SET007 Axioms: SET007+24.ax


%------------------------------------------------------------------------------
% File     : SET007+24 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Binary Operations Applied to Functions
% 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    : funcop_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  117 (  18 unit)
%            Number of atoms       :  793 ( 108 equality)
%            Maximal formula depth :   17 (   8 average)
%            Number of connectives :  774 (  98 ~  ;   2  |; 366  &)
%                                         (   2 <=>; 306 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   1 propositional; 0-3 arity)
%            Number of functors    :   31 (   1 constant; 0-6 arity)
%            Number of variables   :  395 (   0 singleton; 394 !;   1 ?)
%            Maximal term depth    :    5 (   1 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(fc1_funcop_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) )).

fof(fc2_funcop_1,axiom,(
    ! [A] :
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) )).

fof(fc3_funcop_1,axiom,(
    ! [A,B] :
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) )).

fof(fc4_funcop_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_relat_1(k3_funcop_1(A,B,C))
        & v1_funct_1(k3_funcop_1(A,B,C)) ) ) )).

fof(fc5_funcop_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k4_funcop_1(A,B,C))
        & v1_funct_1(k4_funcop_1(A,B,C)) ) ) )).

fof(fc6_funcop_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_relat_1(k5_funcop_1(A,B,C))
        & v1_funct_1(k5_funcop_1(A,B,C)) ) ) )).

fof(rc1_funcop_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) )).

fof(fc7_funcop_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) )).

fof(fc8_funcop_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(B,A))
        & v1_funct_1(k5_relat_1(B,A))
        & v1_funcop_1(k5_relat_1(B,A)) ) ) )).

fof(fc9_funcop_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) )).

fof(t1_funcop_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( A = k2_zfmisc_1(B,C)
         => ( B = k1_xboole_0
            | C = k1_xboole_0
            | ( k1_relat_1(A) = B
              & k2_relat_1(A) = C ) ) ) ) )).

fof(t2_funcop_1,axiom,(
    ! [A] : k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A)) )).

fof(t3_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( k1_relat_1(A) = k1_relat_1(B)
               => k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B)) ) ) ) ) )).

fof(t4_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_xboole_0
              & k1_relat_1(B) = k1_xboole_0 )
           => A = B ) ) ) )).

fof(d1_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k1_funcop_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => ( ! [D,E] :
                        ( k1_funct_1(A,C) = k4_tarski(D,E)
                       => k1_funct_1(B,C) = k4_tarski(E,D) )
                    & ~ ( k1_funct_1(A,C) != k1_funct_1(B,C)
                        & ! [D,E] : k1_funct_1(A,C) != k4_tarski(D,E) ) ) ) ) ) ) ) )).

fof(t5_funcop_1,axiom,(
    $true )).

fof(t6_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)) ) ) )).

fof(t7_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : k1_funcop_1(k7_relat_1(A,B)) = k7_relat_1(k1_funcop_1(A),B) ) )).

fof(t8_funcop_1,axiom,(
    $true )).

fof(t9_funcop_1,axiom,(
    ! [A] : k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A) )).

fof(t10_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B) ) ) )).

fof(t11_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C)) ) ) )).

fof(d2_funcop_1,axiom,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) )).

fof(t12_funcop_1,axiom,(
    $true )).

fof(t13_funcop_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) )).

fof(t14_funcop_1,axiom,(
    ! [A,B] :
      ( A != k1_xboole_0
     => k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B) ) )).

fof(t15_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( k2_relat_1(A) = k1_tarski(B)
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) )).

fof(t16_funcop_1,axiom,(
    ! [A] :
      ( k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0
      & k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 ) )).

fof(t17_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ! [C] :
              ( r2_hidden(C,k1_relat_1(A))
             => k1_funct_1(A,C) = B )
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) )).

fof(t18_funcop_1,axiom,(
    ! [A,B,C] : k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B) )).

fof(t19_funcop_1,axiom,(
    ! [A,B] :
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) )).

fof(t20_funcop_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(B,C)
     => k10_relat_1(k2_funcop_1(A,B),C) = A ) )).

fof(t21_funcop_1,axiom,(
    ! [A,B] : k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A )).

fof(t22_funcop_1,axiom,(
    ! [A,B,C] :
      ( ~ r2_hidden(B,C)
     => k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0 ) )).

fof(t23_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r2_hidden(C,k1_relat_1(A))
         => k5_relat_1(k2_funcop_1(B,C),A) = k2_funcop_1(B,k1_funct_1(A,C)) ) ) )).

fof(t24_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ~ ( B != k1_xboole_0
            & r2_hidden(C,k1_relat_1(A))
            & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0 ) ) )).

fof(t25_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C) ) )).

fof(t26_funcop_1,axiom,(
    ! [A,B,C] : k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B)) )).

fof(d3_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A) ) ) ) )).

fof(t27_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( k1_relat_1(D) = k1_relat_1(k3_funcop_1(C,A,B))
                      & ! [E] :
                          ( r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B)))
                         => k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) ) )
                   => D = k3_funcop_1(C,A,B) ) ) ) ) ) )).

fof(t28_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B)))
                 => k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) )).

fof(t29_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D,E] :
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( k7_relat_1(A,D) = k7_relat_1(B,D)
                   => k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D) ) ) ) ) ) )).

fof(t30_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D,E] :
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( k7_relat_1(A,D) = k7_relat_1(B,D)
                   => k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D) ) ) ) ) ) )).

fof(t31_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) )).

fof(t32_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C) ) ) ) ) )).

fof(d4_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) ) ) )).

fof(t33_funcop_1,axiom,(
    $true )).

fof(t34_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) ) ) )).

fof(t35_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] :
              ( r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D)))
             => k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D) ) ) ) )).

fof(t36_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ! [E] :
                  ( k7_relat_1(A,C) = k7_relat_1(B,C)
                 => k7_relat_1(k4_funcop_1(D,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C) ) ) ) ) )).

fof(t37_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D) ) ) ) )).

fof(t38_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D) ) ) ) )).

fof(t39_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D) ) ) )).

fof(d5_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) ) ) )).

fof(t40_funcop_1,axiom,(
    $true )).

fof(t41_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) ) ) )).

fof(t42_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] :
              ( r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A)))
             => k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)) ) ) ) )).

fof(t43_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ! [E] :
                  ( k7_relat_1(A,C) = k7_relat_1(B,C)
                 => k7_relat_1(k5_funcop_1(D,E,A),C) = k7_relat_1(k5_funcop_1(D,E,B),C) ) ) ) ) )).

fof(t44_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A)) ) ) ) )).

fof(t45_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B) ) ) ) )).

fof(t46_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B)) ) ) )).

fof(t47_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( v1_funct_1(k3_funcop_1(C,D,E))
                        & v1_funct_2(k3_funcop_1(C,D,E),A,B)
                        & m2_relset_1(k3_funcop_1(C,D,E),A,B) ) ) ) ) ) ) )).

fof(t48_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) )).

fof(t49_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ! [G] :
                                ( m1_subset_1(G,A)
                               => k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) )
                           => F = k6_funcop_1(B,A,C,D,E) ) ) ) ) ) ) ) )).

fof(t50_funcop_1,axiom,(
    $true )).

fof(t51_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,B)
                        & m2_relset_1(E,B,B) )
                     => k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)) ) ) ) ) ) )).

fof(t52_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,B)
                        & m2_relset_1(E,B,B) )
                     => k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))) = k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) ) ) ) ) ) )).

fof(t53_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D) ) ) ) ) )).

fof(t54_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) ) ) ) ) )).

fof(t55_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) ) ) ) ) )).

fof(t56_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) )).

fof(t57_funcop_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(C,B)
     => ( v1_funct_1(k2_funcop_1(A,C))
        & v1_funct_2(k2_funcop_1(A,C),A,B)
        & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) )).

fof(t58_funcop_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,B)
         => ( v1_funct_1(k2_funcop_1(A,C))
            & v1_funct_2(k2_funcop_1(A,C),A,B)
            & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ) )).

fof(t59_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( v1_funct_1(k4_funcop_1(C,D,E))
                        & v1_funct_2(k4_funcop_1(C,D,E),A,B)
                        & m2_relset_1(k4_funcop_1(C,D,E),A,B) ) ) ) ) ) ) )).

fof(t60_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) ) ) ) ) ) ) )).

fof(t61_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ( ! [G] :
                                ( m1_subset_1(G,B)
                               => k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) )
                           => D = k7_funcop_1(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(t62_funcop_1,axiom,(
    $true )).

fof(t63_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) )).

fof(t64_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) )).

fof(t65_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( v1_funct_1(k5_funcop_1(C,E,D))
                        & v1_funct_2(k5_funcop_1(C,E,D),A,B)
                        & m2_relset_1(k5_funcop_1(C,E,D),A,B) ) ) ) ) ) ) )).

fof(t66_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) ) ) ) ) ) ) )).

fof(t67_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ( ! [G] :
                                ( m1_subset_1(G,B)
                               => k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) )
                           => D = k8_funcop_1(A,B,C,F,E) ) ) ) ) ) ) ) )).

fof(t68_funcop_1,axiom,(
    $true )).

fof(t69_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D) ) ) ) ) ) )).

fof(t70_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) )).

fof(t71_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))) ) ) ) ) ) )).

fof(t72_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => m2_relset_1(k2_relat_1(D),B,C) ) ) ) ) )).

fof(t73_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)) ) ) ) ) )).

fof(t74_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F)) ) ) ) ) ) ) ) )).

fof(t75_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) ) ) ) ) ) ) ) )).

fof(t76_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( v2_binop_1(C,B)
                           => k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) ) ) ) ) ) ) ) )).

fof(t77_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D) = k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) ) ) ) ) ) ) ) )).

fof(t78_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F)) = k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) ) ) ) ) ) ) ) )).

fof(t79_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( v1_binop_1(C,B)
                       => k8_funcop_1(B,A,C,E,D) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) ) )).

fof(t80_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( v1_binop_1(C,B)
                       => k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D) ) ) ) ) ) ) )).

fof(t81_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( v3_binop_1(C,B)
                   => k6_funcop_1(B,A,C,D,D) = D ) ) ) ) ) )).

fof(t82_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( v3_binop_1(C,A)
                       => k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) )).

fof(t83_funcop_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( v3_binop_1(C,A)
                       => k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) )).

fof(t84_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A))
               => k1_relat_1(k3_funcop_1(A,B,C)) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) ) ) ) ) )).

fof(d6_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funcop_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) )).

fof(dt_k1_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_funcop_1(A))
        & v1_funct_1(k1_funcop_1(A)) ) ) )).

fof(involutiveness_k1_funcop_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_funcop_1(k1_funcop_1(A)) = A ) )).

fof(dt_k2_funcop_1,axiom,(
    $true )).

fof(dt_k3_funcop_1,axiom,(
    $true )).

fof(dt_k4_funcop_1,axiom,(
    $true )).

fof(dt_k5_funcop_1,axiom,(
    $true )).

fof(dt_k6_funcop_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => ( v1_funct_1(k6_funcop_1(A,B,C,D,E))
        & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) ) ) )).

fof(redefinition_k6_funcop_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E) ) )).

fof(dt_k7_funcop_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k7_funcop_1(A,B,C,D,E))
        & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) ) ) )).

fof(redefinition_k7_funcop_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m1_subset_1(E,A) )
     => k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E) ) )).

fof(dt_k8_funcop_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => ( v1_funct_1(k8_funcop_1(A,B,C,D,E))
        & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) ) ) )).

fof(redefinition_k8_funcop_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E) ) )).

fof(dt_k9_funcop_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(B,C))
        & m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
     => m2_relset_1(k9_funcop_1(A,B,C,D),B,C) ) )).

fof(redefinition_k9_funcop_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(B,C))
        & m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
     => k9_funcop_1(A,B,C,D) = k2_relat_1(D) ) )).

fof(dt_k10_funcop_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(B,C))
        & m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
     => ( v1_funct_1(k10_funcop_1(A,B,C,D))
        & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B))
        & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) ) ) )).

fof(involutiveness_k10_funcop_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(B,C))
        & m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
     => k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)) = D ) )).

fof(redefinition_k10_funcop_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(B,C))
        & m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
     => k10_funcop_1(A,B,C,D) = k1_funcop_1(D) ) )).
%------------------------------------------------------------------------------