SET007 Axioms: SET007+116.ax


%------------------------------------------------------------------------------
% File     : SET007+116 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Propositional Calculus
% 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    : lukasi_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   93 (   0 unit)
%            Number of atoms       :  391 (   0 equality)
%            Maximal formula depth :   11 (   7 average)
%            Number of connectives :  298 (   0 ~  ;   0  |;  19  &)
%                                         (  12 <=>; 267 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    5 (   0 propositional; 1-3 arity)
%            Number of functors    :    7 (   4 constant; 0-2 arity)
%            Number of variables   :  226 (   0 singleton; 226 !;   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_lukasi_1,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)
             => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C))),k4_cqc_the1) ) ) ) )).

fof(t2_lukasi_1,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)
             => ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
               => r2_hidden(k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C)),k4_cqc_the1) ) ) ) ) )).

fof(t3_lukasi_1,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)
             => ( ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
                  & r2_hidden(k12_cqc_lang(B,C),k4_cqc_the1) )
               => r2_hidden(k12_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) )).

fof(t4_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(A,A),k4_cqc_the1) ) )).

fof(t5_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t6_lukasi_1,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)
             => r2_hidden(k12_cqc_lang(k12_cqc_lang(k12_cqc_lang(A,B),C),k12_cqc_lang(B,C)),k4_cqc_the1) ) ) ) )).

fof(t7_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(A,k12_cqc_lang(k12_cqc_lang(A,B),B)),k4_cqc_the1) ) ) )).

fof(t8_lukasi_1,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)
             => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(B,k12_cqc_lang(A,C))),k4_cqc_the1) ) ) ) )).

fof(t9_lukasi_1,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)
             => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(C,A),k12_cqc_lang(C,B))),k4_cqc_the1) ) ) ) )).

fof(t10_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(A,B)),k12_cqc_lang(A,B)),k4_cqc_the1) ) ) )).

fof(t11_lukasi_1,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)
             => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C))),k4_cqc_the1) ) ) ) )).

fof(t12_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(k10_cqc_lang(k9_cqc_lang),A),k4_cqc_the1) ) )).

fof(t13_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(A,k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(B,A),k4_cqc_the1) ) ) ) )).

fof(t14_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(A,k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),B),k4_cqc_the1) ) ) ) )).

fof(t15_lukasi_1,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)
             => ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
               => r2_hidden(k12_cqc_lang(B,k12_cqc_lang(A,C)),k4_cqc_the1) ) ) ) ) )).

fof(t16_lukasi_1,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)
             => ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
                  & r2_hidden(B,k4_cqc_the1) )
               => r2_hidden(k12_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) )).

fof(t17_lukasi_1,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)
             => ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
                  & r2_hidden(B,k4_cqc_the1)
                  & r2_hidden(A,k4_cqc_the1) )
               => r2_hidden(C,k4_cqc_the1) ) ) ) ) )).

fof(t18_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(A,B)),k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) ) ) ) )).

fof(t19_lukasi_1,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)
             => ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
               => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C)),k4_cqc_the1) ) ) ) ) )).

fof(t20_lukasi_1,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)
             => ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
                  & r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) )
               => r2_hidden(k12_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) )).

fof(t21_lukasi_1,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)
             => ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
                  & r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
                  & r2_hidden(A,k4_cqc_the1) )
               => r2_hidden(C,k4_cqc_the1) ) ) ) ) )).

fof(t22_lukasi_1,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)
             => ! [D] :
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
                      & r2_hidden(k12_cqc_lang(A,k12_cqc_lang(C,D)),k4_cqc_the1) )
                   => r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,D)),k4_cqc_the1) ) ) ) ) ) )).

fof(t23_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(A,k9_cqc_lang),k4_cqc_the1) ) )).

fof(t24_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k12_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t25_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),A),k4_cqc_the1) ) )).

fof(t26_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(B),k10_cqc_lang(A))),k4_cqc_the1) ) ) )).

fof(t27_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(A))),k4_cqc_the1) ) )).

fof(t28_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B),k12_cqc_lang(A,B)),k4_cqc_the1)
            & r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B)),k4_cqc_the1) ) ) ) )).

fof(t29_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))),k12_cqc_lang(A,B)),k4_cqc_the1)
            & r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B)))),k4_cqc_the1) ) ) ) )).

fof(t30_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(B)),k12_cqc_lang(B,k10_cqc_lang(A))),k4_cqc_the1) ) ) )).

fof(t31_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),B),k12_cqc_lang(k10_cqc_lang(B),A)),k4_cqc_the1) ) ) )).

fof(t32_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(A)),k10_cqc_lang(A)),k4_cqc_the1) ) )).

fof(t33_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k10_cqc_lang(A),k12_cqc_lang(A,B)),k4_cqc_the1) ) ) )).

fof(t34_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
          <=> r2_hidden(k12_cqc_lang(k10_cqc_lang(B),k10_cqc_lang(A)),k4_cqc_the1) ) ) ) )).

fof(t35_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(B,A),k4_cqc_the1) ) ) ) )).

fof(t36_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ( r2_hidden(A,k4_cqc_the1)
      <=> r2_hidden(k10_cqc_lang(k10_cqc_lang(A)),k4_cqc_the1) ) ) )).

fof(t37_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
          <=> r2_hidden(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))),k4_cqc_the1) ) ) ) )).

fof(t38_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
          <=> r2_hidden(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B),k4_cqc_the1) ) ) ) )).

fof(t39_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(A,k10_cqc_lang(B)),k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(B,k10_cqc_lang(A)),k4_cqc_the1) ) ) ) )).

fof(t40_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(k12_cqc_lang(k10_cqc_lang(A),B),k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(k10_cqc_lang(B),A),k4_cqc_the1) ) ) ) )).

fof(t41_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C)))) ) ) ) )).

fof(t42_lukasi_1,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,B))
               => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C))) ) ) ) ) )).

fof(t43_lukasi_1,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,B))
                  & v2_cqc_the1(k12_cqc_lang(B,C)) )
               => v2_cqc_the1(k12_cqc_lang(A,C)) ) ) ) ) )).

fof(t44_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => v2_cqc_the1(k12_cqc_lang(A,A)) ) )).

fof(t45_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,A))) ) ) )).

fof(t46_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(A)
           => v2_cqc_the1(k12_cqc_lang(B,A)) ) ) ) )).

fof(t47_lukasi_1,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(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(B,k12_cqc_lang(A,C)))) ) ) ) )).

fof(t48_lukasi_1,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(B,k12_cqc_lang(A,C))) ) ) ) ) )).

fof(t49_lukasi_1,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(B) )
               => v2_cqc_the1(k12_cqc_lang(A,C)) ) ) ) ) )).

fof(t50_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ( v2_cqc_the1(k12_cqc_lang(A,k9_cqc_lang))
        & v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k9_cqc_lang),A)) ) ) )).

fof(t51_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(k12_cqc_lang(A,B),B))) ) ) )).

fof(t52_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(A,B)),k12_cqc_lang(A,B))) ) ) )).

fof(t53_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(A,B)))
           => v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) )).

fof(t54_lukasi_1,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(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C)))) ) ) ) )).

fof(t55_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(A,C))) ) ) ) ) )).

fof(t56_lukasi_1,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(A,B)) )
               => v2_cqc_the1(k12_cqc_lang(A,C)) ) ) ) ) )).

fof(t57_lukasi_1,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(k12_cqc_lang(k12_cqc_lang(A,B),C),k12_cqc_lang(B,C))) ) ) ) )).

fof(t58_lukasi_1,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(k12_cqc_lang(A,B),C))
               => v2_cqc_the1(k12_cqc_lang(B,C)) ) ) ) ) )).

fof(t59_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(C,A),k12_cqc_lang(C,B)))) ) ) ) )).

fof(t60_lukasi_1,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,B))
               => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(C,A),k12_cqc_lang(C,B))) ) ) ) ) )).

fof(t61_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(B),k10_cqc_lang(A)))) ) ) )).

fof(t62_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k12_cqc_lang(B,A))) ) ) )).

fof(t63_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)))
          <=> v2_cqc_the1(k12_cqc_lang(B,A)) ) ) ) )).

fof(t64_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => v2_cqc_the1(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(A)))) ) )).

fof(t65_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),A)) ) )).

fof(t66_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ( v2_cqc_the1(k10_cqc_lang(k10_cqc_lang(A)))
      <=> v2_cqc_the1(A) ) ) )).

fof(t67_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B),k12_cqc_lang(A,B))) ) ) )).

fof(t68_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B))
          <=> v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) )).

fof(t69_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))),k12_cqc_lang(A,B))) ) ) )).

fof(t70_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))))
          <=> v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) )).

fof(t71_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(B)),k12_cqc_lang(B,k10_cqc_lang(A)))) ) ) )).

fof(t72_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(k12_cqc_lang(A,k10_cqc_lang(B)))
           => v2_cqc_the1(k12_cqc_lang(B,k10_cqc_lang(A))) ) ) ) )).

fof(t73_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),B),k12_cqc_lang(k10_cqc_lang(B),A))) ) ) )).

fof(t74_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(A),B))
           => v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(B),A)) ) ) ) )).

fof(t75_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( r3_cqc_the1(D,k12_cqc_lang(A,B))
                   => r3_cqc_the1(D,k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C))) ) ) ) ) ) )).

fof(t76_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( ( r3_cqc_the1(D,k12_cqc_lang(A,B))
                      & r3_cqc_the1(D,k12_cqc_lang(B,C)) )
                   => r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) )).

fof(t77_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => r3_cqc_the1(B,k12_cqc_lang(A,A)) ) ) )).

fof(t78_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,A)
               => r3_cqc_the1(C,k12_cqc_lang(B,A)) ) ) ) ) )).

fof(t79_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,A)
               => r3_cqc_the1(C,k12_cqc_lang(k12_cqc_lang(A,B),B)) ) ) ) ) )).

fof(t80_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
                   => r3_cqc_the1(D,k12_cqc_lang(B,k12_cqc_lang(A,C))) ) ) ) ) ) )).

fof(t81_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
                      & r3_cqc_the1(D,B) )
                   => r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) )).

fof(t82_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,k12_cqc_lang(A,k12_cqc_lang(A,B)))
               => r3_cqc_the1(C,k12_cqc_lang(A,B)) ) ) ) ) )).

fof(t83_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( r3_cqc_the1(D,k12_cqc_lang(k12_cqc_lang(A,B),C))
                   => r3_cqc_the1(D,k12_cqc_lang(B,C)) ) ) ) ) ) )).

fof(t84_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
                   => r3_cqc_the1(D,k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C))) ) ) ) ) ) )).

fof(t85_lukasi_1,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)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                 => ( ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
                      & r3_cqc_the1(D,k12_cqc_lang(A,B)) )
                   => r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) )).

fof(t86_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)))
              <=> r3_cqc_the1(C,k12_cqc_lang(B,A)) ) ) ) ) )).

fof(t87_lukasi_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( r3_cqc_the1(B,k10_cqc_lang(k10_cqc_lang(A)))
          <=> r3_cqc_the1(B,A) ) ) ) )).

fof(t88_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))))
              <=> r3_cqc_the1(C,k12_cqc_lang(A,B)) ) ) ) ) )).

fof(t89_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B))
              <=> r3_cqc_the1(C,k12_cqc_lang(A,B)) ) ) ) ) )).

fof(t90_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,k12_cqc_lang(A,k10_cqc_lang(B)))
               => r3_cqc_the1(C,k12_cqc_lang(B,k10_cqc_lang(A))) ) ) ) ) )).

fof(t91_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( r3_cqc_the1(C,k12_cqc_lang(k10_cqc_lang(A),B))
               => r3_cqc_the1(C,k12_cqc_lang(k10_cqc_lang(B),A)) ) ) ) ) )).

fof(t92_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( ( r3_cqc_the1(C,k12_cqc_lang(A,k10_cqc_lang(B)))
                  & r3_cqc_the1(C,B) )
               => r3_cqc_the1(C,k10_cqc_lang(A)) ) ) ) ) )).

fof(t93_lukasi_1,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,k1_zfmisc_1(k7_cqc_lang))
             => ( ( r3_cqc_the1(C,k12_cqc_lang(k10_cqc_lang(A),B))
                  & r3_cqc_the1(C,k10_cqc_lang(B)) )
               => r3_cqc_the1(C,A) ) ) ) ) )).
%------------------------------------------------------------------------------