SET007 Axioms: SET007+120.ax


%------------------------------------------------------------------------------
% File     : SET007+120 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Calculus of Propositions
% 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    : procal_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   58 (   0 unit)
%            Number of atoms       :  215 (   0 equality)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  157 (   0 ~  ;   0  |;   7  &)
%                                         (   0 <=>; 150 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    2 (   0 propositional; 2-3 arity)
%            Number of functors    :    8 (   3 constant; 0-2 arity)
%            Number of variables   :  133 (   0 singleton; 133 !;   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_procal_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k10_cqc_lang(k11_cqc_lang(A,k10_cqc_lang(A))),k4_cqc_the1) ) )).

fof(t2_procal_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k13_cqc_lang(A,k10_cqc_lang(A)),k4_cqc_the1) ) )).

fof(t3_procal_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,k13_cqc_lang(A,B)),k4_cqc_the1) ) ) )).

fof(t4_procal_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,k13_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t5_procal_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(k13_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(A),B)),k4_cqc_the1) ) ) )).

fof(t6_procal_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(k13_cqc_lang(A,B)),k11_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B))),k4_cqc_the1) ) ) )).

fof(t7_procal_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(k11_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k10_cqc_lang(k13_cqc_lang(A,B))),k4_cqc_the1) ) ) )).

fof(t8_procal_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(k13_cqc_lang(A,B),k13_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t9_procal_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k13_cqc_lang(k10_cqc_lang(A),A),k4_cqc_the1) ) )).

fof(t10_procal_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(k13_cqc_lang(A,B)),k10_cqc_lang(A)),k4_cqc_the1) ) ) )).

fof(t11_procal_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(k13_cqc_lang(A,A),A),k4_cqc_the1) ) )).

fof(t12_procal_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(A,k13_cqc_lang(A,A)),k4_cqc_the1) ) )).

fof(t13_procal_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(k11_cqc_lang(A,k10_cqc_lang(A)),B),k4_cqc_the1) ) ) )).

fof(t14_procal_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),k13_cqc_lang(k10_cqc_lang(A),B)),k4_cqc_the1) ) ) )).

fof(t15_procal_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(k11_cqc_lang(A,B),k10_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(B)))),k4_cqc_the1) ) ) )).

fof(t16_procal_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(k12_cqc_lang(A,k10_cqc_lang(B))),k11_cqc_lang(A,B)),k4_cqc_the1) ) ) )).

fof(t17_procal_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(k11_cqc_lang(A,B)),k13_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B))),k4_cqc_the1) ) ) )).

fof(t18_procal_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(k13_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k10_cqc_lang(k11_cqc_lang(A,B))),k4_cqc_the1) ) ) )).

fof(t19_procal_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(k11_cqc_lang(A,B),A),k4_cqc_the1) ) ) )).

fof(t20_procal_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(k11_cqc_lang(A,B),k13_cqc_lang(A,B)),k4_cqc_the1) ) ) )).

fof(t21_procal_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(k11_cqc_lang(A,B),B),k4_cqc_the1) ) ) )).

fof(t22_procal_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(A,k11_cqc_lang(A,A)),k4_cqc_the1) ) )).

fof(t23_procal_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(k14_cqc_lang(A,B),k12_cqc_lang(A,B)),k4_cqc_the1) ) ) )).

fof(t24_procal_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(k14_cqc_lang(A,B),k12_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t25_procal_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(k13_cqc_lang(k13_cqc_lang(A,B),C),k13_cqc_lang(A,k13_cqc_lang(B,C))),k4_cqc_the1) ) ) ) )).

fof(t26_procal_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(k11_cqc_lang(k11_cqc_lang(A,B),C),k11_cqc_lang(A,k11_cqc_lang(B,C))),k4_cqc_the1) ) ) ) )).

fof(t27_procal_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(k13_cqc_lang(A,k13_cqc_lang(B,C)),k13_cqc_lang(k13_cqc_lang(A,B),C)),k4_cqc_the1) ) ) ) )).

fof(t28_procal_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,k11_cqc_lang(A,B))),k4_cqc_the1) ) ) )).

fof(t29_procal_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(k12_cqc_lang(B,A),k14_cqc_lang(A,B))),k4_cqc_the1) ) ) )).

fof(t30_procal_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(k14_cqc_lang(k13_cqc_lang(A,B),k13_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t31_procal_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(k11_cqc_lang(A,B),C),k12_cqc_lang(A,k12_cqc_lang(B,C))),k4_cqc_the1) ) ) ) )).

fof(t32_procal_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(k11_cqc_lang(A,B),C)),k4_cqc_the1) ) ) ) )).

fof(t33_procal_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(A,C),k12_cqc_lang(A,k11_cqc_lang(B,C)))),k4_cqc_the1) ) ) ) )).

fof(t34_procal_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(k13_cqc_lang(A,B),C),k13_cqc_lang(k12_cqc_lang(A,C),k12_cqc_lang(B,C))),k4_cqc_the1) ) ) ) )).

fof(t35_procal_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,B),k12_cqc_lang(k13_cqc_lang(A,C),B))),k4_cqc_the1) ) ) ) )).

fof(t36_procal_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(k11_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(C,B)),k12_cqc_lang(k13_cqc_lang(A,C),B)),k4_cqc_the1) ) ) ) )).

fof(t37_procal_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,k11_cqc_lang(B,k10_cqc_lang(B))),k10_cqc_lang(A)),k4_cqc_the1) ) ) )).

fof(t38_procal_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(k11_cqc_lang(k13_cqc_lang(A,B),k13_cqc_lang(A,C)),k13_cqc_lang(A,k11_cqc_lang(B,C))),k4_cqc_the1) ) ) ) )).

fof(t39_procal_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(k11_cqc_lang(A,k13_cqc_lang(B,C)),k13_cqc_lang(k11_cqc_lang(A,B),k11_cqc_lang(A,C))),k4_cqc_the1) ) ) ) )).

fof(t40_procal_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(k11_cqc_lang(k13_cqc_lang(A,B),k13_cqc_lang(C,B)),k13_cqc_lang(k11_cqc_lang(A,C),B)),k4_cqc_the1) ) ) ) )).

fof(t41_procal_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(k11_cqc_lang(k13_cqc_lang(A,B),C),k13_cqc_lang(k11_cqc_lang(A,C),k11_cqc_lang(B,C))),k4_cqc_the1) ) ) ) )).

fof(t42_procal_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(k13_cqc_lang(A,B),k4_cqc_the1) ) ) ) )).

fof(t43_procal_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(k13_cqc_lang(B,A),k4_cqc_the1) ) ) ) )).

fof(t44_procal_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(k11_cqc_lang(A,B),k4_cqc_the1)
           => r2_hidden(A,k4_cqc_the1) ) ) ) )).

fof(t45_procal_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(k11_cqc_lang(A,B),k4_cqc_the1)
           => r2_hidden(B,k4_cqc_the1) ) ) ) )).

fof(t46_procal_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(k11_cqc_lang(A,B),k4_cqc_the1)
           => r2_hidden(k13_cqc_lang(A,B),k4_cqc_the1) ) ) ) )).

fof(t47_procal_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(B,k4_cqc_the1) )
           => r2_hidden(k11_cqc_lang(A,B),k4_cqc_the1) ) ) ) )).

fof(t48_procal_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(k13_cqc_lang(A,C),k13_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ) )).

fof(t49_procal_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(k13_cqc_lang(C,A),k13_cqc_lang(C,B)),k4_cqc_the1) ) ) ) ) )).

fof(t50_procal_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(k11_cqc_lang(C,A),k11_cqc_lang(C,B)),k4_cqc_the1) ) ) ) ) )).

fof(t51_procal_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(k11_cqc_lang(A,C),k11_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ) )).

fof(t52_procal_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(A,C),k4_cqc_the1) )
               => r2_hidden(k12_cqc_lang(A,k11_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ) )).

fof(t53_procal_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(C,B),k4_cqc_the1) )
               => r2_hidden(k12_cqc_lang(k13_cqc_lang(A,C),B),k4_cqc_the1) ) ) ) ) )).

fof(t54_procal_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(k13_cqc_lang(A,B),k4_cqc_the1)
              & r2_hidden(k10_cqc_lang(A),k4_cqc_the1) )
           => r2_hidden(B,k4_cqc_the1) ) ) ) )).

fof(t55_procal_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(k13_cqc_lang(A,B),k4_cqc_the1)
              & r2_hidden(k10_cqc_lang(B),k4_cqc_the1) )
           => r2_hidden(A,k4_cqc_the1) ) ) ) )).

fof(t56_procal_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,B),k4_cqc_the1)
                      & r2_hidden(k12_cqc_lang(C,D),k4_cqc_the1) )
                   => r2_hidden(k12_cqc_lang(k11_cqc_lang(A,C),k11_cqc_lang(B,D)),k4_cqc_the1) ) ) ) ) ) )).

fof(t57_procal_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,B),k4_cqc_the1)
                      & r2_hidden(k12_cqc_lang(C,D),k4_cqc_the1) )
                   => r2_hidden(k12_cqc_lang(k13_cqc_lang(A,C),k13_cqc_lang(B,D)),k4_cqc_the1) ) ) ) ) ) )).

fof(t58_procal_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(k11_cqc_lang(A,k10_cqc_lang(B)),k10_cqc_lang(A)),k4_cqc_the1)
           => r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) ) ) ) )).
%------------------------------------------------------------------------------