SET007 Axioms: SET007+134.ax


%------------------------------------------------------------------------------
% File     : SET007+134 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Calculus of Quantifiers. Deduction Theorem
% 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    : cqc_the2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   96 (   4 unit)
%            Number of atoms       :  463 (  19 equality)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :  397 (  30 ~  ;  14  |;  25  &)
%                                         (  15 <=>; 313 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   1 propositional; 0-3 arity)
%            Number of functors    :   25 (   4 constant; 0-3 arity)
%            Number of variables   :  268 (   0 singleton; 268 !;   0 ?)
%            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(t1_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,C)))
               => v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),C)) ) ) ) ) )).

fof(t2_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,C)))
               => v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(B,A),C)) ) ) ) ) )).

fof(t3_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),C))
               => v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,C))) ) ) ) ) )).

fof(t4_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),C))
               => v2_cqc_the1(k12_cqc_lang(B,k12_cqc_lang(A,C))) ) ) ) ) )).

fof(t5_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_hidden(B,k24_qc_lang1(k14_qc_lang1(C,A)))
              <=> ( r2_hidden(B,k24_qc_lang1(A))
                  & B != C ) ) ) ) ) )).

fof(t6_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_hidden(B,k24_qc_lang1(k5_qc_lang2(C,A)))
              <=> ( r2_hidden(B,k24_qc_lang1(A))
                  & B != C ) ) ) ) ) )).

fof(t7_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_hidden(C,k24_qc_lang1(k2_qc_lang2(A,B)))
              <=> ( r2_hidden(C,k24_qc_lang1(A))
                  | r2_hidden(C,k24_qc_lang1(B)) ) ) ) ) ) )).

fof(t8_cqc_the2,axiom,(
    $true )).

fof(t9_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_hidden(C,k24_qc_lang1(k13_qc_lang1(A,B)))
              <=> ( r2_hidden(C,k24_qc_lang1(A))
                  | r2_hidden(C,k24_qc_lang1(B)) ) ) ) ) ) )).

fof(t10_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_hidden(C,k24_qc_lang1(k3_qc_lang2(A,B)))
              <=> ( r2_hidden(C,k24_qc_lang1(A))
                  | r2_hidden(C,k24_qc_lang1(B)) ) ) ) ) ) )).

fof(t11_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(B,k24_qc_lang1(k6_qc_lang2(B,C,A)))
                & ~ r2_hidden(C,k24_qc_lang1(k6_qc_lang2(B,C,A))) ) ) ) ) )).

fof(t12_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(B,k24_qc_lang1(k7_qc_lang2(B,C,A)))
                & ~ r2_hidden(C,k24_qc_lang1(k7_qc_lang2(B,C,A))) ) ) ) ) )).

fof(t13_cqc_the2,axiom,(
    $true )).

fof(t14_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => k17_cqc_lang(k2_qc_lang2(A,B),C) = k2_qc_lang2(k17_cqc_lang(A,C),k17_cqc_lang(B,C)) ) ) ) )).

fof(t15_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => k17_cqc_lang(k3_qc_lang2(A,B),C) = k3_qc_lang2(k17_cqc_lang(A,C),k17_cqc_lang(B,C)) ) ) ) )).

fof(t16_cqc_the2,axiom,(
    $true )).

fof(t17_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( B != C
               => k17_cqc_lang(k16_cqc_lang(B,A),C) = k5_qc_lang2(B,k17_cqc_lang(A,C)) ) ) ) ) )).

fof(t18_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k12_cqc_lang(A,k16_cqc_lang(B,A))) ) ) )).

fof(t19_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(A)
           => v2_cqc_the1(k16_cqc_lang(B,A)) ) ) ) )).

fof(t20_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k16_cqc_lang(B,A))) ) ) )).

fof(t21_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k16_cqc_lang(C,A))) ) ) ) )).

fof(t22_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k12_cqc_lang(A,B))
               => ( r2_hidden(C,k24_qc_lang1(B))
                  | v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,A),B)) ) ) ) ) ) )).

fof(t23_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( ~ r2_hidden(B,k24_qc_lang1(A))
           => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,A),A)) ) ) ) )).

fof(t24_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(k16_cqc_lang(B,A))
           => ( r2_hidden(B,k24_qc_lang1(A))
              | v2_cqc_the1(A) ) ) ) ) )).

fof(t25_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ( ( A = k17_cqc_lang(C,D)
                          & B = k17_cqc_lang(C,E) )
                       => ( r2_hidden(E,k24_qc_lang1(C))
                          | v2_cqc_the1(k12_cqc_lang(A,k16_cqc_lang(E,B))) ) ) ) ) ) ) ) )).

fof(t26_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(A)
           => v2_cqc_the1(k15_cqc_lang(B,A)) ) ) ) )).

fof(t27_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( ~ r2_hidden(B,k24_qc_lang1(A))
           => v2_cqc_the1(k12_cqc_lang(A,k15_cqc_lang(B,A))) ) ) ) )).

fof(t28_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ( ( A = k17_cqc_lang(C,D)
                          & B = k17_cqc_lang(C,E) )
                       => ( r2_hidden(D,k24_qc_lang1(C))
                          | v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(D,A),B)) ) ) ) ) ) ) ) )).

fof(t29_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(B,k24_qc_lang1(A))
               => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(B,A))) ) ) ) ) )).

fof(t30_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ( ( A = k17_cqc_lang(C,D)
                          & B = k17_cqc_lang(C,E) )
                       => ( r2_hidden(D,k24_qc_lang1(C))
                          | r2_hidden(E,k24_qc_lang1(A))
                          | v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(D,A),k15_cqc_lang(E,B))) ) ) ) ) ) ) ) )).

fof(t31_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(B,k24_qc_lang1(A))
               => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,A),k16_cqc_lang(C,A))) ) ) ) ) )).

fof(t32_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ( ( A = k17_cqc_lang(C,D)
                          & B = k17_cqc_lang(C,E) )
                       => ( r2_hidden(D,k24_qc_lang1(B))
                          | r2_hidden(E,k24_qc_lang1(C))
                          | v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(D,A),k16_cqc_lang(E,B))) ) ) ) ) ) ) ) )).

fof(t33_cqc_the2,axiom,(
    $true )).

fof(t34_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)))) ) ) ) )).

fof(t35_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(A,B)))
               => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))) ) ) ) ) )).

fof(t36_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k14_cqc_lang(A,B)),k14_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)))) ) ) ) )).

fof(t37_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k15_cqc_lang(C,k14_cqc_lang(A,B)))
               => v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))) ) ) ) ) )).

fof(t38_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) )).

fof(t39_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(A,B)))
               => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) )).

fof(t40_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))))
                & v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)),k15_cqc_lang(C,k11_cqc_lang(A,B)))) ) ) ) ) )).

fof(t41_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)))) ) ) ) )).

fof(t42_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k15_cqc_lang(C,k11_cqc_lang(A,B)))
              <=> v2_cqc_the1(k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))) ) ) ) ) )).

fof(t43_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k13_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)),k15_cqc_lang(C,k13_cqc_lang(A,B)))) ) ) ) )).

fof(t44_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k13_cqc_lang(A,B)),k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))))
                & v2_cqc_the1(k12_cqc_lang(k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)),k16_cqc_lang(C,k13_cqc_lang(A,B)))) ) ) ) ) )).

fof(t45_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k14_cqc_lang(k16_cqc_lang(C,k13_cqc_lang(A,B)),k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) )).

fof(t46_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k16_cqc_lang(C,k13_cqc_lang(A,B)))
              <=> v2_cqc_the1(k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) )).

fof(t47_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) )).

fof(t48_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k16_cqc_lang(C,k11_cqc_lang(A,B)))
               => v2_cqc_the1(k11_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) )).

fof(t49_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k15_cqc_lang(B,A)))
            & v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))))) ) ) ) )).

fof(t50_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k15_cqc_lang(B,A))) ) ) )).

fof(t51_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k16_cqc_lang(B,A)))
            & v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,A),k16_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))))) ) ) ) )).

fof(t52_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k14_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k16_cqc_lang(B,A))) ) ) )).

fof(t53_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))),k15_cqc_lang(B,A)))
            & v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))))) ) ) ) )).

fof(t54_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k14_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))),k15_cqc_lang(B,A))) ) ) )).

fof(t55_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k15_cqc_lang(B,A)),k16_cqc_lang(B,k10_cqc_lang(A))))
            & v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A)),k10_cqc_lang(k15_cqc_lang(B,A)))) ) ) ) )).

fof(t56_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k14_cqc_lang(k10_cqc_lang(k15_cqc_lang(B,A)),k16_cqc_lang(B,k10_cqc_lang(A)))) ) ) )).

fof(t57_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,A)),k15_cqc_lang(B,k10_cqc_lang(A))))
            & v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(A)),k10_cqc_lang(k16_cqc_lang(B,A)))) ) ) ) )).

fof(t58_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(A)),k10_cqc_lang(k16_cqc_lang(B,A)))) ) ) )).

fof(t59_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,k15_cqc_lang(C,A)),k15_cqc_lang(C,k15_cqc_lang(B,A))))
                & v2_cqc_the1(k2_qc_lang2(k6_qc_lang2(B,C,A),k6_qc_lang2(C,B,A))) ) ) ) ) )).

fof(t60_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ( ( A = k17_cqc_lang(C,D)
                          & B = k17_cqc_lang(C,E) )
                       => ( r2_hidden(E,k24_qc_lang1(C))
                          | v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(D,k15_cqc_lang(E,B)),k15_cqc_lang(D,A))) ) ) ) ) ) ) ) )).

fof(t61_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k16_cqc_lang(C,A)),k16_cqc_lang(C,k16_cqc_lang(B,A))))
                & v2_cqc_the1(k2_qc_lang2(k7_qc_lang2(B,C,A),k7_qc_lang2(C,B,A))) ) ) ) ) )).

fof(t62_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ( ( A = k17_cqc_lang(C,D)
                          & B = k17_cqc_lang(C,E) )
                       => ( r2_hidden(E,k24_qc_lang1(C))
                          | v2_cqc_the1(k2_qc_lang2(k16_cqc_lang(D,A),k7_qc_lang2(D,E,B))) ) ) ) ) ) ) ) )).

fof(t63_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k15_cqc_lang(C,A)),k15_cqc_lang(C,k16_cqc_lang(B,A)))) ) ) ) )).

fof(t64_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k16_cqc_lang(B,k14_cqc_lang(A,A))) ) ) )).

fof(t65_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B))))
                & v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B)),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) )).

fof(t66_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k14_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) )).

fof(t67_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k16_cqc_lang(C,k12_cqc_lang(A,B)))
              <=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) )).

fof(t68_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(A,k15_cqc_lang(C,B)))) ) ) ) )).

fof(t69_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k15_cqc_lang(C,A),B))) ) ) ) )).

fof(t70_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k11_cqc_lang(A,B)))) ) ) ) ) )).

fof(t71_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_cqc_the1(k11_cqc_lang(A,k15_cqc_lang(C,B)))
               => ( r2_hidden(C,k24_qc_lang1(A))
                  | v2_cqc_the1(k15_cqc_lang(C,k11_cqc_lang(A,B))) ) ) ) ) ) )).

fof(t72_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(k13_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k13_cqc_lang(A,B))))
                  & v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k13_cqc_lang(A,B)),k13_cqc_lang(A,k15_cqc_lang(C,B)))) ) ) ) ) ) )).

fof(t73_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k14_cqc_lang(k13_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k13_cqc_lang(A,B)))) ) ) ) ) )).

fof(t74_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k13_cqc_lang(A,k15_cqc_lang(C,B)))
                <=> v2_cqc_the1(k15_cqc_lang(C,k13_cqc_lang(A,B))) ) ) ) ) ) )).

fof(t75_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k11_cqc_lang(A,B))))
                  & v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(A,k16_cqc_lang(C,B)))) ) ) ) ) ) )).

fof(t76_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k14_cqc_lang(k11_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k11_cqc_lang(A,B)))) ) ) ) ) )).

fof(t77_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k11_cqc_lang(A,k16_cqc_lang(C,B)))
                <=> v2_cqc_the1(k16_cqc_lang(C,k11_cqc_lang(A,B))) ) ) ) ) ) )).

fof(t78_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(A,k15_cqc_lang(C,B))))
                  & v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) ) )).

fof(t79_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k14_cqc_lang(k12_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) )).

fof(t80_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(A,B)))
                <=> v2_cqc_the1(k12_cqc_lang(A,k15_cqc_lang(C,B))) ) ) ) ) ) )).

fof(t81_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(B,A)),k12_cqc_lang(k15_cqc_lang(C,B),A))) ) ) ) ) )).

fof(t82_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k15_cqc_lang(C,A),B),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) )).

fof(t83_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,B),A))
                <=> v2_cqc_the1(k16_cqc_lang(C,k12_cqc_lang(B,A))) ) ) ) ) ) )).

fof(t84_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k16_cqc_lang(C,B),A),k15_cqc_lang(C,k12_cqc_lang(B,A))))
                  & v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(B,A)),k12_cqc_lang(k16_cqc_lang(C,B),A))) ) ) ) ) ) )).

fof(t85_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k14_cqc_lang(k12_cqc_lang(k16_cqc_lang(C,B),A),k15_cqc_lang(C,k12_cqc_lang(B,A)))) ) ) ) ) )).

fof(t86_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,B),A))
                <=> v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(B,A))) ) ) ) ) ) )).

fof(t87_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(A,k16_cqc_lang(C,B)))) ) ) ) ) )).

fof(t88_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) )).

fof(t89_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => v2_cqc_the1(k14_cqc_lang(k12_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) )).

fof(t90_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ~ r2_hidden(C,k24_qc_lang1(A))
               => ( v2_cqc_the1(k12_cqc_lang(A,k16_cqc_lang(C,B)))
                <=> v2_cqc_the1(k16_cqc_lang(C,k12_cqc_lang(A,B))) ) ) ) ) ) )).

fof(t91_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r3_cqc_the1(k6_domain_1(k7_cqc_lang,A),A) ) )).

fof(t92_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => k1_cqc_the1(k4_subset_1(k7_cqc_lang,k6_domain_1(k7_cqc_lang,A),k6_domain_1(k7_cqc_lang,B))) = k1_cqc_the1(k6_domain_1(k7_cqc_lang,k11_cqc_lang(A,B))) ) ) )).

fof(t93_cqc_the2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( r3_cqc_the1(k7_domain_1(k7_cqc_lang,A,B),C)
              <=> r3_cqc_the1(k6_domain_1(k7_cqc_lang,k11_cqc_lang(A,B)),C) ) ) ) ) )).

fof(t94_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r3_cqc_the1(A,B)
               => r3_cqc_the1(A,k15_cqc_lang(C,B)) ) ) ) ) )).

fof(t95_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ( ~ r2_hidden(D,k24_qc_lang1(B))
                   => r3_cqc_the1(A,k12_cqc_lang(k15_cqc_lang(D,k12_cqc_lang(B,C)),k12_cqc_lang(B,k15_cqc_lang(D,C)))) ) ) ) ) ) )).

fof(t96_cqc_the2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( v6_qc_lang1(B)
                  & r3_cqc_the1(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,B)),C) )
               => r3_cqc_the1(A,k12_cqc_lang(B,C)) ) ) ) ) )).
%------------------------------------------------------------------------------