE a (\c v1. h4/pair/pair__CASE v1 (\L v3. h4/list/list__CASE v3 (h4/combin/I T) (\v4 rs. h4/pair/pair__CASE v4 (\d R. h4/combin/I (h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ dark__shadow__row__tupled (h4/pair/_2C c (h4/pair/_2C L rs))))))))
% Assm: h4/integer/int__div0: !j i. ~(j = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__div i j = h4/bool/COND (h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j) (h4/bool/COND (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num i) (h4/integer/Num j))) (h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num (h4/integer/int__neg i)) (h4/integer/Num j)))) (h4/bool/COND (h4/arithmetic/MOD (h4/integer/Num (h4/integer/int__neg i)) (h4/integer/Num j) = h4/num/0) (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) (h4/bool/COND (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num i) (h4/integer/Num (h4/integer/int__neg j))))) (h4/bool/COND (h4/arithmetic/MOD (h4/integer/Num i) (h4/integer/Num (h4/integer/int__neg j)) = h4/num/0) (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num (h4/integer/int__neg i)) (h4/integer/Num (h4/integer/int__neg j)))))
% 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/Omega/dark__shadow__row__def_c1: !rs d c R L. h4/Omega/dark__shadow__row c L (h4/list/CONS (h4/pair/_2C d R) rs) <=> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ h4/Omega/dark__shadow__row c L rs
% Assm: h4/Omega/dark__shadow__FORALL: !uppers lowers. h4/Omega/dark__shadow uppers lowers <=> (!c d L R. h4/bool/IN (h4/pair/_2C c L) (h4/list/LIST__TO__SET uppers) /\ h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET lowers) ==> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))
% Assm: h4/integer/INT__LE__RADD: !z y x. h4/integer/int__le (h4/integer/int__add x z) (h4/integer/int__add y z) <=> h4/integer/int__le x y
% Assm: h4/integer/int__gt0: !y x. h4/integer/int__gt x y <=> h4/integer/int__lt y x
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/EXISTS__REFL: !a. ?x. x = a
% 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/integer/INT__ADD__LINV: !x. h4/integer/int__add (h4/integer/int__neg x) x = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/int__le0: !y x. h4/integer/int__le x y <=> ~h4/integer/int__lt y x
% Assm: h4/integer/INT__MUL__COMM: !y x. h4/integer/int__mul x y = h4/integer/int__mul y x
% Assm: h4/Omega/dark__shadow__row__curried__def: !x2 x1 x. h4/Omega/dark__shadow__row x x1 x2 <=> h4/Omega/dark__shadow__row__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% 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/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% 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/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Goal: !y x. h4/integer/int__le x y <=> h4/integer/int__ge (h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__of__num h4/num/0)
%   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_HolSmts_r095]: !y x. h4/integer/int__ge (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__le y x
% Assm [h4s_HolSmts_r089]: !y x. h4/integer/int__ge x y <=> h4/integer/int__ge (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r099]: !y x. h4/integer/int__gt x y <=> ~h4/integer/int__ge (h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_ADDu_u_RID]: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> 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_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% 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_NOTu_u_NOT]: !t. ~ ~t <=> t
% 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_integers_INTu_u_ADDu_u_REDUCEu_c1]: !p. h4/integer/int__add p (h4/integer/int__of__num h4/num/0) = p
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_integers_INTu_u_NOTu_u_LE]: !y x. ~h4/integer/int__le x y <=> h4/integer/int__lt y x
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_integers_INTu_u_NEGNEG]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integers_INTu_u_NEGu_u_ADD]: !y x. h4/integer/int__neg (h4/integer/int__add x y) = h4/integer/int__add (h4/integer/int__neg x) (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_NEGu_u_RMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c0]: !p. h4/integer/int__add (h4/integer/int__of__num h4/num/0) p = p
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_integers_INTu_u_NEGu_u_0]: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_intu_u_ariths_leu_u_moveu_u_allu_u_right]: !y x. h4/integer/int__le x y <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add y (h4/integer/int__neg x))
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_integers_intu_u_ge0]: !y x. h4/integer/int__ge x y <=> h4/integer/int__le y x
% Assm [h4s_HolSmts_r091]: !z y x. h4/integer/int__ge x (h4/integer/int__add y z) <=> h4/integer/int__le (h4/integer/int__add y (h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x))) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r094]: !y x. h4/integer/int__ge (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) y) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r090]: !y x. h4/integer/int__ge x y <=> h4/integer/int__le (h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r100]: !z y x. h4/integer/int__gt x (h4/integer/int__add y z) <=> ~h4/integer/int__ge (h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__neg y)
% Assm [h4s_HolSmts_r106]: !y x. h4/integer/int__le x y <=> h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_intu_u_ariths_leu_u_contextu_u_rwt2]: !y x c. h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add c x) ==> h4/integer/int__lt y (h4/integer/int__neg x) ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add (h4/integer/int__neg c) y) <=> F)
% 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_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_HolSmts_r098]: !y x. h4/integer/int__gt x y <=> ~h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y)) (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r067]: !z y x. x = h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) <=> h4/integer/int__add x (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) z) = h4/integer/int__of__num h4/num/0
% Assm [h4s_HolSmts_r065]: !y x. x = y <=> h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) = h4/integer/int__of__num h4/num/0
% Assm [h4s_HolSmts_r070]: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add y (h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) = h4/integer/int__of__num h4/num/0
% Assm [h4s_HolSmts_r073]: !z y x. x = h4/integer/int__add (h4/integer/int__neg y) z <=> h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) = y
% Assm [h4s_HolSmts_r066]: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) = y
% Assm [h4s_HolSmts_r077]: !z y x. h4/integer/int__add x y = z <=> h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) = h4/integer/int__neg x
% Assm [h4s_HolSmts_r072]: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add z (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) = h4/integer/int__neg y
% Assm [h4s_HolSmts_r075]: !z y x. h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) y = z <=> h4/integer/int__add x (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) = h4/integer/int__neg z
% Assm [h4s_HolSmts_r093]: !y x. h4/integer/int__ge (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__neg y) <=> h4/integer/int__le x y
% Assm [h4s_HolSmts_r092]: !x. h4/integer/int__ge (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__le x (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r105]: !x. h4/integer/int__le (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__ge x (h4/integer/int__of__num h4/num/0)
% Assm [h4s_HolSmts_r069]: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add x (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z)) = h4/integer/int__of__num h4/num/0
% Assm [h4s_HolSmts_r068]: !z y x. x = h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) y) z <=> h4/integer/int__add y (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) z) x) = h4/integer/int__of__num h4/num/0
% Assm [h4s_HolSmts_r071]: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add y (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) z) = h4/integer/int__of__num h4/num/0
% Assm [h4s_HolSmts_r078]: !z y x w v a. h4/integer/int__add a (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x) (h4/integer/int__add (h4/integer/int__mul v y) (h4/integer/int__mul w z))) = h4/integer/int__of__num h4/num/0 <=> h4/integer/int__add x (h4/integer/int__add (h4/integer/int__mul (h4/integer/int__neg v) y) (h4/integer/int__mul (h4/integer/int__neg w) z)) = a
% Assm [h4s_intu_u_ariths_equ_u_moveu_u_allu_u_right]: !y x. x = y <=> h4/integer/int__of__num h4/num/0 = h4/integer/int__add y (h4/integer/int__neg x)
% Assm [h4s_intu_u_ariths_equ_u_contextu_u_rwt1]: !y x c. h4/integer/int__of__num h4/num/0 = h4/integer/int__add c x ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add c y) <=> h4/integer/int__le x y)
% Assm [h4s_integers_INTu_u_LEu_u_REDUCEu_c2]: !n. h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) <=> F
% Assm [h4s_intu_u_ariths_equ_u_contextu_u_rwt2]: !y x c. h4/integer/int__of__num h4/num/0 = h4/integer/int__add c x ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add (h4/integer/int__neg c) y) <=> h4/integer/int__le (h4/integer/int__neg x) y)
% Assm [h4s_integers_INTu_u_LEu_u_ANTISYM]: !y x. h4/integer/int__le x y /\ h4/integer/int__le y x <=> x = y
% Assm [h4s_bools_CONJu_u_COMM]: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm [h4s_integers_INTu_u_EQu_u_NEG]: !y x. h4/integer/int__neg x = h4/integer/int__neg y <=> x = y
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_ORu_u_CLAUSESu_c4]: !t. t \/ t <=> t
% Assm [h4s_HolSmts_r074]: !y x. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x = h4/integer/int__neg 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_HolSmts_r103]: !y x. h4/integer/int__le x y <=> h4/integer/int__ge y x
% Assm [h4s_integers_INTu_u_GEu_u_CALCULATE]: !y x. h4/integer/int__ge x y <=> h4/integer/int__le y x
% Assm [h4s_Omegas_darku_u_shadowu_u_rowu_u_tupledu_u_primitiveu_u_def]: !_10. (!d dark__shadow__row__tupled c L rs R. ?v. (v <=> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ happ dark__shadow__row__tupled (h4/pair/_2C c (h4/pair/_2C L rs))) /\ (happ (happ (happ (happ (happ (happ _10 d) dark__shadow__row__tupled) c) L) rs) R <=> h4/combin/I v)) ==> (!_9. (!dark__shadow__row__tupled c L rs d. happ (happ (happ (happ (happ _9 dark__shadow__row__tupled) c) L) rs) d = happ (happ (happ (happ (happ _10 d) dark__shadow__row__tupled) c) L) rs) ==> (!_8. (!v4 dark__shadow__row__tupled c L rs. happ (happ (happ (happ (happ _8 v4) dark__shadow__row__tupled) c) L) rs <=> h4/pair/pair__CASE v4 (happ (happ (happ (happ _9 dark__shadow__row__tupled) c) L) rs)) ==> (!_7. (!dark__shadow__row__tupled c L v4. happ (happ (happ (happ _7 dark__shadow__row__tupled) c) L) v4 = happ (happ (happ (happ _8 v4) dark__shadow__row__tupled) c) L) ==> (!_6. (!dark__shadow__row__tupled c L v3. happ (happ (happ (happ _6 dark__shadow__row__tupled) c) L) v3 <=> h4/list/list__CASE v3 (h4/combin/I T) (happ (happ (happ _7 dark__shadow__row__tupled) c) L)) ==> (!_5. (!dark__shadow__row__tupled c L. happ (happ (happ _5 dark__shadow__row__tupled) c) L = happ (happ (happ _6 dark__shadow__row__tupled) c) L) ==> (!_4. (!dark__shadow__row__tupled c v1. happ (happ (happ _4 dark__shadow__row__tupled) c) v1 <=> h4/pair/pair__CASE v1 (happ (happ _5 dark__shadow__row__tupled) c)) ==> (!_3. (!dark__shadow__row__tupled c. happ (happ _3 dark__shadow__row__tupled) c = happ (happ _4 dark__shadow__row__tupled) c) ==> (!_2. (!dark__shadow__row__tupled a. happ (happ _2 dark__shadow__row__tupled) a <=> h4/pair/pair__CASE a (happ _3 dark__shadow__row__tupled)) ==> (!_1. (!dark__shadow__row__tupled. happ _1 dark__shadow__row__tupled = happ _2 dark__shadow__row__tupled) ==> (!_0. (!R_27. happ _0 R_27 <=> h4/relation/WF R_27 /\ (!R d rs L c. happ (happ R_27 (h4/pair/_2C c (h4/pair/_2C L rs))) (h4/pair/_2C c (h4/pair/_2C L (h4/list/CONS (h4/pair/_2C d R) rs))))) ==> h4/Omega/dark__shadow__row__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_integers_intu_u_div0]: !j i. ~(j = h4/integer/int__of__num h4/num/0) ==> (?v. (v <=> h4/arithmetic/MOD (h4/integer/Num i) (h4/integer/Num (h4/integer/int__neg j)) = h4/num/0) /\ (?v'. (v' <=> h4/arithmetic/MOD (h4/integer/Num (h4/integer/int__neg i)) (h4/integer/Num j) = h4/num/0) /\ h4/integer/int__div i j = h4/bool/COND (h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j) (h4/bool/COND (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num i) (h4/integer/Num j))) (h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num (h4/integer/int__neg i)) (h4/integer/Num j)))) (h4/bool/COND v' (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) (h4/bool/COND (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num i) (h4/integer/Num (h4/integer/int__neg j))))) (h4/bool/COND v (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (h4/integer/int__of__num (h4/arithmetic/DIV (h4/integer/Num (h4/integer/int__neg i)) (h4/integer/Num (h4/integer/int__neg j)))))))
% 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_Omegas_darku_u_shadowu_u_rowu_u_defu_c1]: !rs d c R L. h4/Omega/dark__shadow__row c L (h4/list/CONS (h4/pair/_2C d R) rs) <=> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ h4/Omega/dark__shadow__row c L rs
% Assm [h4s_Omegas_darku_u_shadowu_u_FORALL]: !uppers lowers. h4/Omega/dark__shadow uppers lowers <=> (!c d L R. h4/bool/IN (h4/pair/_2C c L) (h4/list/LIST__TO__SET uppers) /\ h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET lowers) ==> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))
% Assm [h4s_integers_INTu_u_LEu_u_RADD]: !z y x. h4/integer/int__le (h4/integer/int__add x z) (h4/integer/int__add y z) <=> h4/integer/int__le x y
% Assm [h4s_integers_intu_u_gt0]: !y x. h4/integer/int__gt x y <=> h4/integer/int__lt y x
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_EXISTSu_u_REFL]: !a. ?x. x = a
% 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_integers_INTu_u_ADDu_u_LINV]: !x. h4/integer/int__add (h4/integer/int__neg x) x = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_intu_u_le0]: !y x. h4/integer/int__le x y <=> ~h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_MULu_u_COMM]: !y x. h4/integer/int__mul x y = h4/integer/int__mul y x
% Assm [h4s_Omegas_darku_u_shadowu_u_rowu_u_curriedu_u_def]: !x2 x1 x. h4/Omega/dark__shadow__row x x1 x2 <=> happ h4/Omega/dark__shadow__row__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% 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_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% 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_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Goal: !y x. h4/integer/int__le x y <=> h4/integer/int__ge (h4/integer/int__add y (h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x)) (h4/integer/int__of__num h4/num/0)
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_Q1434161,TV_Q1434157]: ![V_f, V_g]: (![V_x]: s(TV_Q1434157,happ(s(t_fun(TV_Q1434161,TV_Q1434157),V_f),s(TV_Q1434161,V_x))) = s(TV_Q1434157,happ(s(t_fun(TV_Q1434161,TV_Q1434157),V_g),s(TV_Q1434161,V_x))) => s(t_fun(TV_Q1434161,TV_Q1434157),V_f) = s(t_fun(TV_Q1434161,TV_Q1434157),V_g))).
fof(ah4s_HolSmts_r095, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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,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_y))))),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_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_HolSmts_r089, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_ge(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,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_y))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_HolSmts_r099, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) <=> ~ (p(s(t_bool,h4s_integers_intu_u_ge(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,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))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))).
fof(ah4s_bools_TRUTH, axiom, 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_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_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_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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_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_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_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_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,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_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_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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => 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_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_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_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_bools_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_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EXISTSu_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_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_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_integers_INTu_u_NOTu_u_LE, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_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_NEGu_u_ADD, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(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,h4s_integers_intu_u_neg(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_NEGu_u_RMUL, 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,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_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_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_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_integers_INTu_u_NEGu_u_0, 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_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_intu_u_ariths_leu_u_moveu_u_allu_u_right, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(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_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_y),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))))))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_integers_intu_u_ge0, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_HolSmts_r091, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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_le(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_add(s(t_h4s_integers_int,V_z),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))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_HolSmts_r094, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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_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))),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = 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,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_y))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_HolSmts_r090, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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_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,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,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_HolSmts_r100, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_gt(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)))))) <=> ~ (p(s(t_bool,h4s_integers_intu_u_ge(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_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))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))))))))).
fof(ah4s_HolSmts_r106, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(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_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_y))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_intu_u_ariths_leu_u_contextu_u_rwt2, axiom, ![V_y, V_x, V_c]: (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_add(s(t_h4s_integers_int,V_c),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,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))))) => 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_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_c))),s(t_h4s_integers_int,V_y))))) = s(t_bool,f)))).
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_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_HolSmts_r098, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_gt(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,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,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_y))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))).
fof(ah4s_HolSmts_r067, axiom, ![V_z, V_y, V_x]: (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,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_z))))) <=> 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,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_y))),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_HolSmts_r065, axiom, ![V_y, V_x]: (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_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_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_HolSmts_r070, axiom, ![V_z, V_y, V_x]: (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,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_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))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_HolSmts_r073, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,V_x) = 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,V_y))),s(t_h4s_integers_int,V_z))) <=> 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_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))))) = s(t_h4s_integers_int,V_y))).
fof(ah4s_HolSmts_r066, axiom, ![V_z, V_y, V_x]: (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,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_z))))) = s(t_h4s_integers_int,V_y))).
fof(ah4s_HolSmts_r077, 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,V_y))) = s(t_h4s_integers_int,V_z) <=> 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,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_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))).
fof(ah4s_HolSmts_r072, axiom, ![V_z, V_y, V_x]: (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,V_z),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))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))))).
fof(ah4s_HolSmts_r075, axiom, ![V_z, V_y, V_x]: (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_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))),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,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_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_z))))).
fof(ah4s_HolSmts_r093, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(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,V_y)))).
fof(ah4s_HolSmts_r092, axiom, ![V_x]: s(t_bool,h4s_integers_intu_u_ge(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))),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_le(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_HolSmts_r105, axiom, ![V_x]: s(t_bool,h4s_integers_intu_u_le(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))),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_ge(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_HolSmts_r069, axiom, ![V_z, V_y, V_x]: (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,V_x),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_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_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,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_z))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_HolSmts_r068, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,V_x) = 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_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_y))),s(t_h4s_integers_int,V_z))) <=> 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_add(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_z))),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_HolSmts_r071, axiom, ![V_z, V_y, V_x]: (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,V_y),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_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))),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_HolSmts_r078, axiom, ![V_z, V_y, V_x, V_w, V_v, V_a]: (s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_a),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_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))),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_v),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_z))))))))) = 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_add(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_v))),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_w))),s(t_h4s_integers_int,V_z))))))) = s(t_h4s_integers_int,V_a))).
fof(ah4s_intu_u_ariths_equ_u_moveu_u_allu_u_right, axiom, ![V_y, V_x]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y) <=> s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) = 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,V_x))))))).
fof(ah4s_intu_u_ariths_equ_u_contextu_u_rwt1, axiom, ![V_y, V_x, V_c]: (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_c),s(t_h4s_integers_int,V_x))) => 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_add(s(t_h4s_integers_int,V_c),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,V_y))))).
fof(ah4s_integers_INTu_u_LEu_u_REDUCEu_c2, axiom, ![V_n]: 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_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_bool,f)).
fof(ah4s_intu_u_ariths_equ_u_contextu_u_rwt2, axiom, ![V_y, V_x, V_c]: (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_c),s(t_h4s_integers_int,V_x))) => 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_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_c))),s(t_h4s_integers_int,V_y))))) = s(t_bool,h4s_integers_intu_u_le(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_LEu_u_ANTISYM, 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_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y))).
fof(ah4s_bools_CONJu_u_COMM, 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))))).
fof(ah4s_integers_INTu_u_EQu_u_NEG, axiom, ![V_y, 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_neg(s(t_h4s_integers_int,V_y))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_HolSmts_r074, axiom, ![V_y, 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))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_HolSmts_r103, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_GEu_u_CALCULATE, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(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_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_Omegas_darku_u_shadowu_u_rowu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_10]: (![V_d, V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_rs, V_R]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,h4s_integers_intu_u_sub(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,V_d))),s(t_h4s_integers_int,V_L))),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,V_c))),s(t_h4s_integers_int,V_R))))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(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,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))))))))),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,V_d))),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,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))))))) & s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))))),V_uu_10),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),s(t_h4s_integers_int,V_R))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_9]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_rs, V_d]: s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),s(t_h4s_nums_num,V_d))) = s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))))),V_uu_10),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) => ![V_uu_8]: (![V_v4, V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_rs]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))) => ![V_uu_7]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))) => ![V_uu_6]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_v3]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v3))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v3),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))))) => ![V_uu_5]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))) => ![V_uu_4]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_v1))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_v1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))))) => ![V_uu_3]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c]: s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))) = s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))) => ![V_uu_2]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),V_a))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),V_a),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))))) => ![V_uu_1]: (![V_darku_u_shadowu_u_rowu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))) => ![V_uu_0]: (![V_Ru_27]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_Ru_27)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_Ru_27)))) & ![V_R, V_d, V_rs, V_L, V_c]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_Ru_27),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_omegas_darku_u_shadowu_u_rowu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_1))))))))))))))).
fof(ah4s_integers_intu_u_div0, axiom, ![V_j, V_i]: (~ (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)))) => ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_i))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_j))))))) = s(t_h4s_nums_num,h4s_nums_0)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_i))))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_j))))) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_j))) = s(t_h4s_integers_int,h4s_bools_cond(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))),s(t_h4s_integers_int,h4s_bools_cond(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_i))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_i))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_j))))))),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_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_i))))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_j))))))))),s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,V_vi_),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_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,h4s_bools_cond(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_i))),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_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_i))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_j))))))))))),s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,V_v),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_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,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_i))))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_j))))))))))))))))).
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_Omegas_darku_u_shadowu_u_rowu_u_defu_c1, axiom, ![V_rs, V_d, V_c, V_R, V_L]: (p(s(t_bool,h4s_omegas_darku_u_shadowu_u_row(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))) <=> (p(s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,h4s_integers_intu_u_sub(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,V_d))),s(t_h4s_integers_int,V_L))),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,V_c))),s(t_h4s_integers_int,V_R))))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(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,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))))))))),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,V_d))),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_omegas_darku_u_shadowu_u_row(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_FORALL, axiom, ![V_uppers, V_lowers]: (p(s(t_bool,h4s_omegas_darku_u_shadow(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) <=> ![V_c, V_d, V_L, V_R]: ((p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))))) & p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))))) => p(s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,h4s_integers_intu_u_sub(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,V_d))),s(t_h4s_integers_int,V_L))),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,V_c))),s(t_h4s_integers_int,V_R))))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(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,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))))))))),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,V_d))),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_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_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),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_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_intu_u_gt0, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (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,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
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_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_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_EXISTSu_u_REFL, axiom, ![TV_u_27a]: ![V_a]: ?[V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_a)).
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_integers_INTu_u_ADDu_u_LINV, axiom, ![V_x]: 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,V_x))),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_le0, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) <=> ~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_integers_INTu_u_MULu_u_COMM, axiom, ![V_y, V_x]: 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,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_Omegas_darku_u_shadowu_u_rowu_u_curriedu_u_def, axiom, ![V_x2, V_x1, V_x]: s(t_bool,h4s_omegas_darku_u_shadowu_u_row(s(t_h4s_nums_num,V_x),s(t_h4s_integers_int,V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x2))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_omegas_darku_u_shadowu_u_rowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x2)))))))).
fof(ah4s_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = 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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
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_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_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),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_m)))))).
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_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_ADDu_u_SYM, axiom, ![V_n, V_m]: 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_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: 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_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
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_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,V_p)))).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
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_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
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_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_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_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(ch4s_HolSmts_r107, conjecture, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_ge(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,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))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
