SET007 Axioms: SET007+293.ax


%------------------------------------------------------------------------------
% File     : SET007+293 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Opposite Categories and Contravariant Functors
% 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    : oppcat_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   95 (   0 unit)
%            Number of atoms       :  630 (  83 equality)
%            Maximal formula depth :   17 (   8 average)
%            Number of connectives :  547 (  12 ~  ;   0  |; 243  &)
%                                         (  11 <=>; 281 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   0 propositional; 1-4 arity)
%            Number of functors    :   31 (   1 constant; 0-6 arity)
%            Number of variables   :  293 (   0 singleton; 291 !;   2 ?)
%            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_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v2_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)))
        & l1_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))) ) ) )).

fof(d1_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k2_oppcat_1(A) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)) ) )).

fof(t2_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k2_oppcat_1(k2_oppcat_1(A)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) )).

fof(d2_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k3_oppcat_1(A,B) = B ) ) )).

fof(d3_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => k4_oppcat_1(A,B) = k3_oppcat_1(k2_oppcat_1(A),B) ) ) )).

fof(t3_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k3_oppcat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) = B ) ) )).

fof(t4_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k4_oppcat_1(A,k3_oppcat_1(A,B)) = B ) ) )).

fof(t5_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => k3_oppcat_1(A,k4_oppcat_1(A,B)) = B ) ) )).

fof(d4_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k5_oppcat_1(A,B) = B ) ) )).

fof(d5_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => k6_oppcat_1(A,B) = k5_oppcat_1(k2_oppcat_1(A),B) ) ) )).

fof(t6_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k5_oppcat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = B ) ) )).

fof(t7_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k6_oppcat_1(A,k5_oppcat_1(A,B)) = B ) ) )).

fof(t8_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => k5_oppcat_1(A,k6_oppcat_1(A,B)) = B ) ) )).

fof(t9_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_cat_1(A,B)
            & k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k2_cat_1(A,B) ) ) ) )).

fof(t10_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => ( k2_cat_1(A,k6_oppcat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),B)
            & k3_cat_1(A,k6_oppcat_1(A,B)) = k2_cat_1(k2_oppcat_1(A),B) ) ) ) )).

fof(t11_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k3_oppcat_1(A,k2_cat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B))
            & k3_oppcat_1(A,k3_cat_1(A,B)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) ) ) ) )).

fof(t12_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => ( k4_oppcat_1(A,k2_cat_1(k2_oppcat_1(A),B)) = k3_cat_1(A,k6_oppcat_1(A,B))
            & k4_oppcat_1(A,k3_cat_1(k2_oppcat_1(A),B)) = k2_cat_1(A,k6_oppcat_1(A,B)) ) ) ) )).

fof(t13_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> r2_hidden(k5_oppcat_1(A,D),k6_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))) ) ) ) ) ) )).

fof(t14_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(k2_oppcat_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(k2_oppcat_1(A)))
                 => ( r2_hidden(D,k6_cat_1(k2_oppcat_1(A),B,C))
                  <=> r2_hidden(k6_oppcat_1(A,D),k6_cat_1(A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))) ) ) ) ) ) )).

fof(t15_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => m1_cat_1(k5_oppcat_1(A,D),k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B)) ) ) ) ) ) )).

fof(t16_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(k2_oppcat_1(A)))
             => ! [D] :
                  ( m1_cat_1(D,k2_oppcat_1(A),B,C)
                 => ( k6_cat_1(k2_oppcat_1(A),B,C) != k1_xboole_0
                   => m1_cat_1(k6_oppcat_1(A,D),A,k4_oppcat_1(A,C),k4_oppcat_1(A,B)) ) ) ) ) ) )).

fof(t17_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => k5_oppcat_1(A,k4_cat_1(A,B,C)) = k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) ) ) ) ) )).

fof(t18_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B))
               => k5_oppcat_1(A,k4_cat_1(A,B,C)) = k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) ) ) ) ) )).

fof(t19_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k2_oppcat_1(A)))
             => ( k2_cat_1(k2_oppcat_1(A),C) = k3_cat_1(k2_oppcat_1(A),B)
               => k6_oppcat_1(A,k4_cat_1(k2_oppcat_1(A),B,C)) = k4_cat_1(A,k6_oppcat_1(A,C),k6_oppcat_1(A,B)) ) ) ) ) )).

fof(t20_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,C,D) != k1_xboole_0
                              & k5_oppcat_1(A,k9_cat_1(A,B,C,D,E,F)) != k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,F),k5_oppcat_1(A,E)) ) ) ) ) ) ) ) )).

fof(t21_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k5_oppcat_1(A,k10_cat_1(A,B)) = k10_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) ) ) )).

fof(t22_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => k6_oppcat_1(A,k10_cat_1(k2_oppcat_1(A),B)) = k10_cat_1(A,k4_oppcat_1(A,B)) ) ) )).

fof(t23_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v3_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A))
          <=> v4_cat_1(B,A) ) ) ) )).

fof(t24_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v4_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A))
          <=> v3_cat_1(B,A) ) ) ) )).

fof(t25_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v5_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A))
          <=> v5_cat_1(B,A) ) ) ) )).

fof(t26_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v7_cat_1(B,A)
          <=> v6_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A)) ) ) ) )).

fof(t27_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v7_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A))
          <=> v6_cat_1(B,A) ) ) ) )).

fof(d6_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
                    & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
                 => ( D = k7_oppcat_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u2_cat_1(A))
                       => k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,E) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,k5_oppcat_1(A,E)) ) ) ) ) ) ) )).

fof(t28_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(k2_oppcat_1(A)))
                 => k8_funct_2(u2_cat_1(A),u2_cat_1(B),k7_oppcat_1(A,B,C),k6_oppcat_1(A,D)) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,D) ) ) ) ) )).

fof(t29_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,k2_oppcat_1(A),B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) ) ) ) ) )).

fof(t30_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,k2_oppcat_1(A),B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
                 => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) ) ) ) ) )).

fof(d7_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( m1_oppcat_1(C,A,B)
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_cat_1(B))
                          & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
                        & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                         => ( k2_cat_1(A,E) = k3_cat_1(A,D)
                           => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) ) ) ) )).

fof(t31_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
                       => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) )).

fof(t32_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) )).

fof(t33_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
                    & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) )).

fof(t34_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ( k2_cat_1(A,E) = k3_cat_1(A,D)
                       => k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) )).

fof(t35_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,k2_oppcat_1(A),B)
             => m1_oppcat_1(k7_oppcat_1(A,B,C),A,B) ) ) ) )).

fof(t36_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m1_oppcat_1(D,A,B)
                 => ! [E] :
                      ( m1_oppcat_1(E,B,C)
                     => m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) )).

fof(t37_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,k2_oppcat_1(A),B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) ) ) ) ) )).

fof(t38_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,k2_oppcat_1(A),B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
                 => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) ) ) ) ) )).

fof(t39_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,k2_oppcat_1(A),B)
             => m2_cat_1(k7_oppcat_1(A,B,C),A,B) ) ) ) )).

fof(d8_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
                    & m2_relset_1(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
                 => ( D = k8_oppcat_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u2_cat_1(k2_oppcat_1(A)))
                       => k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),D,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_oppcat_1(A,E)) ) ) ) ) ) ) )).

fof(d9_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)))
                    & m2_relset_1(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) )
                 => ( D = k9_oppcat_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u2_cat_1(A))
                       => k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)),D,E) = k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) )).

fof(t40_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),k8_oppcat_1(A,B,C),k5_oppcat_1(A,D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D) ) ) ) ) )).

fof(t41_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
                 => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)) ) ) ) ) )).

fof(t42_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) ) ) ) ) )).

fof(t43_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) )).

fof(t44_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
                 => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)) ) ) ) ) )).

fof(t45_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) ) ) ) ) )).

fof(t46_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) )).

fof(t47_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k5_oppcat_1(A,D)) = k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) )).

fof(t48_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => k7_oppcat_1(A,B,k8_oppcat_1(A,B,C)) = C ) ) ) )).

fof(t49_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
             => k8_oppcat_1(A,B,k7_oppcat_1(A,B,C)) = C ) ) ) )).

fof(t50_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)) = k8_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)) ) ) ) )).

fof(t51_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v1_cat_1(B)
            & v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => k9_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)) = C ) ) ) )).

fof(t52_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v1_cat_1(B)
            & v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(B),u2_cat_1(A))
                & m2_relset_1(C,u2_cat_1(B),u2_cat_1(A)) )
             => k8_oppcat_1(k2_oppcat_1(B),A,k8_oppcat_1(B,A,C)) = C ) ) ) )).

fof(t53_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
                    & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C))
                        & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) )
                     => k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),u2_cat_1(C),k8_oppcat_1(A,B,D),E) ) ) ) ) ) )).

fof(t54_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
                    & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C))
                        & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) )
                     => k9_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(C)),D,k9_oppcat_1(B,C,E)) ) ) ) ) ) )).

fof(t55_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
                    & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C))
                        & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) )
                     => k9_oppcat_1(k2_oppcat_1(A),C,k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E))) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),u2_cat_1(k2_oppcat_1(C)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,D)),k9_oppcat_1(k2_oppcat_1(B),C,k8_oppcat_1(B,C,E))) ) ) ) ) ) )).

fof(t56_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => m2_cat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B) ) ) ) )).

fof(t57_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => m2_cat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)) ) ) ) )).

fof(t58_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => m1_oppcat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B) ) ) ) )).

fof(t59_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => m1_oppcat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)) ) ) ) )).

fof(t60_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m1_oppcat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) )).

fof(t61_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m1_oppcat_1(E,B,C)
                     => m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) )).

fof(t62_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) )).

fof(t63_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) )).

fof(t64_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => m2_cat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)) ) ) ) )).

fof(t65_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_oppcat_1(C,A,B)
             => m1_oppcat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)) ) ) ) )).

fof(d10_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k10_oppcat_1(A) = k9_oppcat_1(A,A,k15_cat_1(A)) ) )).

fof(d11_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k11_oppcat_1(A) = k8_oppcat_1(A,A,k15_cat_1(A)) ) )).

fof(t66_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(A)),k10_oppcat_1(A),B) = k5_oppcat_1(A,B) ) ) )).

fof(t67_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(A)),k12_cat_1(A,k2_oppcat_1(A),k10_oppcat_1(A)),B) = k3_oppcat_1(A,B) ) ) )).

fof(t68_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),k11_oppcat_1(A),B) = k6_oppcat_1(A,B) ) ) )).

fof(t69_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(A),k12_cat_1(k2_oppcat_1(A),A,k11_oppcat_1(A)),B) = k4_oppcat_1(A,B) ) ) )).

fof(t70_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( k8_oppcat_1(A,B,C) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),u2_cat_1(B),k11_oppcat_1(A),C)
                & k9_oppcat_1(A,B,C) = k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(B)),C,k10_oppcat_1(B)) ) ) ) ) )).

fof(dt_m1_oppcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_oppcat_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
            & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) )).

fof(existence_m1_oppcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m1_oppcat_1(C,A,B) ) )).

fof(dt_k1_oppcat_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k1_oppcat_1(A,B,C,D))
        & m2_relset_1(k1_oppcat_1(A,B,C,D),k2_zfmisc_1(B,A),C) ) ) )).

fof(redefinition_k1_oppcat_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k1_oppcat_1(A,B,C,D) = k2_funct_4(D) ) )).

fof(dt_k2_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_1(k2_oppcat_1(A))
        & v2_cat_1(k2_oppcat_1(A))
        & l1_cat_1(k2_oppcat_1(A)) ) ) )).

fof(dt_k3_oppcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k3_oppcat_1(A,B),u1_cat_1(k2_oppcat_1(A))) ) )).

fof(dt_k4_oppcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) )
     => m1_subset_1(k4_oppcat_1(A,B),u1_cat_1(A)) ) )).

fof(dt_k5_oppcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k5_oppcat_1(A,B),u2_cat_1(k2_oppcat_1(A))) ) )).

fof(dt_k6_oppcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) )
     => m1_subset_1(k6_oppcat_1(A,B),u2_cat_1(A)) ) )).

fof(dt_k7_oppcat_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
        & m1_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
     => ( v1_funct_1(k7_oppcat_1(A,B,C))
        & v1_funct_2(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B))
        & m2_relset_1(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B)) ) ) )).

fof(dt_k8_oppcat_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
        & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
     => ( v1_funct_1(k8_oppcat_1(A,B,C))
        & v1_funct_2(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
        & m2_relset_1(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) ) ) )).

fof(dt_k9_oppcat_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
        & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
     => ( v1_funct_1(k9_oppcat_1(A,B,C))
        & v1_funct_2(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)))
        & m2_relset_1(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) ) ) )).

fof(dt_k10_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m1_oppcat_1(k10_oppcat_1(A),A,k2_oppcat_1(A)) ) )).

fof(dt_k11_oppcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m1_oppcat_1(k11_oppcat_1(A),k2_oppcat_1(A),A) ) )).
%------------------------------------------------------------------------------