SET007 Axioms: SET007+42.ax


%------------------------------------------------------------------------------
% File     : SET007+42 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Complex Numbers - Basic Theorems
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : xcmplx_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  237 (   2 unit)
%            Number of atoms       :  934 ( 352 equality)
%            Maximal formula depth :   13 (   7 average)
%            Number of connectives :  779 (  82 ~  ;  18  |;  30  &)
%                                         (   0 <=>; 649 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    3 (   1 propositional; 0-2 arity)
%            Number of functors    :   11 (   5 constant; 0-2 arity)
%            Number of variables   :  581 (   0 singleton; 581 !;   0 ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).

fof(t2_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B)
               => A = C ) ) ) ) )).

fof(t3_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A = k2_xcmplx_0(A,B)
           => B = np__0 ) ) ) )).

fof(t4_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).

fof(t5_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k3_xcmplx_0(B,A) = k3_xcmplx_0(C,A)
               => ( A = np__0
                  | B = C ) ) ) ) ) )).

fof(t6_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( k3_xcmplx_0(A,B) = np__0
              & A != np__0
              & B != np__0 ) ) ) )).

fof(t7_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k3_xcmplx_0(B,A) = A
           => ( A = np__0
              | B = np__1 ) ) ) ) )).

fof(t8_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) )).

fof(t9_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) )).

fof(t10_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) )).

fof(t11_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(np__2,A) = k2_xcmplx_0(A,A) ) )).

fof(t12_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(np__3,A) = k2_xcmplx_0(k2_xcmplx_0(A,A),A) ) )).

fof(t13_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(np__4,A) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A) ) )).

fof(t14_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,A) = np__0 ) )).

fof(t15_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k6_xcmplx_0(A,B) = np__0
           => A = B ) ) ) )).

fof(t16_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k6_xcmplx_0(A,B) = A
           => B = np__0 ) ) ) )).

fof(t17_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k6_xcmplx_0(A,k6_xcmplx_0(B,B)) ) ) )).

fof(t18_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k6_xcmplx_0(A,k6_xcmplx_0(A,B)) = B ) ) )).

fof(t19_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,B)
               => A = C ) ) ) ) )).

fof(t20_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k6_xcmplx_0(A,B) = k6_xcmplx_0(A,C)
               => B = C ) ) ) ) )).

fof(t21_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) )).

fof(t22_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,B) = k6_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) )).

fof(t23_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)) = k6_xcmplx_0(C,B) ) ) ) )).

fof(t24_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D)
                   => k6_xcmplx_0(A,C) = k6_xcmplx_0(B,D) ) ) ) ) ) )).

fof(t25_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k2_xcmplx_0(A,k6_xcmplx_0(B,B)) ) ) )).

fof(t26_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k6_xcmplx_0(k2_xcmplx_0(A,B),B) ) ) )).

fof(t27_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k2_xcmplx_0(k6_xcmplx_0(A,B),B) ) ) )).

fof(t28_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(A,B) = k2_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) )).

fof(t29_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) )).

fof(t30_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(C,B),A) ) ) ) )).

fof(t31_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(A,B) = k6_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(C,B)) ) ) ) )).

fof(t32_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,B) = k6_xcmplx_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) )).

fof(t33_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D)
                   => k6_xcmplx_0(A,C) = k6_xcmplx_0(D,B) ) ) ) ) ) )).

fof(t34_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D)
                   => k2_xcmplx_0(A,D) = k2_xcmplx_0(B,C) ) ) ) ) ) )).

fof(t35_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k2_xcmplx_0(A,B) = k6_xcmplx_0(C,D)
                   => k2_xcmplx_0(A,D) = k6_xcmplx_0(C,B) ) ) ) ) ) )).

fof(t36_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,k2_xcmplx_0(B,C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).

fof(t37_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).

fof(t38_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(A,k6_xcmplx_0(C,B)) ) ) ) )).

fof(t39_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,B) = k2_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(C,B)) ) ) ) )).

fof(t40_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k6_xcmplx_0(B,C)) = k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) )).

fof(t41_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) ) ) ) ) )).

fof(t42_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) )).

fof(t43_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) )).

fof(t44_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) )).

fof(t45_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) )).

fof(t46_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) )).

fof(t47_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) )).

fof(t48_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k7_xcmplx_0(A,C),B) ) ) ) )).

fof(t49_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,np__0) = np__0 ) )).

fof(t50_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k7_xcmplx_0(A,B) = np__0 ) ) ) )).

fof(t51_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k7_xcmplx_0(B,k7_xcmplx_0(A,A)) ) ) ) )).

fof(t52_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => k7_xcmplx_0(A,k7_xcmplx_0(A,B)) = B ) ) ) )).

fof(t53_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k7_xcmplx_0(B,A) = k7_xcmplx_0(C,A)
               => ( A = np__0
                  | B = C ) ) ) ) ) )).

fof(t54_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(A,B) != np__0
           => B = k7_xcmplx_0(A,k7_xcmplx_0(A,B)) ) ) ) )).

fof(t55_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k7_xcmplx_0(B,C) = k7_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) ) ) ) ) )).

fof(t56_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(np__1,k7_xcmplx_0(np__1,A)) = A ) )).

fof(t57_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(np__1,k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) )).

fof(t58_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(A,B) = np__1
           => A = B ) ) ) )).

fof(t59_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(np__1,A) = k7_xcmplx_0(np__1,B)
           => A = B ) ) ) )).

fof(t60_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( A != np__0
       => k7_xcmplx_0(A,A) = np__1 ) ) )).

fof(t61_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(A,B) = A
           => ( A = np__0
              | B = np__1 ) ) ) ) )).

fof(t62_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,np__0) = np__0 ) )).

fof(t63_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)) = k7_xcmplx_0(k2_xcmplx_0(A,C),B) ) ) ) )).

fof(t64_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) )).

fof(t65_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(k2_xcmplx_0(A,A),np__2) = A ) )).

fof(t66_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(k7_xcmplx_0(A,np__2),k7_xcmplx_0(A,np__2)) = A ) )).

fof(t67_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A = k7_xcmplx_0(k2_xcmplx_0(A,B),np__2)
           => A = B ) ) ) )).

fof(t68_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),np__3) = A ) )).

fof(t69_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__3),k7_xcmplx_0(A,np__3)),k7_xcmplx_0(A,np__3)) = A ) )).

fof(t70_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),np__4) = A ) )).

fof(t71_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)) = A ) )).

fof(t72_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)) = k7_xcmplx_0(A,np__2) ) )).

fof(t73_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(k2_xcmplx_0(A,A),np__4) = k7_xcmplx_0(A,np__2) ) )).

fof(t74_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k3_xcmplx_0(A,B) = np__1
           => A = k7_xcmplx_0(np__1,B) ) ) ) )).

fof(t75_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).

fof(t76_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(C,B),A) ) ) ) )).

fof(t77_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) )).

fof(t78_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,C),B) ) ) ) )).

fof(t79_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(A,k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C) ) ) ) )).

fof(t80_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(A,k7_xcmplx_0(C,B)) ) ) ) )).

fof(t81_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(C,B),A) ) ) ) )).

fof(t82_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(C,k7_xcmplx_0(A,B)) ) ) ) )).

fof(t83_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(A,B),C) ) ) ) )).

fof(t84_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k7_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,C),B),D) ) ) ) ) )).

fof(t85_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k7_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)) ) ) ) ) )).

fof(t86_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k3_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(C,B)) ) ) ) ) )).

fof(t87_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ! [E] :
                      ( v1_xcmplx_0(E)
                     => k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))) = k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) ) ) ) ) ) )).

fof(t88_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => k3_xcmplx_0(k7_xcmplx_0(B,A),A) = B ) ) ) )).

fof(t89_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k3_xcmplx_0(B,k7_xcmplx_0(A,A)) ) ) ) )).

fof(t90_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k7_xcmplx_0(k3_xcmplx_0(B,A),A) ) ) ) )).

fof(t91_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k3_xcmplx_0(B,C) = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(C,A)) ) ) ) ) )).

fof(t92_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k7_xcmplx_0(B,C) = k7_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) ) ) ) ) )).

fof(t93_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k7_xcmplx_0(B,C) = k3_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(C,A)),A) ) ) ) ) )).

fof(t94_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k3_xcmplx_0(B,C) = k7_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(A,C)) ) ) ) ) )).

fof(t95_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B)
                   => ( A = np__0
                      | B = np__0
                      | k7_xcmplx_0(C,B) = k7_xcmplx_0(D,A) ) ) ) ) ) ) )).

fof(t96_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k7_xcmplx_0(C,B) = k7_xcmplx_0(D,A)
                   => ( A = np__0
                      | B = np__0
                      | k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B) ) ) ) ) ) ) )).

fof(t97_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k3_xcmplx_0(C,A) = k7_xcmplx_0(D,B)
                   => ( A = np__0
                      | B = np__0
                      | k3_xcmplx_0(C,B) = k7_xcmplx_0(D,A) ) ) ) ) ) ) )).

fof(t98_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k7_xcmplx_0(B,C) = k3_xcmplx_0(A,k7_xcmplx_0(k7_xcmplx_0(B,A),C)) ) ) ) ) )).

fof(t99_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k7_xcmplx_0(B,C) = k3_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(A,C)) ) ) ) ) )).

fof(t100_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(A,k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(A,B) ) ) )).

fof(t101_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(A,k7_xcmplx_0(np__1,B)) = k3_xcmplx_0(A,B) ) ) )).

fof(t102_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(np__1,B),C),A) ) ) ) )).

fof(t103_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) ) ) )).

fof(t104_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(C,A)) ) ) ) )).

fof(t105_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(A,C)) ) ) ) )).

fof(t106_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,C),k7_xcmplx_0(A,B)) ) ) ) )).

fof(t107_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( A != np__0
       => k3_xcmplx_0(A,k7_xcmplx_0(np__1,A)) = np__1 ) ) )).

fof(t108_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(np__1,A)) ) ) ) )).

fof(t109_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k3_xcmplx_0(B,k3_xcmplx_0(k7_xcmplx_0(np__1,A),A)) ) ) ) )).

fof(t110_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k3_xcmplx_0(k3_xcmplx_0(B,k7_xcmplx_0(np__1,A)),A) ) ) ) )).

fof(t111_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k7_xcmplx_0(B,k3_xcmplx_0(A,k7_xcmplx_0(np__1,A))) ) ) ) )).

fof(t112_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) = np__0 ) ) ) )).

fof(t113_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A)) != np__1 ) ) ) )).

fof(t114_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k2_xcmplx_0(k7_xcmplx_0(B,A),C) = k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(A,C)),A) ) ) ) ) )).

fof(t115_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k2_xcmplx_0(B,C) = k3_xcmplx_0(A,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) ) ) ) ) )).

fof(t116_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k2_xcmplx_0(B,C) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) ) ) ) ) )).

fof(t117_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ~ ( A != np__0
                      & B != np__0
                      & k2_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) ) ) ) ) ) )).

fof(t118_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => k2_xcmplx_0(A,B) = k3_xcmplx_0(A,k2_xcmplx_0(np__1,k7_xcmplx_0(B,A))) ) ) ) )).

fof(t119_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__2,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__2,B))) = k7_xcmplx_0(A,B) ) ) )).

fof(t120_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__3,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))) = k7_xcmplx_0(A,B) ) ) )).

fof(t121_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)) = k7_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) )).

fof(t122_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,k7_xcmplx_0(A,np__2)) = k7_xcmplx_0(A,np__2) ) )).

fof(t123_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) )).

fof(t124_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B)
                   => ( A = np__0
                      | B = np__0
                      | A = B
                      | k7_xcmplx_0(C,A) = k7_xcmplx_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B)) ) ) ) ) ) ) )).

fof(t125_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) )).

fof(t126_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) )).

fof(t127_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k6_xcmplx_0(k7_xcmplx_0(B,A),C) = k7_xcmplx_0(k6_xcmplx_0(B,k3_xcmplx_0(C,A)),A) ) ) ) ) )).

fof(t128_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k6_xcmplx_0(B,k7_xcmplx_0(C,A)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),C),A) ) ) ) ) )).

fof(t129_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k6_xcmplx_0(B,C) = k3_xcmplx_0(A,k6_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) ) ) ) ) )).

fof(t130_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k6_xcmplx_0(B,C) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) ) ) ) ) )).

fof(t131_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ~ ( A != np__0
                      & B != np__0
                      & k6_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) ) ) ) ) ) )).

fof(t132_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => k6_xcmplx_0(A,B) = k3_xcmplx_0(A,k6_xcmplx_0(np__1,k7_xcmplx_0(B,A))) ) ) ) )).

fof(t133_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => B = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,B),C),C),A) ) ) ) ) )).

fof(t134_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k4_xcmplx_0(A) = k4_xcmplx_0(B)
           => A = B ) ) ) )).

fof(t135_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( k4_xcmplx_0(A) = np__0
       => A = np__0 ) ) )).

fof(t136_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k2_xcmplx_0(A,k4_xcmplx_0(B)) = np__0
           => A = B ) ) ) )).

fof(t137_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)) ) ) )).

fof(t138_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k2_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) ) ) )).

fof(t139_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B) ) ) )).

fof(t140_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) )).

fof(t141_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).

fof(t142_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k2_xcmplx_0(A,B) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B))) ) ) )).

fof(t143_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k6_xcmplx_0(A,B)) = k6_xcmplx_0(B,A) ) ) )).

fof(t144_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k6_xcmplx_0(k4_xcmplx_0(A),B) = k6_xcmplx_0(k4_xcmplx_0(B),A) ) ) )).

fof(t145_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k6_xcmplx_0(k4_xcmplx_0(B),k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) )).

fof(t146_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),C),B) ) ) ) )).

fof(t147_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A) ) ) ) )).

fof(t148_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) ) ) ) )).

fof(t149_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)) = k4_xcmplx_0(k6_xcmplx_0(B,C)) ) ) ) )).

fof(t150_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(np__0,A) = k4_xcmplx_0(A) ) )).

fof(t151_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k2_xcmplx_0(A,B) = k6_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).

fof(t152_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => A = k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) ) ) )).

fof(t153_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k6_xcmplx_0(A,B) = k2_xcmplx_0(C,k4_xcmplx_0(B))
               => A = C ) ) ) ) )).

fof(t154_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(C))
               => B = C ) ) ) ) )).

fof(t155_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) ) ) ) )).

fof(t156_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),C),A) ) ) ) )).

fof(t157_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(A,k6_xcmplx_0(k4_xcmplx_0(B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).

fof(t158_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A) ) ) ) )).

fof(t159_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) ) ) ) )).

fof(t160_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) ) ) ) )).

fof(t161_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k2_xcmplx_0(A,B)) = k6_xcmplx_0(k4_xcmplx_0(B),A) ) ) )).

fof(t162_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),B) ) ) )).

fof(t163_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k6_xcmplx_0(A,B) ) ) )).

fof(t164_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k2_xcmplx_0(A,B) = k4_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) )).

fof(t165_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),B),A) ) ) ) )).

fof(t166_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),A),B) ) ) ) )).

fof(t167_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) )).

fof(t168_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C)) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) )).

fof(t169_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C)) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) )).

fof(t170_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C)) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) )).

fof(t171_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).

fof(t172_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).

fof(t173_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).

fof(t174_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).

fof(t175_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).

fof(t176_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k4_xcmplx_0(A),B) = k3_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).

fof(t177_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k3_xcmplx_0(A,B) ) ) )).

fof(t178_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(B))) = k3_xcmplx_0(A,B) ) ) )).

fof(t179_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(A),B)) = k3_xcmplx_0(A,B) ) ) )).

fof(t180_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(k4_xcmplx_0(np__1),A) = k4_xcmplx_0(A) ) )).

fof(t181_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)) = A ) )).

fof(t182_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k3_xcmplx_0(B,A) = k4_xcmplx_0(A)
           => ( A = np__0
              | B = k4_xcmplx_0(np__1) ) ) ) ) )).

fof(t183_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ~ ( k3_xcmplx_0(A,A) = np__1
          & A != np__1
          & A != k4_xcmplx_0(np__1) ) ) )).

fof(t184_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(k4_xcmplx_0(A),k3_xcmplx_0(np__2,A)) = A ) )).

fof(t185_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k6_xcmplx_0(A,B),C) = k3_xcmplx_0(k6_xcmplx_0(B,A),k4_xcmplx_0(C)) ) ) ) )).

fof(t186_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,A),C)) ) ) ) )).

fof(t187_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,k3_xcmplx_0(np__2,A)) = k4_xcmplx_0(A) ) )).

fof(t188_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k4_xcmplx_0(A),B) ) ) )).

fof(t189_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(A,k4_xcmplx_0(B)) = k4_xcmplx_0(k7_xcmplx_0(A,B)) ) ) )).

fof(t190_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k7_xcmplx_0(A,k4_xcmplx_0(B))) = k7_xcmplx_0(A,B) ) ) )).

fof(t191_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(A),B)) = k7_xcmplx_0(A,B) ) ) )).

fof(t192_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k7_xcmplx_0(A,B) ) ) )).

fof(t193_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(k4_xcmplx_0(A),B) = k7_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).

fof(t194_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(A) = k7_xcmplx_0(A,k4_xcmplx_0(np__1)) ) )).

fof(t195_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => A = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)) ) )).

fof(t196_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(A,B) = k4_xcmplx_0(np__1)
           => ( A = k4_xcmplx_0(B)
              & B = k4_xcmplx_0(A) ) ) ) ) )).

fof(t197_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(A,B) = k4_xcmplx_0(A)
           => ( A = np__0
              | B = k4_xcmplx_0(np__1) ) ) ) ) )).

fof(t198_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( A != np__0
       => k7_xcmplx_0(k4_xcmplx_0(A),A) = k4_xcmplx_0(np__1) ) ) )).

fof(t199_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( A != np__0
       => k7_xcmplx_0(A,k4_xcmplx_0(A)) = k4_xcmplx_0(np__1) ) ) )).

fof(t200_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ~ ( A != np__0
          & A = k7_xcmplx_0(np__1,A)
          & A != np__1
          & A != k4_xcmplx_0(np__1) ) ) )).

fof(t201_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B)
                   => ( A = np__0
                      | B = np__0
                      | A = k4_xcmplx_0(B)
                      | k7_xcmplx_0(C,A) = k7_xcmplx_0(k2_xcmplx_0(C,D),k2_xcmplx_0(A,B)) ) ) ) ) ) ) )).

fof(t202_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k5_xcmplx_0(A) = k5_xcmplx_0(B)
           => A = B ) ) ) )).

fof(t203_xcmplx_1,axiom,(
    k5_xcmplx_0(np__0) = np__0 )).

fof(t204_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( A != np__0
           => B = k3_xcmplx_0(k3_xcmplx_0(B,A),k5_xcmplx_0(A)) ) ) ) )).

fof(t205_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).

fof(t206_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))) = k3_xcmplx_0(k5_xcmplx_0(A),B) ) ) )).

fof(t207_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))) = k3_xcmplx_0(A,B) ) ) )).

fof(t208_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__0 ) ) ) )).

fof(t209_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = np__0 ) ) ) )).

fof(t210_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__1
           => A = B ) ) ) )).

fof(t211_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k3_xcmplx_0(A,B) = np__1
           => A = k5_xcmplx_0(B) ) ) ) )).

fof(t212_xcmplx_1,axiom,(
    $true )).

fof(t213_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k2_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k2_xcmplx_0(A,B),k5_xcmplx_0(k3_xcmplx_0(A,B))) ) ) ) )).

fof(t214_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( A != np__0
              & B != np__0
              & k6_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k6_xcmplx_0(B,A),k5_xcmplx_0(k3_xcmplx_0(A,B))) ) ) ) )).

fof(t215_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k5_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) )).

fof(t216_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k7_xcmplx_0(B,A) ) ) )).

fof(t217_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(np__1,A) = k5_xcmplx_0(A) ) )).

fof(t218_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(np__1,k5_xcmplx_0(A)) = A ) )).

fof(t219_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k5_xcmplx_0(k7_xcmplx_0(np__1,A)) = A ) )).

fof(t220_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ( k7_xcmplx_0(np__1,A) = k5_xcmplx_0(B)
           => A = B ) ) ) )).

fof(t221_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(A,k5_xcmplx_0(B)) = k3_xcmplx_0(A,B) ) ) )).

fof(t222_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(A,C)) ) ) ) )).

fof(t223_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(k5_xcmplx_0(A),B) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).

fof(t224_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)) ) )).

fof(t225_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ~ ( A != np__0
          & A = k5_xcmplx_0(A)
          & A != np__1
          & A != k4_xcmplx_0(np__1) ) ) )).

fof(t226_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C) ) ) ) )).

fof(t227_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C) ) ) ) )).

fof(t228_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C) ) ) ) )).

fof(t229_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C) ) ) ) )).

fof(t230_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k6_xcmplx_0(k6_xcmplx_0(A,A),B) = k4_xcmplx_0(B) ) ) )).

fof(t231_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),A),B) = k4_xcmplx_0(B) ) ) )).

fof(t232_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k6_xcmplx_0(k6_xcmplx_0(A,B),A) = k4_xcmplx_0(B) ) ) )).

fof(t233_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),A) = k4_xcmplx_0(B) ) ) )).

fof(t234_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ~ ( B != np__0
              & ! [C] :
                  ( v1_xcmplx_0(C)
                 => A != k7_xcmplx_0(B,C) ) ) ) ) )).

fof(t235_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ! [E] :
                      ( v1_xcmplx_0(E)
                     => k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))) = k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) ) ) ) ) ) )).

fof(t236_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(A,B),C),D),B) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,k7_xcmplx_0(D,C)),B),k3_xcmplx_0(k7_xcmplx_0(D,C),A)) ) ) ) ) )).

fof(t237_xcmplx_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( A != np__0
               => k2_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k2_xcmplx_0(B,k7_xcmplx_0(C,A))) ) ) ) ) )).
%------------------------------------------------------------------------------