%   ORIGINAL: h4/complex/COMPLEX__SCALAR__LMUL__SUB
% 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/complex/complex__scalar__lmul0: !z k. h4/complex/complex__scalar__lmul k z = h4/pair/_2C (h4/realax/real__mul k (h4/complex/RE z)) (h4/realax/real__mul k (h4/complex/IM z))
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/complex/COMPLEX__SCALAR__LMUL: !z l k. h4/complex/complex__scalar__lmul k (h4/complex/complex__scalar__lmul l z) = h4/complex/complex__scalar__lmul (h4/realax/real__mul k l) z
% Assm: h4/complex/COMPLEX__SCALAR__LMUL__NEG: !z k. h4/complex/complex__neg (h4/complex/complex__scalar__lmul k z) = h4/complex/complex__scalar__lmul (h4/realax/real__neg k) z
% Assm: h4/complex/COMPLEX__SCALAR__LMUL__ADD: !z l k. h4/complex/complex__scalar__lmul (h4/realax/real__add k l) z = h4/complex/complex__add (h4/complex/complex__scalar__lmul k z) (h4/complex/complex__scalar__lmul l z)
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/complex/IM0: !z. h4/complex/IM z = h4/pair/SND z
% Assm: h4/complex/RE0: !z. h4/complex/RE z = h4/pair/FST z
% Assm: h4/complex/complex__sub0: !z w. h4/complex/complex__sub z w = h4/complex/complex__add z (h4/complex/complex__neg w)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/complex/COMPLEX__NEG__SCALAR__LMUL: !z k. h4/complex/complex__scalar__lmul k (h4/complex/complex__neg z) = h4/complex/complex__scalar__lmul (h4/realax/real__neg k) z
% Assm: h4/complex/complex__neg0: !z. h4/complex/complex__neg z = h4/pair/_2C (h4/realax/real__neg (h4/complex/RE z)) (h4/realax/real__neg (h4/complex/IM z))
% Assm: h4/complex/COMPLEX__ADD__COMM: !z w. h4/complex/complex__add z w = h4/complex/complex__add w z
% Assm: h4/real/REAL__MUL__ASSOC: !z y x. h4/realax/real__mul x (h4/realax/real__mul y z) = h4/realax/real__mul (h4/realax/real__mul x y) z
% Assm: h4/complex/COMPLEX__SUB__ADD: !z w. h4/complex/complex__add (h4/complex/complex__sub z w) w = z
% Assm: h4/real/REAL__NEG__LMUL: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/real__neg x) y
% Assm: h4/real/REAL__ADD__RDISTRIB: !z y x. h4/realax/real__mul (h4/realax/real__add x y) z = h4/realax/real__add (h4/realax/real__mul x z) (h4/realax/real__mul y z)
% Assm: h4/complex/complex__add0: !z w. h4/complex/complex__add z w = h4/pair/_2C (h4/realax/real__add (h4/complex/RE z) (h4/complex/RE w)) (h4/realax/real__add (h4/complex/IM z) (h4/complex/IM w))
% Assm: h4/complex/COMPLEX__EQ__SUB__LADD: !z w v. z = h4/complex/complex__sub w v <=> h4/complex/complex__add z v = w
% Assm: h4/complex/COMPLEX__NEG__SUB: !z w. h4/complex/complex__neg (h4/complex/complex__sub z w) = h4/complex/complex__sub w z
% Assm: h4/complex/COMPLEX__ADD__ASSOC: !z w v. h4/complex/complex__add z (h4/complex/complex__add w v) = h4/complex/complex__add (h4/complex/complex__add z w) v
% Assm: h4/complex/COMPLEX__NEGNEG: !z. h4/complex/complex__neg (h4/complex/complex__neg z) = z
% Assm: h4/complex/COMPLEX__SUB__RDISTRIB: !z w v. h4/complex/complex__mul (h4/complex/complex__sub z w) v = h4/complex/complex__sub (h4/complex/complex__mul z v) (h4/complex/complex__mul w v)
% Assm: h4/complex/COMPLEX__ADD__SUB: !z w. h4/complex/complex__sub (h4/complex/complex__add z w) z = w
% Assm: h4/complex/COMPLEX__ADD__RID: !z. h4/complex/complex__add z (h4/complex/complex__of__num h4/num/0) = z
% Assm: h4/complex/COMPLEX__SUB__SUB: !z w. h4/complex/complex__sub (h4/complex/complex__sub z w) z = h4/complex/complex__neg w
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/complex/COMPLEX__NEG__ADD: !z w. h4/complex/complex__neg (h4/complex/complex__add z w) = h4/complex/complex__add (h4/complex/complex__neg z) (h4/complex/complex__neg w)
% Assm: h4/complex/COMPLEX__OF__REAL__SUB: !y x. h4/complex/complex__sub (h4/complex/complex__of__real x) (h4/complex/complex__of__real y) = h4/complex/complex__of__real (h4/real/real__sub x y)
% Assm: h4/real/REAL__MUL__LNEG: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm: h4/real/REAL__MUL__RNEG: !y x. h4/realax/real__mul x (h4/realax/real__neg y) = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm: h4/complex/COMPLEX__SUB__LDISTRIB: !z w v. h4/complex/complex__mul z (h4/complex/complex__sub w v) = h4/complex/complex__sub (h4/complex/complex__mul z w) (h4/complex/complex__mul z v)
% Assm: h4/complex/COMPLEX__ADD__RINV: !z. h4/complex/complex__add z (h4/complex/complex__neg z) = h4/complex/complex__of__num h4/num/0
% Assm: h4/complex/COMPLEX__ADD2__SUB2: !z w v u. h4/complex/complex__sub (h4/complex/complex__add z w) (h4/complex/complex__add u v) = h4/complex/complex__add (h4/complex/complex__sub z u) (h4/complex/complex__sub w v)
% Assm: h4/complex/COMPLEX__ADD__LINV: !z. h4/complex/complex__add (h4/complex/complex__neg z) z = h4/complex/complex__of__num h4/num/0
% Assm: h4/complex/COMPLEX__SUB__LNEG: !z w. h4/complex/complex__sub (h4/complex/complex__neg z) w = h4/complex/complex__neg (h4/complex/complex__add z w)
% Assm: h4/complex/COMPLEX__SUB__NEG2: !z w. h4/complex/complex__sub (h4/complex/complex__neg z) (h4/complex/complex__neg w) = h4/complex/complex__sub w z
% Assm: h4/complex/COMPLEX__SUB__TRIANGLE: !z w v. h4/complex/complex__add (h4/complex/complex__sub z w) (h4/complex/complex__sub w v) = h4/complex/complex__sub z v
% Assm: h4/complex/COMPLEX__SUB__0: !z w. h4/complex/complex__sub z w = h4/complex/complex__of__num h4/num/0 <=> z = w
% Assm: h4/complex/COMPLEX__SUB__RAT: !z w v u. ~(w = h4/complex/complex__of__num h4/num/0) /\ ~(v = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__sub (h4/complex/complex__div z w) (h4/complex/complex__div u v) = h4/complex/complex__div (h4/complex/complex__sub (h4/complex/complex__mul z v) (h4/complex/complex__mul w u)) (h4/complex/complex__mul w v)
% Assm: h4/complex/COMPLEX__DIV__SUB: !z w v. h4/complex/complex__sub (h4/complex/complex__div z v) (h4/complex/complex__div w v) = h4/complex/complex__div (h4/complex/complex__sub z w) v
% Assm: h4/complex/COMPLEX__EQ__SUB__RADD: !z w v. h4/complex/complex__sub z w = v <=> z = h4/complex/complex__add v w
% Assm: h4/complex/COMPLEX__SUB__INV2: !z w. ~(z = h4/complex/complex__of__num h4/num/0) /\ ~(w = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__sub (h4/complex/complex__inv z) (h4/complex/complex__inv w) = h4/complex/complex__div (h4/complex/complex__sub w z) (h4/complex/complex__mul z w)
% Assm: h4/complex/COMPLEX__SUB__RZERO: !z. h4/complex/complex__sub z (h4/complex/complex__of__num h4/num/0) = z
% Assm: h4/complex/COMPLEX__SUB__REFL: !z. h4/complex/complex__sub z z = h4/complex/complex__of__num h4/num/0
% Assm: h4/complex/COMPLEX__SUB__ADD2: !z w. h4/complex/complex__add w (h4/complex/complex__sub z w) = z
% Assm: h4/complex/COMPLEX__SUB__SUB2: !z w. h4/complex/complex__sub z (h4/complex/complex__sub z w) = w
% Assm: h4/complex/COMPLEX__DIFFSQ: !z w. h4/complex/complex__mul (h4/complex/complex__add z w) (h4/complex/complex__sub z w) = h4/complex/complex__sub (h4/complex/complex__mul z z) (h4/complex/complex__mul w w)
% Assm: h4/complex/COMPLEX__SUB__RNEG: !z w. h4/complex/complex__sub z (h4/complex/complex__neg w) = h4/complex/complex__add z w
% Assm: h4/complex/COMPLEX__SUB__LZERO: !z. h4/complex/complex__sub (h4/complex/complex__of__num h4/num/0) z = h4/complex/complex__neg z
% Assm: h4/complex/COMPLEX__ADD__SUB2: !z w. h4/complex/complex__sub z (h4/complex/complex__add z w) = h4/complex/complex__neg w
% Assm: h4/complex/COMPLEX__ADD__LID: !z. h4/complex/complex__add (h4/complex/complex__of__num h4/num/0) z = z
% Assm: h4/complex/complex__div0: !z w. h4/complex/complex__div z w = h4/complex/complex__mul z (h4/complex/complex__inv w)
% Assm: h4/complex/COMPLEX__EQ__RADD: !z w v. h4/complex/complex__add z v = h4/complex/complex__add w v <=> z = w
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/real/real__sub0: !y x. h4/real/real__sub x y = h4/realax/real__add x (h4/realax/real__neg y)
% Assm: h4/complex/COMPLEX__OF__REAL__NEG: !x. h4/complex/complex__neg (h4/complex/complex__of__real x) = h4/complex/complex__of__real (h4/realax/real__neg x)
% Assm: h4/complex/COMPLEX__OF__REAL__ADD: !y x. h4/complex/complex__add (h4/complex/complex__of__real x) (h4/complex/complex__of__real y) = h4/complex/complex__of__real (h4/realax/real__add x y)
% Assm: h4/complex/COMPLEX__NEG__RMUL: !z w. h4/complex/complex__neg (h4/complex/complex__mul z w) = h4/complex/complex__mul z (h4/complex/complex__neg w)
% Assm: h4/complex/COMPLEX__LNEG__UNIQ: !z w. h4/complex/complex__add z w = h4/complex/complex__of__num h4/num/0 <=> z = h4/complex/complex__neg w
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/complex/COMPLEX__NEG__0: h4/complex/complex__neg (h4/complex/complex__of__num h4/num/0) = h4/complex/complex__of__num h4/num/0
% Assm: h4/complex/COMPLEX__MUL__COMM: !z w. h4/complex/complex__mul z w = h4/complex/complex__mul w z
% Assm: h4/complex/COMPLEX__ADD__LDISTRIB: !z w v. h4/complex/complex__mul z (h4/complex/complex__add w v) = h4/complex/complex__add (h4/complex/complex__mul z w) (h4/complex/complex__mul z v)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/powser/POWDIFF: !y x n. h4/real/real__sub (h4/real/pow x (h4/num/SUC n)) (h4/real/pow y (h4/num/SUC n)) = h4/realax/real__mul (h4/real/real__sub x y) (h4/real/sum (h4/pair/_2C h4/num/0 (h4/num/SUC n)) (\p. h4/realax/real__mul (h4/real/pow x p) (h4/real/pow y (h4/arithmetic/_2D n p))))
% Assm: h4/complex/COMPLEX__INV__MUL: !z w. ~(z = h4/complex/complex__of__num h4/num/0) /\ ~(w = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__inv (h4/complex/complex__mul z w) = h4/complex/complex__mul (h4/complex/complex__inv z) (h4/complex/complex__inv w)
% Assm: h4/complex/COMPLEX__MUL__LID: !z. h4/complex/complex__mul (h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) z = z
% Assm: h4/complex/COMPLEX__MUL__RINV: !z. ~(z = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__mul z (h4/complex/complex__inv z) = h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/complex/COMPLEX__MUL__RID: !z. h4/complex/complex__mul z (h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = z
% Assm: h4/complex/COMPLEX__MUL__LINV: !z. ~(z = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__mul (h4/complex/complex__inv z) z = h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/complex/COMPLEX__MUL__ASSOC: !z w v. h4/complex/complex__mul z (h4/complex/complex__mul w v) = h4/complex/complex__mul (h4/complex/complex__mul z w) v
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/complex/COMPLEX__ADD__RAT: !z w v u. ~(w = h4/complex/complex__of__num h4/num/0) /\ ~(v = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__add (h4/complex/complex__div z w) (h4/complex/complex__div u v) = h4/complex/complex__div (h4/complex/complex__add (h4/complex/complex__mul z v) (h4/complex/complex__mul w u)) (h4/complex/complex__mul w v)
% Assm: h4/complex/COMPLEX__NEG__LDIV: !z w. h4/complex/complex__neg (h4/complex/complex__div z w) = h4/complex/complex__div (h4/complex/complex__neg z) w
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/complex/COMPLEX__ADD__LID__UNIQ: !z w. h4/complex/complex__add z w = w <=> z = h4/complex/complex__of__num h4/num/0
% Assm: h4/complex/COMPLEX__EQ__LADD: !z w v. h4/complex/complex__add z w = h4/complex/complex__add z v <=> w = v
% Assm: h4/complex/COMPLEX__ADD__RDISTRIB: !z w v. h4/complex/complex__mul (h4/complex/complex__add z w) v = h4/complex/complex__add (h4/complex/complex__mul z v) (h4/complex/complex__mul w v)
% Assm: h4/powser/POWDIFF__LEMMA: !y x n. h4/real/sum (h4/pair/_2C h4/num/0 (h4/num/SUC n)) (\p. h4/realax/real__mul (h4/real/pow x p) (h4/real/pow y (h4/arithmetic/_2D (h4/num/SUC n) p))) = h4/realax/real__mul y (h4/real/sum (h4/pair/_2C h4/num/0 (h4/num/SUC n)) (\p. h4/realax/real__mul (h4/real/pow x p) (h4/real/pow y (h4/arithmetic/_2D n p))))
% Assm: h4/real/sum0_c1: !n m f. h4/real/sum (h4/pair/_2C n (h4/num/SUC m)) f = h4/realax/real__add (h4/real/sum (h4/pair/_2C n m) f) (f (h4/arithmetic/_2B n m))
% Assm: h4/real/sum0_c0: !n f. h4/real/sum (h4/pair/_2C n h4/num/0) f = h4/real/real__of__num h4/num/0
% Assm: h4/real/pow0_c0: !x. h4/real/pow x h4/num/0 = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/pow0_c1: !x n. h4/real/pow x (h4/num/SUC n) = h4/realax/real__mul x (h4/real/pow x n)
% Assm: h4/real/REAL__SUB__LDISTRIB: !z y x. h4/realax/real__mul x (h4/real/real__sub y z) = h4/real/real__sub (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm: h4/real/REAL__MUL__RID: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm: h4/real/REAL__ADD__LID__UNIQ: !y x. h4/realax/real__add x y = y <=> x = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__MUL__SYM: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm: h4/real/REAL__ADD__LID: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm: h4/real/REAL__ADD__LINV: !x. h4/realax/real__add (h4/realax/real__neg x) x = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__ADD__ASSOC: !z y x. h4/realax/real__add x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__add x y) z
% Assm: h4/real/REAL__LDISTRIB: !z y x. h4/realax/real__mul x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm: h4/real/REAL__ADD__SYM: !y x. h4/realax/real__add x y = h4/realax/real__add y x
% Assm: h4/arithmetic/SUB__EQUAL__0: !c. h4/arithmetic/_2D c c = h4/num/0
% Goal: !z l k. h4/complex/complex__scalar__lmul (h4/real/real__sub k l) z = h4/complex/complex__sub (h4/complex/complex__scalar__lmul k z) (h4/complex/complex__scalar__lmul l z)
%   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_complexs_complexu_u_scalaru_u_lmul0]: !z k. h4/complex/complex__scalar__lmul k z = h4/pair/_2C (h4/realax/real__mul k (h4/complex/RE z)) (h4/realax/real__mul k (h4/complex/IM z))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_complexs_COMPLEXu_u_SCALARu_u_LMUL]: !z l k. h4/complex/complex__scalar__lmul k (h4/complex/complex__scalar__lmul l z) = h4/complex/complex__scalar__lmul (h4/realax/real__mul k l) z
% Assm [h4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_NEG]: !z k. h4/complex/complex__neg (h4/complex/complex__scalar__lmul k z) = h4/complex/complex__scalar__lmul (h4/realax/real__neg k) z
% Assm [h4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_ADD]: !z l k. h4/complex/complex__scalar__lmul (h4/realax/real__add k l) z = h4/complex/complex__add (h4/complex/complex__scalar__lmul k z) (h4/complex/complex__scalar__lmul l z)
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_complexs_IM0]: !z. h4/complex/IM z = h4/pair/SND z
% Assm [h4s_complexs_RE0]: !z. h4/complex/RE z = h4/pair/FST z
% Assm [h4s_complexs_complexu_u_sub0]: !z w. h4/complex/complex__sub z w = h4/complex/complex__add z (h4/complex/complex__neg w)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_complexs_COMPLEXu_u_NEGu_u_SCALARu_u_LMUL]: !z k. h4/complex/complex__scalar__lmul k (h4/complex/complex__neg z) = h4/complex/complex__scalar__lmul (h4/realax/real__neg k) z
% Assm [h4s_complexs_complexu_u_neg0]: !z. h4/complex/complex__neg z = h4/pair/_2C (h4/realax/real__neg (h4/complex/RE z)) (h4/realax/real__neg (h4/complex/IM z))
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_COMM]: !z w. h4/complex/complex__add z w = h4/complex/complex__add w z
% Assm [h4s_reals_REALu_u_MULu_u_ASSOC]: !z y x. h4/realax/real__mul x (h4/realax/real__mul y z) = h4/realax/real__mul (h4/realax/real__mul x y) z
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_ADD]: !z w. h4/complex/complex__add (h4/complex/complex__sub z w) w = z
% Assm [h4s_reals_REALu_u_NEGu_u_LMUL]: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/real__neg x) y
% Assm [h4s_reals_REALu_u_ADDu_u_RDISTRIB]: !z y x. h4/realax/real__mul (h4/realax/real__add x y) z = h4/realax/real__add (h4/realax/real__mul x z) (h4/realax/real__mul y z)
% Assm [h4s_complexs_complexu_u_add0]: !z w. h4/complex/complex__add z w = h4/pair/_2C (h4/realax/real__add (h4/complex/RE z) (h4/complex/RE w)) (h4/realax/real__add (h4/complex/IM z) (h4/complex/IM w))
% Assm [h4s_complexs_COMPLEXu_u_EQu_u_SUBu_u_LADD]: !z w v. z = h4/complex/complex__sub w v <=> h4/complex/complex__add z v = w
% Assm [h4s_complexs_COMPLEXu_u_NEGu_u_SUB]: !z w. h4/complex/complex__neg (h4/complex/complex__sub z w) = h4/complex/complex__sub w z
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_ASSOC]: !z w v. h4/complex/complex__add z (h4/complex/complex__add w v) = h4/complex/complex__add (h4/complex/complex__add z w) v
% Assm [h4s_complexs_COMPLEXu_u_NEGNEG]: !z. h4/complex/complex__neg (h4/complex/complex__neg z) = z
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_RDISTRIB]: !z w v. h4/complex/complex__mul (h4/complex/complex__sub z w) v = h4/complex/complex__sub (h4/complex/complex__mul z v) (h4/complex/complex__mul w v)
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_SUB]: !z w. h4/complex/complex__sub (h4/complex/complex__add z w) z = w
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_RID]: !z. h4/complex/complex__add z (h4/complex/complex__of__num h4/num/0) = z
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_SUB]: !z w. h4/complex/complex__sub (h4/complex/complex__sub z w) z = h4/complex/complex__neg w
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_complexs_COMPLEXu_u_NEGu_u_ADD]: !z w. h4/complex/complex__neg (h4/complex/complex__add z w) = h4/complex/complex__add (h4/complex/complex__neg z) (h4/complex/complex__neg w)
% Assm [h4s_complexs_COMPLEXu_u_OFu_u_REALu_u_SUB]: !y x. h4/complex/complex__sub (h4/complex/complex__of__real x) (h4/complex/complex__of__real y) = h4/complex/complex__of__real (h4/real/real__sub x y)
% Assm [h4s_reals_REALu_u_MULu_u_LNEG]: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm [h4s_reals_REALu_u_MULu_u_RNEG]: !y x. h4/realax/real__mul x (h4/realax/real__neg y) = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_LDISTRIB]: !z w v. h4/complex/complex__mul z (h4/complex/complex__sub w v) = h4/complex/complex__sub (h4/complex/complex__mul z w) (h4/complex/complex__mul z v)
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_RINV]: !z. h4/complex/complex__add z (h4/complex/complex__neg z) = h4/complex/complex__of__num h4/num/0
% Assm [h4s_complexs_COMPLEXu_u_ADD2u_u_SUB2]: !z w v u. h4/complex/complex__sub (h4/complex/complex__add z w) (h4/complex/complex__add u v) = h4/complex/complex__add (h4/complex/complex__sub z u) (h4/complex/complex__sub w v)
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_LINV]: !z. h4/complex/complex__add (h4/complex/complex__neg z) z = h4/complex/complex__of__num h4/num/0
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_LNEG]: !z w. h4/complex/complex__sub (h4/complex/complex__neg z) w = h4/complex/complex__neg (h4/complex/complex__add z w)
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_NEG2]: !z w. h4/complex/complex__sub (h4/complex/complex__neg z) (h4/complex/complex__neg w) = h4/complex/complex__sub w z
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_TRIANGLE]: !z w v. h4/complex/complex__add (h4/complex/complex__sub z w) (h4/complex/complex__sub w v) = h4/complex/complex__sub z v
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_0]: !z w. h4/complex/complex__sub z w = h4/complex/complex__of__num h4/num/0 <=> z = w
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_RAT]: !z w v u. ~(w = h4/complex/complex__of__num h4/num/0) /\ ~(v = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__sub (h4/complex/complex__div z w) (h4/complex/complex__div u v) = h4/complex/complex__div (h4/complex/complex__sub (h4/complex/complex__mul z v) (h4/complex/complex__mul w u)) (h4/complex/complex__mul w v)
% Assm [h4s_complexs_COMPLEXu_u_DIVu_u_SUB]: !z w v. h4/complex/complex__sub (h4/complex/complex__div z v) (h4/complex/complex__div w v) = h4/complex/complex__div (h4/complex/complex__sub z w) v
% Assm [h4s_complexs_COMPLEXu_u_EQu_u_SUBu_u_RADD]: !z w v. h4/complex/complex__sub z w = v <=> z = h4/complex/complex__add v w
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_INV2]: !z w. ~(z = h4/complex/complex__of__num h4/num/0) /\ ~(w = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__sub (h4/complex/complex__inv z) (h4/complex/complex__inv w) = h4/complex/complex__div (h4/complex/complex__sub w z) (h4/complex/complex__mul z w)
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_RZERO]: !z. h4/complex/complex__sub z (h4/complex/complex__of__num h4/num/0) = z
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_REFL]: !z. h4/complex/complex__sub z z = h4/complex/complex__of__num h4/num/0
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_ADD2]: !z w. h4/complex/complex__add w (h4/complex/complex__sub z w) = z
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_SUB2]: !z w. h4/complex/complex__sub z (h4/complex/complex__sub z w) = w
% Assm [h4s_complexs_COMPLEXu_u_DIFFSQ]: !z w. h4/complex/complex__mul (h4/complex/complex__add z w) (h4/complex/complex__sub z w) = h4/complex/complex__sub (h4/complex/complex__mul z z) (h4/complex/complex__mul w w)
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_RNEG]: !z w. h4/complex/complex__sub z (h4/complex/complex__neg w) = h4/complex/complex__add z w
% Assm [h4s_complexs_COMPLEXu_u_SUBu_u_LZERO]: !z. h4/complex/complex__sub (h4/complex/complex__of__num h4/num/0) z = h4/complex/complex__neg z
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_SUB2]: !z w. h4/complex/complex__sub z (h4/complex/complex__add z w) = h4/complex/complex__neg w
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_LID]: !z. h4/complex/complex__add (h4/complex/complex__of__num h4/num/0) z = z
% Assm [h4s_complexs_complexu_u_div0]: !z w. h4/complex/complex__div z w = h4/complex/complex__mul z (h4/complex/complex__inv w)
% Assm [h4s_complexs_COMPLEXu_u_EQu_u_RADD]: !z w v. h4/complex/complex__add z v = h4/complex/complex__add w v <=> z = w
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_reals_realu_u_sub0]: !y x. h4/real/real__sub x y = h4/realax/real__add x (h4/realax/real__neg y)
% Assm [h4s_complexs_COMPLEXu_u_OFu_u_REALu_u_NEG]: !x. h4/complex/complex__neg (h4/complex/complex__of__real x) = h4/complex/complex__of__real (h4/realax/real__neg x)
% Assm [h4s_complexs_COMPLEXu_u_OFu_u_REALu_u_ADD]: !y x. h4/complex/complex__add (h4/complex/complex__of__real x) (h4/complex/complex__of__real y) = h4/complex/complex__of__real (h4/realax/real__add x y)
% Assm [h4s_complexs_COMPLEXu_u_NEGu_u_RMUL]: !z w. h4/complex/complex__neg (h4/complex/complex__mul z w) = h4/complex/complex__mul z (h4/complex/complex__neg w)
% Assm [h4s_complexs_COMPLEXu_u_LNEGu_u_UNIQ]: !z w. h4/complex/complex__add z w = h4/complex/complex__of__num h4/num/0 <=> z = h4/complex/complex__neg w
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_complexs_COMPLEXu_u_NEGu_u_0]: h4/complex/complex__neg (h4/complex/complex__of__num h4/num/0) = h4/complex/complex__of__num h4/num/0
% Assm [h4s_complexs_COMPLEXu_u_MULu_u_COMM]: !z w. h4/complex/complex__mul z w = h4/complex/complex__mul w z
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_LDISTRIB]: !z w v. h4/complex/complex__mul z (h4/complex/complex__add w v) = h4/complex/complex__add (h4/complex/complex__mul z w) (h4/complex/complex__mul z v)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_powsers_POWDIFF]: !_0. (!x y n p. happ (happ (happ (happ _0 x) y) n) p = h4/realax/real__mul (h4/real/pow x p) (h4/real/pow y (h4/arithmetic/_2D n p))) ==> (!y x n. h4/real/real__sub (h4/real/pow x (h4/num/SUC n)) (h4/real/pow y (h4/num/SUC n)) = h4/realax/real__mul (h4/real/real__sub x y) (h4/real/sum (h4/pair/_2C h4/num/0 (h4/num/SUC n)) (happ (happ (happ _0 x) y) n)))
% Assm [h4s_complexs_COMPLEXu_u_INVu_u_MUL]: !z w. ~(z = h4/complex/complex__of__num h4/num/0) /\ ~(w = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__inv (h4/complex/complex__mul z w) = h4/complex/complex__mul (h4/complex/complex__inv z) (h4/complex/complex__inv w)
% Assm [h4s_complexs_COMPLEXu_u_MULu_u_LID]: !z. h4/complex/complex__mul (h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) z = z
% Assm [h4s_complexs_COMPLEXu_u_MULu_u_RINV]: !z. ~(z = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__mul z (h4/complex/complex__inv z) = h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_complexs_COMPLEXu_u_MULu_u_RID]: !z. h4/complex/complex__mul z (h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = z
% Assm [h4s_complexs_COMPLEXu_u_MULu_u_LINV]: !z. ~(z = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__mul (h4/complex/complex__inv z) z = h4/complex/complex__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_complexs_COMPLEXu_u_MULu_u_ASSOC]: !z w v. h4/complex/complex__mul z (h4/complex/complex__mul w v) = h4/complex/complex__mul (h4/complex/complex__mul z w) v
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_RAT]: !z w v u. ~(w = h4/complex/complex__of__num h4/num/0) /\ ~(v = h4/complex/complex__of__num h4/num/0) ==> h4/complex/complex__add (h4/complex/complex__div z w) (h4/complex/complex__div u v) = h4/complex/complex__div (h4/complex/complex__add (h4/complex/complex__mul z v) (h4/complex/complex__mul w u)) (h4/complex/complex__mul w v)
% Assm [h4s_complexs_COMPLEXu_u_NEGu_u_LDIV]: !z w. h4/complex/complex__neg (h4/complex/complex__div z w) = h4/complex/complex__div (h4/complex/complex__neg z) w
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_LIDu_u_UNIQ]: !z w. h4/complex/complex__add z w = w <=> z = h4/complex/complex__of__num h4/num/0
% Assm [h4s_complexs_COMPLEXu_u_EQu_u_LADD]: !z w v. h4/complex/complex__add z w = h4/complex/complex__add z v <=> w = v
% Assm [h4s_complexs_COMPLEXu_u_ADDu_u_RDISTRIB]: !z w v. h4/complex/complex__mul (h4/complex/complex__add z w) v = h4/complex/complex__add (h4/complex/complex__mul z v) (h4/complex/complex__mul w v)
% Assm [h4s_powsers_POWDIFFu_u_LEMMA]: !_1. (!x y n p. happ (happ (happ (happ _1 x) y) n) p = h4/realax/real__mul (h4/real/pow x p) (h4/real/pow y (h4/arithmetic/_2D n p))) ==> (!_0. (!x y n p. happ (happ (happ (happ _0 x) y) n) p = h4/realax/real__mul (h4/real/pow x p) (h4/real/pow y (h4/arithmetic/_2D (h4/num/SUC n) p))) ==> (!y x n. h4/real/sum (h4/pair/_2C h4/num/0 (h4/num/SUC n)) (happ (happ (happ _0 x) y) n) = h4/realax/real__mul y (h4/real/sum (h4/pair/_2C h4/num/0 (h4/num/SUC n)) (happ (happ (happ _1 x) y) n))))
% Assm [h4s_reals_sum0u_c1]: !n m f. h4/real/sum (h4/pair/_2C n (h4/num/SUC m)) f = h4/realax/real__add (h4/real/sum (h4/pair/_2C n m) f) (happ f (h4/arithmetic/_2B n m))
% Assm [h4s_reals_sum0u_c0]: !n f. h4/real/sum (h4/pair/_2C n h4/num/0) f = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_pow0u_c0]: !x. h4/real/pow x h4/num/0 = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_pow0u_c1]: !x n. h4/real/pow x (h4/num/SUC n) = h4/realax/real__mul x (h4/real/pow x n)
% Assm [h4s_reals_REALu_u_SUBu_u_LDISTRIB]: !z y x. h4/realax/real__mul x (h4/real/real__sub y z) = h4/real/real__sub (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm [h4s_reals_REALu_u_MULu_u_RID]: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm [h4s_reals_REALu_u_ADDu_u_LIDu_u_UNIQ]: !y x. h4/realax/real__add x y = y <=> x = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_MULu_u_SYM]: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm [h4s_reals_REALu_u_ADDu_u_LID]: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm [h4s_reals_REALu_u_ADDu_u_LINV]: !x. h4/realax/real__add (h4/realax/real__neg x) x = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_ADDu_u_ASSOC]: !z y x. h4/realax/real__add x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__add x y) z
% Assm [h4s_reals_REALu_u_LDISTRIB]: !z y x. h4/realax/real__mul x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm [h4s_reals_REALu_u_ADDu_u_SYM]: !y x. h4/realax/real__add x y = h4/realax/real__add y x
% Assm [h4s_arithmetics_SUBu_u_EQUALu_u_0]: !c. h4/arithmetic/_2D c c = h4/num/0
% Goal: !z l k. h4/complex/complex__scalar__lmul (h4/real/real__sub k l) z = h4/complex/complex__sub (h4/complex/complex__scalar__lmul k z) (h4/complex/complex__scalar__lmul l z)
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_Q1351608,TV_Q1351604]: ![V_f, V_g]: (![V_x]: s(TV_Q1351604,happ(s(t_fun(TV_Q1351608,TV_Q1351604),V_f),s(TV_Q1351608,V_x))) = s(TV_Q1351604,happ(s(t_fun(TV_Q1351608,TV_Q1351604),V_g),s(TV_Q1351608,V_x))) => s(t_fun(TV_Q1351608,TV_Q1351604),V_f) = s(t_fun(TV_Q1351608,TV_Q1351604),V_g))).
fof(ah4s_complexs_complexu_u_scalaru_u_lmul0, axiom, ![V_z, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_complexs_COMPLEXu_u_SCALARu_u_LMUL, axiom, ![V_z, V_l, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_l),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,V_l))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_NEG, axiom, ![V_z, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_k))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_ADD, axiom, ![V_z, V_l, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,V_l))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_l),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))))).
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_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_complexs_IM0, axiom, ![V_z]: s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_realaxs_real,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_RE0, axiom, ![V_z]: s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_realaxs_real,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_complexu_u_sub0, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))).
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_complexs_COMPLEXu_u_NEGu_u_SCALARu_u_LMUL, axiom, ![V_z, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_k))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_complexu_u_neg0, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))))))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_COMM, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_reals_REALu_u_MULu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_z)))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_ADD, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_reals_REALu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_ADDu_u_RDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_z))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_complexs_complexu_u_add0, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))))).
fof(ah4s_complexs_COMPLEXu_u_EQu_u_SUBu_u_LADD, axiom, ![V_z, V_w, V_v]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))).
fof(ah4s_complexs_COMPLEXu_u_NEGu_u_SUB, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_ASSOC, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))).
fof(ah4s_complexs_COMPLEXu_u_NEGNEG, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_RDISTRIB, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_SUB, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_RID, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_SUB, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))).
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_complexs_COMPLEXu_u_NEGu_u_ADD, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))).
fof(ah4s_complexs_COMPLEXu_u_OFu_u_REALu_u_SUB, axiom, ![V_y, V_x]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,V_x))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_MULu_u_LNEG, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_MULu_u_RNEG, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_LDISTRIB, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_RINV, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_complexs_COMPLEXu_u_ADD2u_u_SUB2, axiom, ![V_z, V_w, V_v, V_u]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_u),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_u))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_LINV, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_LNEG, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_NEG2, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_TRIANGLE, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_0, axiom, ![V_z, V_w]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_RAT, axiom, ![V_z, V_w, V_v, V_u]: ((~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_u),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_u))))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))))).
fof(ah4s_complexs_COMPLEXu_u_DIVu_u_SUB, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))).
fof(ah4s_complexs_COMPLEXu_u_EQu_u_SUBu_u_RADD, axiom, ![V_z, V_w, V_v]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_INV2, axiom, ![V_z, V_w]: ((~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_RZERO, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_REFL, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_ADD2, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_SUB2, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)).
fof(ah4s_complexs_COMPLEXu_u_DIFFSQ, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_RNEG, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))).
fof(ah4s_complexs_COMPLEXu_u_SUBu_u_LZERO, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_SUB2, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_LID, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_complexu_u_div0, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))).
fof(ah4s_complexs_COMPLEXu_u_EQu_u_RADD, axiom, ![V_z, V_w, V_v]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_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_NOTu_u_NOT, axiom, ![V_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_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_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_reals_realu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_complexs_COMPLEXu_u_OFu_u_REALu_u_NEG, axiom, ![V_x]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_complexs_COMPLEXu_u_OFu_u_REALu_u_ADD, axiom, ![V_y, V_x]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,V_x))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_complexs_COMPLEXu_u_NEGu_u_RMUL, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))))).
fof(ah4s_complexs_COMPLEXu_u_LNEGu_u_UNIQ, axiom, ![V_z, V_w]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_complexs_COMPLEXu_u_NEGu_u_0, axiom, s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_complexs_COMPLEXu_u_MULu_u_COMM, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_LDISTRIB, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))))).
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_powsers_POWDIFF, axiom, ![V_uu_0]: (![V_x, V_y, V_n, V_p]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)))),V_uu_0),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_p))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_y),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))))) => ![V_y, V_x, V_n]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_y),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)))),V_uu_0),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))),s(t_h4s_nums_num,V_n))))))))).
fof(ah4s_complexs_COMPLEXu_u_INVu_u_MUL, axiom, ![V_z, V_w]: ((~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))))).
fof(ah4s_complexs_COMPLEXu_u_MULu_u_LID, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_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_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_COMPLEXu_u_MULu_u_RINV, axiom, ![V_z]: (~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_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_complexs_COMPLEXu_u_MULu_u_RID, axiom, ![V_z]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_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_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)).
fof(ah4s_complexs_COMPLEXu_u_MULu_u_LINV, axiom, ![V_z]: (~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_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_complexs_COMPLEXu_u_MULu_u_ASSOC, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_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_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_RAT, axiom, ![V_z, V_w, V_v, V_u]: ((~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_u),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_u))))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))))))).
fof(ah4s_complexs_COMPLEXu_u_NEGu_u_LDIV, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_div(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_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_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_LIDu_u_UNIQ, axiom, ![V_z, V_w]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_complexs_COMPLEXu_u_EQu_u_LADD, axiom, ![V_z, V_w, V_v]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))).
fof(ah4s_complexs_COMPLEXu_u_ADDu_u_RDISTRIB, axiom, ![V_z, V_w, V_v]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_add(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v)))))).
fof(ah4s_powsers_POWDIFFu_u_LEMMA, axiom, ![V_uu_1]: (![V_x, V_y, V_n, V_p]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)))),V_uu_1),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_p))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_y),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))))) => ![V_uu_0]: (![V_x, V_y, V_n, V_p]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)))),V_uu_0),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_p))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_y),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))))))) => ![V_y, V_x, V_n]: s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)))),V_uu_0),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))),s(t_h4s_nums_num,V_n))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)))),V_uu_1),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))),s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_reals_sum0u_c1, axiom, ![V_n, V_m, V_f]: s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f),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_reals_sum0u_c0, axiom, ![V_n, V_f]: s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_reals_pow0u_c0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_realaxs_real,h4s_reals_realu_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_reals_pow0u_c1, axiom, ![V_x, V_n]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_reals_REALu_u_SUBu_u_LDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_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_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_ADDu_u_LIDu_u_UNIQ, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,V_y) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_reals_REALu_u_MULu_u_SYM, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_ADDu_u_LID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_ADDu_u_LINV, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_reals_REALu_u_ADDu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_z)))).
fof(ah4s_reals_REALu_u_LDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_ADDu_u_SYM, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_arithmetics_SUBu_u_EQUALu_u_0, axiom, ![V_c]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_c),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ch4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_SUB, conjecture, ![V_z, V_l, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,V_l))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_l),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))))).
