SET007 Axioms: SET007+130.ax


%------------------------------------------------------------------------------
% File     : SET007+130 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Intuitionistic Propositional Calculus with Modal Operator. Part I
% 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    : intpro_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  145 (  18 unit)
%            Number of atoms       :  603 (  20 equality)
%            Maximal formula depth :   26 (   6 average)
%            Number of connectives :  462 (   4 ~  ;   1  |; 129  &)
%                                         (  23 <=>; 305 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   29 (  14 constant; 0-2 arity)
%            Number of variables   :  281 (   0 singleton; 280 !;   1 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_intpro_1,axiom,(
    ! [A] :
      ( v7_intpro_1(A)
     => ( ~ v1_xboole_0(A)
        & v1_intpro_1(A)
        & v2_intpro_1(A)
        & v3_intpro_1(A)
        & v4_intpro_1(A)
        & v5_intpro_1(A)
        & v6_intpro_1(A) ) ) )).

fof(cc2_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k5_numbers)))
     => ( ( v1_intpro_1(A)
          & v2_intpro_1(A)
          & v3_intpro_1(A)
          & v4_intpro_1(A)
          & v5_intpro_1(A)
          & v6_intpro_1(A) )
       => v7_intpro_1(A) ) ) )).

fof(fc1_intpro_1,axiom,
    ( ~ v1_xboole_0(k1_intpro_1)
    & v1_intpro_1(k1_intpro_1)
    & v2_intpro_1(k1_intpro_1)
    & v3_intpro_1(k1_intpro_1)
    & v4_intpro_1(k1_intpro_1)
    & v5_intpro_1(k1_intpro_1)
    & v6_intpro_1(k1_intpro_1)
    & v7_intpro_1(k1_intpro_1) )).

fof(rc1_intpro_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_intpro_1(A)
      & v2_intpro_1(A)
      & v3_intpro_1(A)
      & v4_intpro_1(A)
      & v5_intpro_1(A)
      & v6_intpro_1(A)
      & v7_intpro_1(A) ) )).

fof(fc2_intpro_1,axiom,
    ( ~ v1_xboole_0(k1_intpro_1)
    & v1_fraenkel(k1_intpro_1)
    & v1_intpro_1(k1_intpro_1)
    & v2_intpro_1(k1_intpro_1)
    & v3_intpro_1(k1_intpro_1)
    & v4_intpro_1(k1_intpro_1)
    & v5_intpro_1(k1_intpro_1)
    & v6_intpro_1(k1_intpro_1)
    & v7_intpro_1(k1_intpro_1) )).

fof(cc3_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A) ) ) )).

fof(fc3_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => v8_intpro_1(k7_intpro_1(A)) ) )).

fof(fc4_intpro_1,axiom,(
    v8_intpro_1(k8_intpro_1) )).

fof(fc5_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => v9_intpro_1(k11_intpro_1(A)) ) )).

fof(fc6_intpro_1,axiom,(
    v9_intpro_1(k12_intpro_1) )).

fof(fc7_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => v10_intpro_1(k13_intpro_1(A)) ) )).

fof(fc8_intpro_1,axiom,(
    v10_intpro_1(k14_intpro_1) )).

fof(d1_intpro_1,axiom,(
    ! [A] :
      ( v1_intpro_1(A)
    <=> r2_hidden(k12_finseq_1(k5_numbers,np__0),A) ) )).

fof(d2_intpro_1,axiom,(
    ! [A] :
      ( v2_intpro_1(A)
    <=> ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__1),B),C),A) ) ) ) ) )).

fof(d3_intpro_1,axiom,(
    ! [A] :
      ( v3_intpro_1(A)
    <=> ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__2),B),C),A) ) ) ) ) )).

fof(d4_intpro_1,axiom,(
    ! [A] :
      ( v4_intpro_1(A)
    <=> ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__3),B),C),A) ) ) ) ) )).

fof(d5_intpro_1,axiom,(
    ! [A] :
      ( v5_intpro_1(A)
    <=> ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_hidden(k12_finseq_1(k5_numbers,k1_nat_1(np__5,k2_nat_1(np__2,B))),A) ) ) )).

fof(d6_intpro_1,axiom,(
    ! [A] :
      ( v6_intpro_1(A)
    <=> ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r2_hidden(B,A)
           => r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,np__6),B),A) ) ) ) )).

fof(d7_intpro_1,axiom,(
    ! [A] :
      ( v7_intpro_1(A)
    <=> ( r1_tarski(A,k13_finseq_1(k5_numbers))
        & v1_intpro_1(A)
        & v2_intpro_1(A)
        & v3_intpro_1(A)
        & v4_intpro_1(A)
        & v5_intpro_1(A)
        & v6_intpro_1(A) ) ) )).

fof(d8_intpro_1,axiom,(
    ! [A] :
      ( A = k1_intpro_1
    <=> ( v7_intpro_1(A)
        & ! [B] :
            ( v7_intpro_1(B)
           => r1_tarski(A,B) ) ) ) )).

fof(d9_intpro_1,axiom,(
    k2_intpro_1 = k12_finseq_1(k5_numbers,np__0) )).

fof(d10_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => k3_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__1),A),B) ) ) )).

fof(d11_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => k4_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__2),A),B) ) ) )).

fof(d12_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => k5_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__3),A),B) ) ) )).

fof(d13_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => k6_intpro_1(A) = k7_finseq_1(k12_finseq_1(k5_numbers,np__6),A) ) )).

fof(d14_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v8_intpro_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_intpro_1)
           => ! [C] :
                ( m1_subset_1(C,k1_intpro_1)
               => ! [D] :
                    ( m1_subset_1(D,k1_intpro_1)
                   => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),A)
                      & r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),A)
                      & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),A)
                      & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),A)
                      & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),A)
                      & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),A)
                      & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),A)
                      & r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),A)
                      & r2_hidden(k3_intpro_1(k2_intpro_1,B),A)
                      & ( ( r2_hidden(B,A)
                          & r2_hidden(k3_intpro_1(B,C),A) )
                       => r2_hidden(C,A) ) ) ) ) ) ) ) )).

fof(d15_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( B = k7_intpro_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_intpro_1)
               => ( r2_hidden(C,B)
                <=> ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1))
                     => ( ( v8_intpro_1(D)
                          & r1_tarski(A,D) )
                       => r2_hidden(C,D) ) ) ) ) ) ) ) )).

fof(d16_intpro_1,axiom,(
    k8_intpro_1 = k7_intpro_1(k1_subset_1(k1_intpro_1)) )).

fof(d17_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => k9_intpro_1(A) = k3_intpro_1(A,k2_intpro_1) ) )).

fof(d18_intpro_1,axiom,(
    k10_intpro_1 = k3_intpro_1(k2_intpro_1,k2_intpro_1) )).

fof(t1_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k7_intpro_1(A)) ) ) ) )).

fof(t2_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_intpro_1)
                 => r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),k7_intpro_1(A)) ) ) ) ) )).

fof(t3_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k7_intpro_1(A)) ) ) ) )).

fof(t4_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k7_intpro_1(A)) ) ) ) )).

fof(t5_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k7_intpro_1(A)) ) ) ) )).

fof(t6_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k7_intpro_1(A)) ) ) ) )).

fof(t7_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(B,k5_intpro_1(C,B)),k7_intpro_1(A)) ) ) ) )).

fof(t8_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_intpro_1)
                 => r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(k3_intpro_1(D,C),k3_intpro_1(k5_intpro_1(B,D),C))),k7_intpro_1(A)) ) ) ) ) )).

fof(t9_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k2_intpro_1,B),k7_intpro_1(A)) ) ) )).

fof(t10_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( ( r2_hidden(B,k7_intpro_1(A))
                  & r2_hidden(k3_intpro_1(B,C),k7_intpro_1(A)) )
               => r2_hidden(C,k7_intpro_1(A)) ) ) ) ) )).

fof(t11_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( ( v8_intpro_1(A)
              & r1_tarski(B,A) )
           => r1_tarski(k7_intpro_1(B),A) ) ) ) )).

fof(t12_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => r1_tarski(A,k7_intpro_1(A)) ) )).

fof(t13_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( r1_tarski(A,B)
           => r1_tarski(k7_intpro_1(A),k7_intpro_1(B)) ) ) ) )).

fof(t14_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => k7_intpro_1(k7_intpro_1(A)) = k7_intpro_1(A) ) )).

fof(t15_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v8_intpro_1(A)
      <=> k7_intpro_1(A) = A ) ) )).

fof(t16_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v8_intpro_1(A)
       => r1_tarski(k8_intpro_1,A) ) ) )).

fof(t17_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => r2_hidden(k3_intpro_1(A,A),k8_intpro_1) ) )).

fof(t18_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ( r2_hidden(A,k8_intpro_1)
           => r2_hidden(k3_intpro_1(B,A),k8_intpro_1) ) ) ) )).

fof(t19_intpro_1,axiom,(
    r2_hidden(k10_intpro_1,k8_intpro_1) )).

fof(t20_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,A)),k8_intpro_1) ) ) )).

fof(t21_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(B,B)),k8_intpro_1) ) ) )).

fof(t22_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k3_intpro_1(C,A),k3_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t23_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( r2_hidden(k3_intpro_1(A,k3_intpro_1(B,C)),k8_intpro_1)
               => r2_hidden(k3_intpro_1(B,k3_intpro_1(A,C)),k8_intpro_1) ) ) ) ) )).

fof(t24_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(A,C))),k8_intpro_1) ) ) ) )).

fof(t25_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
               => r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(A,C)),k8_intpro_1) ) ) ) ) )).

fof(t26_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
                  & r2_hidden(k3_intpro_1(B,C),k8_intpro_1) )
               => r2_hidden(k3_intpro_1(A,C),k8_intpro_1) ) ) ) ) )).

fof(t27_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_intpro_1)
                 => r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(B,C)),k3_intpro_1(k3_intpro_1(D,B),k3_intpro_1(A,k3_intpro_1(D,C)))),k8_intpro_1) ) ) ) ) )).

fof(t28_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(k3_intpro_1(A,B),C),k3_intpro_1(B,C)),k8_intpro_1) ) ) ) )).

fof(t29_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(B,C)),k3_intpro_1(B,k3_intpro_1(A,C))),k8_intpro_1) ) ) ) )).

fof(t30_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(A,B)),k3_intpro_1(A,B)),k8_intpro_1) ) ) )).

fof(t31_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(A,k3_intpro_1(k3_intpro_1(A,B),B)),k8_intpro_1) ) ) )).

fof(t32_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( ( r2_hidden(k3_intpro_1(A,k3_intpro_1(B,C)),k8_intpro_1)
                  & r2_hidden(B,k8_intpro_1) )
               => r2_hidden(k3_intpro_1(A,C),k8_intpro_1) ) ) ) ) )).

fof(t33_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => r2_hidden(k3_intpro_1(A,k4_intpro_1(A,A)),k8_intpro_1) ) )).

fof(t34_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ( r2_hidden(k4_intpro_1(A,B),k8_intpro_1)
          <=> ( r2_hidden(A,k8_intpro_1)
              & r2_hidden(B,k8_intpro_1) ) ) ) ) )).

fof(t35_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ( r2_hidden(k4_intpro_1(A,B),k8_intpro_1)
          <=> r2_hidden(k4_intpro_1(B,A),k8_intpro_1) ) ) ) )).

fof(t36_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(k4_intpro_1(A,B),C),k3_intpro_1(A,k3_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(t37_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(B,C)),k3_intpro_1(k4_intpro_1(A,B),C)),k8_intpro_1) ) ) ) )).

fof(t38_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k3_intpro_1(A,C),k3_intpro_1(A,k4_intpro_1(B,C)))),k8_intpro_1) ) ) ) )).

fof(t39_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),A),B),k8_intpro_1) ) ) )).

fof(t40_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(k4_intpro_1(k3_intpro_1(A,B),A),C),B),k8_intpro_1) ) ) ) )).

fof(t41_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(C,A),B)),k8_intpro_1) ) ) ) )).

fof(t42_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(A,C),B)),k8_intpro_1) ) ) ) )).

fof(t43_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(k4_intpro_1(A,B),C),k3_intpro_1(k4_intpro_1(A,B),k4_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t44_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(A,C),k4_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(t45_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),k4_intpro_1(A,C)),k4_intpro_1(B,C)),k8_intpro_1) ) ) ) )).

fof(t46_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k4_intpro_1(A,B),k4_intpro_1(B,A)),k8_intpro_1) ) ) )).

fof(t47_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),k4_intpro_1(A,C)),k4_intpro_1(C,B)),k8_intpro_1) ) ) ) )).

fof(t48_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(A,C),k4_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t49_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(C,A),k4_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t50_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(A,k4_intpro_1(B,C)),k4_intpro_1(A,k4_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t51_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,C)),k3_intpro_1(A,k4_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(t52_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(k4_intpro_1(A,B),C),k4_intpro_1(A,k4_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(t53_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k4_intpro_1(A,k4_intpro_1(B,C)),k4_intpro_1(k4_intpro_1(A,B),C)),k8_intpro_1) ) ) ) )).

fof(t54_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => r2_hidden(k3_intpro_1(k5_intpro_1(A,A),A),k8_intpro_1) ) )).

fof(t55_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ( ( r2_hidden(A,k8_intpro_1)
              | r2_hidden(B,k8_intpro_1) )
           => r2_hidden(k5_intpro_1(A,B),k8_intpro_1) ) ) ) )).

fof(t56_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k5_intpro_1(A,B),k5_intpro_1(B,A)),k8_intpro_1) ) ) )).

fof(t57_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ( r2_hidden(k5_intpro_1(A,B),k8_intpro_1)
          <=> r2_hidden(k5_intpro_1(B,A),k8_intpro_1) ) ) ) )).

fof(t58_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,k5_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(t59_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,k5_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t60_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k5_intpro_1(A,C),k5_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(t61_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
               => r2_hidden(k3_intpro_1(k5_intpro_1(A,C),k5_intpro_1(B,C)),k8_intpro_1) ) ) ) ) )).

fof(t62_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k5_intpro_1(C,A),k5_intpro_1(C,B))),k8_intpro_1) ) ) ) )).

fof(t63_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
               => r2_hidden(k3_intpro_1(k5_intpro_1(C,A),k5_intpro_1(C,B)),k8_intpro_1) ) ) ) ) )).

fof(t64_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k5_intpro_1(A,k5_intpro_1(B,C)),k5_intpro_1(B,k5_intpro_1(A,C))),k8_intpro_1) ) ) ) )).

fof(t65_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k5_intpro_1(A,k5_intpro_1(B,C)),k5_intpro_1(k5_intpro_1(A,B),C)),k8_intpro_1) ) ) ) )).

fof(t66_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k5_intpro_1(k5_intpro_1(A,B),C),k5_intpro_1(A,k5_intpro_1(B,C))),k8_intpro_1) ) ) ) )).

fof(d19_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v9_intpro_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_intpro_1)
           => ! [C] :
                ( m1_subset_1(C,k1_intpro_1)
               => ! [D] :
                    ( m1_subset_1(D,k1_intpro_1)
                   => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),A)
                      & r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),A)
                      & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),A)
                      & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),A)
                      & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),A)
                      & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),A)
                      & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),A)
                      & r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),A)
                      & r2_hidden(k3_intpro_1(k2_intpro_1,B),A)
                      & r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),A)
                      & ( ( r2_hidden(B,A)
                          & r2_hidden(k3_intpro_1(B,C),A) )
                       => r2_hidden(C,A) ) ) ) ) ) ) ) )).

fof(t67_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v9_intpro_1(A)
       => v8_intpro_1(A) ) ) )).

fof(d20_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( B = k11_intpro_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_intpro_1)
               => ( r2_hidden(C,B)
                <=> ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1))
                     => ( ( v9_intpro_1(D)
                          & r1_tarski(A,D) )
                       => r2_hidden(C,D) ) ) ) ) ) ) ) )).

fof(d21_intpro_1,axiom,(
    k12_intpro_1 = k11_intpro_1(k1_subset_1(k1_intpro_1)) )).

fof(t68_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => r1_tarski(k7_intpro_1(A),k11_intpro_1(A)) ) )).

fof(t69_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_intpro_1)
                 => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),k11_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k2_intpro_1,B),k11_intpro_1(A))
                    & r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),k11_intpro_1(A)) ) ) ) ) ) )).

fof(t70_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( ( r2_hidden(B,k11_intpro_1(A))
                  & r2_hidden(k3_intpro_1(B,C),k11_intpro_1(A)) )
               => r2_hidden(C,k11_intpro_1(A)) ) ) ) ) )).

fof(t71_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( ( v9_intpro_1(A)
              & r1_tarski(B,A) )
           => r1_tarski(k11_intpro_1(B),A) ) ) ) )).

fof(t72_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => r1_tarski(A,k11_intpro_1(A)) ) )).

fof(t73_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( r1_tarski(A,B)
           => r1_tarski(k11_intpro_1(A),k11_intpro_1(B)) ) ) ) )).

fof(t74_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => k11_intpro_1(k11_intpro_1(A)) = k11_intpro_1(A) ) )).

fof(t75_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v9_intpro_1(A)
      <=> k11_intpro_1(A) = A ) ) )).

fof(t76_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v9_intpro_1(A)
       => r1_tarski(k12_intpro_1,A) ) ) )).

fof(t77_intpro_1,axiom,(
    r1_tarski(k8_intpro_1,k12_intpro_1) )).

fof(d22_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v10_intpro_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_intpro_1)
           => ! [C] :
                ( m1_subset_1(C,k1_intpro_1)
               => ! [D] :
                    ( m1_subset_1(D,k1_intpro_1)
                   => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),A)
                      & r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),A)
                      & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),A)
                      & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),A)
                      & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),A)
                      & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),A)
                      & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),A)
                      & r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),A)
                      & r2_hidden(k3_intpro_1(k2_intpro_1,B),A)
                      & r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),A)
                      & r2_hidden(k3_intpro_1(k6_intpro_1(k3_intpro_1(B,C)),k3_intpro_1(k6_intpro_1(B),k6_intpro_1(C))),A)
                      & r2_hidden(k3_intpro_1(k6_intpro_1(B),B),A)
                      & r2_hidden(k3_intpro_1(k6_intpro_1(B),k6_intpro_1(k6_intpro_1(B))),A)
                      & ( ( r2_hidden(B,A)
                          & r2_hidden(k3_intpro_1(B,C),A) )
                       => r2_hidden(C,A) )
                      & ( r2_hidden(B,A)
                       => r2_hidden(k6_intpro_1(B),A) ) ) ) ) ) ) ) )).

fof(t78_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v10_intpro_1(A)
       => v9_intpro_1(A) ) ) )).

fof(t79_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v10_intpro_1(A)
       => v8_intpro_1(A) ) ) )).

fof(d23_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( B = k13_intpro_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_intpro_1)
               => ( r2_hidden(C,B)
                <=> ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1))
                     => ( ( v10_intpro_1(D)
                          & r1_tarski(A,D) )
                       => r2_hidden(C,D) ) ) ) ) ) ) ) )).

fof(d24_intpro_1,axiom,(
    k14_intpro_1 = k13_intpro_1(k1_subset_1(k1_intpro_1)) )).

fof(t80_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => r1_tarski(k11_intpro_1(A),k13_intpro_1(A)) ) )).

fof(t81_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => r1_tarski(k7_intpro_1(A),k13_intpro_1(A)) ) )).

fof(t82_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_intpro_1)
                 => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),k13_intpro_1(A))
                    & r2_hidden(k3_intpro_1(k2_intpro_1,B),k13_intpro_1(A))
                    & r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),k13_intpro_1(A)) ) ) ) ) ) )).

fof(t83_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => ( ( r2_hidden(B,k13_intpro_1(A))
                  & r2_hidden(k3_intpro_1(B,C),k13_intpro_1(A)) )
               => r2_hidden(C,k13_intpro_1(A)) ) ) ) ) )).

fof(t84_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ! [C] :
              ( m1_subset_1(C,k1_intpro_1)
             => r2_hidden(k3_intpro_1(k6_intpro_1(k3_intpro_1(B,C)),k3_intpro_1(k6_intpro_1(B),k6_intpro_1(C))),k13_intpro_1(A)) ) ) ) )).

fof(t85_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k6_intpro_1(B),B),k13_intpro_1(A)) ) ) )).

fof(t86_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => r2_hidden(k3_intpro_1(k6_intpro_1(B),k6_intpro_1(k6_intpro_1(B))),k13_intpro_1(A)) ) ) )).

fof(t87_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_intpro_1)
         => ( r2_hidden(B,k13_intpro_1(A))
           => r2_hidden(k6_intpro_1(B),k13_intpro_1(A)) ) ) ) )).

fof(t88_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( ( v10_intpro_1(A)
              & r1_tarski(B,A) )
           => r1_tarski(k13_intpro_1(B),A) ) ) ) )).

fof(t89_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => r1_tarski(A,k13_intpro_1(A)) ) )).

fof(t90_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
         => ( r1_tarski(A,B)
           => r1_tarski(k13_intpro_1(A),k13_intpro_1(B)) ) ) ) )).

fof(t91_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => k13_intpro_1(k13_intpro_1(A)) = k13_intpro_1(A) ) )).

fof(t92_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v10_intpro_1(A)
      <=> k13_intpro_1(A) = A ) ) )).

fof(t93_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => ( v10_intpro_1(A)
       => r1_tarski(k14_intpro_1,A) ) ) )).

fof(t94_intpro_1,axiom,(
    r1_tarski(k12_intpro_1,k14_intpro_1) )).

fof(t95_intpro_1,axiom,(
    r1_tarski(k8_intpro_1,k14_intpro_1) )).

fof(dt_k1_intpro_1,axiom,(
    $true )).

fof(dt_k2_intpro_1,axiom,(
    m1_subset_1(k2_intpro_1,k1_intpro_1) )).

fof(dt_k3_intpro_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_intpro_1)
        & m1_subset_1(B,k1_intpro_1) )
     => m1_subset_1(k3_intpro_1(A,B),k1_intpro_1) ) )).

fof(dt_k4_intpro_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_intpro_1)
        & m1_subset_1(B,k1_intpro_1) )
     => m1_subset_1(k4_intpro_1(A,B),k1_intpro_1) ) )).

fof(dt_k5_intpro_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_intpro_1)
        & m1_subset_1(B,k1_intpro_1) )
     => m1_subset_1(k5_intpro_1(A,B),k1_intpro_1) ) )).

fof(dt_k6_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => m1_subset_1(k6_intpro_1(A),k1_intpro_1) ) )).

fof(dt_k7_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => m1_subset_1(k7_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) )).

fof(dt_k8_intpro_1,axiom,(
    m1_subset_1(k8_intpro_1,k1_zfmisc_1(k1_intpro_1)) )).

fof(dt_k9_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_intpro_1)
     => m1_subset_1(k9_intpro_1(A),k1_intpro_1) ) )).

fof(dt_k10_intpro_1,axiom,(
    m1_subset_1(k10_intpro_1,k1_intpro_1) )).

fof(dt_k11_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => m1_subset_1(k11_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) )).

fof(dt_k12_intpro_1,axiom,(
    m1_subset_1(k12_intpro_1,k1_zfmisc_1(k1_intpro_1)) )).

fof(dt_k13_intpro_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
     => m1_subset_1(k13_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) )).

fof(dt_k14_intpro_1,axiom,(
    m1_subset_1(k14_intpro_1,k1_zfmisc_1(k1_intpro_1)) )).
%------------------------------------------------------------------------------