SET007 Axioms: SET007+504.ax


%------------------------------------------------------------------------------
% File     : SET007+504 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebra of Morphisms
% 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    : catalg_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  102 (  14 unit)
%            Number of atoms       :  610 (  94 equality)
%            Maximal formula depth :   24 (   8 average)
%            Number of connectives :  567 (  59 ~  ;   5  |; 264  &)
%                                         (  18 <=>; 221 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   41 (   1 propositional; 0-4 arity)
%            Number of functors    :   74 (   9 constant; 0-6 arity)
%            Number of variables   :  311 (   0 singleton; 288 !;  23 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_catalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v5_msualg_1(B,A)
           => ~ v1_catalg_1(B,A) ) ) ) )).

fof(fc1_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v4_msualg_1(k11_msafree(A,B),A)
        & v5_msualg_1(k11_msafree(A,B),A)
        & v1_msafree1(k11_msafree(A,B),A)
        & ~ v1_catalg_1(k11_msafree(A,B),A) ) ) )).

fof(rc1_catalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A)
          & v5_msualg_1(B,A)
          & v1_msafree1(B,A)
          & ~ v1_catalg_1(B,A) ) ) )).

fof(fc2_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v1_catalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( v1_relat_1(u4_msualg_1(A,B))
        & ~ v3_relat_1(u4_msualg_1(A,B))
        & v1_funct_1(u4_msualg_1(A,B)) ) ) )).

fof(rc2_catalg_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & ~ v3_relat_1(A)
      & v1_funct_1(A) ) )).

fof(fc3_catalg_1,axiom,(
    ! [A] :
      ( v1_msualg_1(k2_catalg_1(A))
      & v1_instalg1(k2_catalg_1(A)) ) )).

fof(fc4_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k2_catalg_1(A))
        & v1_msualg_1(k2_catalg_1(A))
        & ~ v2_msualg_1(k2_catalg_1(A))
        & v1_instalg1(k2_catalg_1(A)) ) ) )).

fof(cc2_catalg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_instalg1(A)
          & v2_catalg_1(A) )
       => ( ~ v3_struct_0(A)
          & ~ v2_msualg_1(A)
          & v1_instalg1(A) ) ) ) )).

fof(rc3_catalg_1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A)
      & v1_instalg1(A)
      & v2_catalg_1(A) ) )).

fof(cc3_catalg_1,axiom,(
    ! [A,B] :
      ( m1_catalg_1(B,A)
     => v2_catalg_1(B) ) )).

fof(cc4_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_catalg_1(B,A)
         => ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & v2_catalg_1(B) ) ) ) )).

fof(rc4_catalg_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_catalg_1(B,A)
      & v1_msualg_1(B)
      & v1_instalg1(B)
      & v2_catalg_1(B) ) )).

fof(fc5_catalg_1,axiom,(
    ! [A] :
      ( v1_msualg_1(k2_catalg_1(A))
      & v1_instalg1(k2_catalg_1(A))
      & v3_catalg_1(k2_catalg_1(A)) ) )).

fof(rc5_catalg_1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A)
      & v1_instalg1(A)
      & v2_catalg_1(A)
      & v3_catalg_1(A) ) )).

fof(rc6_catalg_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_catalg_1(B,A)
      & v1_msualg_1(B)
      & v1_instalg1(B)
      & v2_catalg_1(B)
      & v3_catalg_1(B) ) )).

fof(fc6_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & v2_catalg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B)) ) ) )).

fof(fc7_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_catalg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B)) ) ) )).

fof(fc8_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v2_msualg_1(A)
        & v3_catalg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B)) ) ) )).

fof(fc9_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & v2_catalg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B))
        & v1_finset_1(k2_mcart_1(B))
        & v1_finseq_1(k2_mcart_1(B)) ) ) )).

fof(fc10_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_catalg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B))
        & v1_finset_1(k2_mcart_1(B))
        & v1_finseq_1(k2_mcart_1(B)) ) ) )).

fof(fc11_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v2_msualg_1(A)
        & v3_catalg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B))
        & v1_finset_1(k2_mcart_1(B))
        & v1_finseq_1(k2_mcart_1(B)) ) ) )).

fof(fc12_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v4_msualg_1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A)))
        & v1_msualg_6(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A)))
        & v1_msafree1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A))) ) ) )).

fof(d1_catalg_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] :
              ( ( v1_funcop_1(D)
                & m1_pboole(D,A) )
             => ( D = k1_catalg_1(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k7_relat_1(C,k1_funct_1(B,E)) ) ) ) ) ) )).

fof(t1_catalg_1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k1_catalg_1(A,B,k6_relat_1(k3_card_3(B))),k2_msualg_3(A,B)) ) )).

fof(t2_catalg_1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ! [E] :
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( r2_pboole(A,k2_extens_1(A,k1_catalg_1(A,B,D)),C)
                   => k1_catalg_1(A,B,k5_relat_1(D,E)) = k13_pboole(k1_catalg_1(A,B,D),k1_catalg_1(A,C,E)) ) ) ) ) ) )).

fof(t3_catalg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( m1_pboole(C,B)
         => ! [D] :
              ( m1_pboole(D,B)
             => ( ! [E] :
                    ( r2_hidden(E,B)
                   => ( r1_tarski(k1_funct_1(C,E),k1_relat_1(A))
                      & r1_tarski(k9_relat_1(A,k1_funct_1(C,E)),k1_funct_1(D,E)) ) )
               => m3_pboole(k1_catalg_1(B,C,A),B,C,D) ) ) ) ) )).

fof(t4_catalg_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ( r2_hidden(C,k4_finseq_2(B,A))
          <=> ( k3_finseq_1(C) = B
              & r1_tarski(k2_relat_1(C),A) ) ) ) ) )).

fof(t5_catalg_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => ( r2_hidden(C,k4_finseq_2(B,A))
          <=> k3_finseq_1(C) = B ) ) ) )).

fof(t6_catalg_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) )).

fof(t7_catalg_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( ( B != np__0
          & A = k1_xboole_0 )
      <=> k4_finseq_2(B,A) = k1_xboole_0 ) ) )).

fof(t8_catalg_1,axiom,(
    ! [A,B] :
      ( r2_hidden(B,k4_finseq_2(np__1,A))
    <=> ? [C] :
          ( r2_hidden(C,A)
          & B = k9_finseq_1(C) ) ) )).

fof(t9_catalg_1,axiom,(
    ! [A,B] :
      ( r2_hidden(k9_finseq_1(B),k4_finseq_2(np__1,A))
     => r2_hidden(B,A) ) )).

fof(t10_catalg_1,axiom,(
    ! [A,B] :
      ( r2_hidden(B,k4_finseq_2(np__2,A))
    <=> ? [C,D] :
          ( r2_hidden(C,A)
          & r2_hidden(D,A)
          & B = k10_finseq_1(C,D) ) ) )).

fof(t11_catalg_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(k10_finseq_1(B,C),k4_finseq_2(np__2,A))
     => ( r2_hidden(B,A)
        & r2_hidden(C,A) ) ) )).

fof(t12_catalg_1,axiom,(
    ! [A,B] :
      ( r2_hidden(B,k4_finseq_2(np__3,A))
    <=> ? [C,D,E] :
          ( r2_hidden(C,A)
          & r2_hidden(D,A)
          & r2_hidden(E,A)
          & B = k11_finseq_1(C,D,E) ) ) )).

fof(t13_catalg_1,axiom,(
    ! [A,B,C,D] :
      ( r2_hidden(k11_finseq_1(B,C,D),k4_finseq_2(np__3,A))
     => ( r2_hidden(B,A)
        & r2_hidden(C,A)
        & r2_hidden(D,A) ) ) )).

fof(d2_catalg_1,axiom,(
    $true )).

fof(d3_catalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v1_catalg_1(B,A)
          <=> v3_relat_1(u4_msualg_1(A,B)) ) ) ) )).

fof(d4_catalg_1,axiom,(
    $true )).

fof(d5_catalg_1,axiom,(
    ! [A,B] :
      ( ( v1_msualg_1(B)
        & l1_msualg_1(B) )
     => ( B = k2_catalg_1(A)
      <=> ( u1_struct_0(B) = k2_zfmisc_1(k1_tarski(np__0),k4_finseq_2(np__2,A))
          & u1_msualg_1(B) = k2_xboole_0(k2_zfmisc_1(k1_tarski(np__1),k4_finseq_2(np__1,A)),k2_zfmisc_1(k1_tarski(np__2),k4_finseq_2(np__3,A)))
          & ! [C] :
              ( r2_hidden(C,A)
             => ( k1_funct_1(u2_msualg_1(B),k4_tarski(np__1,k9_finseq_1(C))) = k1_xboole_0
                & k1_funct_1(u3_msualg_1(B),k4_tarski(np__1,k9_finseq_1(C))) = k4_tarski(np__0,k10_finseq_1(C,C)) ) )
          & ! [C,D,E] :
              ( ( r2_hidden(C,A)
                & r2_hidden(D,A)
                & r2_hidden(E,A) )
             => ( k1_funct_1(u2_msualg_1(B),k4_tarski(np__2,k11_finseq_1(C,D,E))) = k10_finseq_1(k4_tarski(np__0,k10_finseq_1(D,E)),k4_tarski(np__0,k10_finseq_1(C,D)))
                & k1_funct_1(u3_msualg_1(B),k4_tarski(np__2,k11_finseq_1(C,D,E))) = k4_tarski(np__0,k10_finseq_1(C,E)) ) ) ) ) ) )).

fof(d6_catalg_1,axiom,(
    ! [A] :
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ( v2_catalg_1(A)
      <=> ? [B] :
            ( m1_instalg1(k2_catalg_1(B),A)
            & u1_struct_0(A) = k2_zfmisc_1(k1_tarski(np__0),k4_finseq_2(np__2,B)) ) ) ) )).

fof(d7_catalg_1,axiom,(
    ! [A,B] :
      ( ( v1_instalg1(B)
        & l1_msualg_1(B) )
     => ( m1_catalg_1(B,A)
      <=> ( m1_instalg1(k2_catalg_1(A),B)
          & u1_struct_0(B) = k2_zfmisc_1(k1_tarski(np__0),k4_finseq_2(np__2,A)) ) ) ) )).

fof(t14_catalg_1,axiom,(
    ! [A,B,C] :
      ( m1_catalg_1(C,A)
     => ( m1_catalg_1(C,B)
       => A = B ) ) )).

fof(d8_catalg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( B = k4_catalg_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D,E] :
                  ( v1_relat_1(E)
                  & v1_funct_1(E)
                  & r2_hidden(k4_tarski(D,E),k2_xboole_0(u1_struct_0(A),u1_msualg_1(A)))
                  & r2_hidden(C,k2_relat_1(E)) ) ) ) ) )).

fof(t15_catalg_1,axiom,(
    ! [A] : k4_catalg_1(k3_catalg_1(A)) = A )).

fof(d9_catalg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v3_catalg_1(A)
      <=> ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k5_numbers)
            & m2_relset_1(B,k5_numbers,k5_numbers)
            & ! [C] :
                ~ ( r2_hidden(C,u1_struct_0(A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ~ ( C = k4_tarski(D,E)
                              & k3_finseq_1(E) = k8_funct_2(k5_numbers,k5_numbers,B,D)
                              & r1_tarski(k2_zfmisc_1(k1_tarski(D),k4_finseq_2(k8_funct_2(k5_numbers,k5_numbers,B,D),k4_catalg_1(A))),u1_struct_0(A)) ) ) ) )
            & ! [C] :
                ~ ( r2_hidden(C,u1_msualg_1(A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ~ ( C = k4_tarski(D,E)
                              & k3_finseq_1(E) = k8_funct_2(k5_numbers,k5_numbers,B,D)
                              & r1_tarski(k2_zfmisc_1(k1_tarski(D),k4_finseq_2(k8_funct_2(k5_numbers,k5_numbers,B,D),k4_catalg_1(A))),u1_msualg_1(A)) ) ) ) ) ) ) ) )).

fof(t16_catalg_1,axiom,(
    ! [A] :
      ( ( v3_catalg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ~ ( ( r2_hidden(B,u1_struct_0(A))
              | r2_hidden(B,u1_msualg_1(A)) )
            & ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v1_finseq_1(D) )
                   => ~ ( B = k4_tarski(C,D)
                        & r1_tarski(k2_relat_1(D),k4_catalg_1(A)) ) ) ) ) ) )).

fof(t17_catalg_1,axiom,(
    ! [A] :
      ( ( v3_catalg_1(A)
        & l1_msualg_1(A) )
     => ! [B,C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D)
                & v1_finseq_1(D) )
             => ( ( ( r2_hidden(k4_tarski(B,C),u1_struct_0(A))
                    & r2_hidden(k4_tarski(B,D),u1_struct_0(A)) )
                  | ( r2_hidden(k4_tarski(B,C),u1_msualg_1(A))
                    & r2_hidden(k4_tarski(B,D),u1_msualg_1(A)) ) )
               => k3_finseq_1(C) = k3_finseq_1(D) ) ) ) ) )).

fof(t18_catalg_1,axiom,(
    ! [A] :
      ( ( v3_catalg_1(A)
        & l1_msualg_1(A) )
     => ! [B,C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D)
                & v1_finseq_1(D) )
             => ( ( k3_finseq_1(D) = k3_finseq_1(C)
                  & r1_tarski(k2_relat_1(D),k4_catalg_1(A)) )
               => ( ( r2_hidden(k4_tarski(B,C),u1_struct_0(A))
                   => r2_hidden(k4_tarski(B,D),u1_struct_0(A)) )
                  & ( r2_hidden(k4_tarski(B,C),u1_msualg_1(A))
                   => r2_hidden(k4_tarski(B,D),u1_msualg_1(A)) ) ) ) ) ) ) )).

fof(t19_catalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & v2_catalg_1(A)
        & v3_catalg_1(A)
        & l1_msualg_1(A) )
     => m1_catalg_1(A,k4_catalg_1(A)) ) )).

fof(d10_catalg_1,axiom,(
    ! [A] : k5_catalg_1(A) = k4_tarski(np__1,k9_finseq_1(A)) )).

fof(d11_catalg_1,axiom,(
    ! [A,B] : k6_catalg_1(A,B) = k4_tarski(np__0,k10_finseq_1(A,B)) )).

fof(d12_catalg_1,axiom,(
    ! [A,B,C] : k7_catalg_1(A,B,C) = k4_tarski(np__2,k11_finseq_1(A,B,C)) )).

fof(t20_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_catalg_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ( r2_hidden(k5_catalg_1(C),u1_msualg_1(B))
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ( r2_hidden(k6_catalg_1(C,D),u1_struct_0(B))
                      & ! [E] :
                          ( m1_subset_1(E,A)
                         => r2_hidden(k7_catalg_1(C,D,E),u1_msualg_1(B)) ) ) ) ) ) ) ) )).

fof(t21_catalg_1,axiom,(
    ! [A,B] :
      ( k5_catalg_1(A) = k5_catalg_1(B)
     => A = B ) )).

fof(t22_catalg_1,axiom,(
    ! [A,B,C,D] :
      ( k6_catalg_1(A,C) = k6_catalg_1(B,D)
     => ( A = B
        & C = D ) ) )).

fof(t23_catalg_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( k7_catalg_1(A,C,E) = k7_catalg_1(B,D,F)
     => ( A = B
        & C = D
        & E = F ) ) )).

fof(t24_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_catalg_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ? [D] :
                  ( m1_subset_1(D,A)
                  & ? [E] :
                      ( m1_subset_1(E,A)
                      & C = k9_catalg_1(A,D,E) ) ) ) ) ) )).

fof(t25_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(k3_catalg_1(A)))
         => ( ( k1_mcart_1(B) = np__1
              & k3_finseq_1(k2_mcart_1(B)) = np__1 )
            | ( k1_mcart_1(B) = np__2
              & k3_finseq_1(k2_mcart_1(B)) = np__3 ) ) ) ) )).

fof(t26_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(k3_catalg_1(A)))
         => ~ ( ( k1_mcart_1(B) = np__1
                | k3_finseq_1(k2_mcart_1(B)) = np__1 )
              & ! [C] :
                  ( m1_subset_1(C,A)
                 => B != k8_catalg_1(A,C) ) ) ) ) )).

fof(t27_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(k3_catalg_1(A)))
         => ~ ( ( k1_mcart_1(B) = np__2
                | k3_finseq_1(k2_mcart_1(B)) = np__3 )
              & ! [C] :
                  ( m1_subset_1(C,A)
                 => ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => B != k10_catalg_1(A,C,D,E) ) ) ) ) ) ) )).

fof(t28_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ( k1_msualg_1(k3_catalg_1(A),k8_catalg_1(A,B)) = k1_xboole_0
            & k2_msualg_1(k3_catalg_1(A),k8_catalg_1(A,B)) = k9_catalg_1(A,B,B) ) ) ) )).

fof(t29_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( k1_msualg_1(k3_catalg_1(A),k10_catalg_1(A,B,C,D)) = k2_finseq_4(u1_struct_0(k3_catalg_1(A)),k9_catalg_1(A,C,D),k9_catalg_1(A,B,C))
                    & k2_msualg_1(k3_catalg_1(A),k10_catalg_1(A,B,C,D)) = k9_catalg_1(A,B,D) ) ) ) ) ) )).

fof(d13_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))))
                    & m2_relset_1(D,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B)))) )
                 => ( D = k11_catalg_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k3_catalg_1(u1_cat_1(A))))
                       => k8_funct_2(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))),D,E) = k4_tarski(np__0,k5_relat_1(k2_mcart_1(E),k12_cat_1(A,B,C))) ) ) ) ) ) ) )).

fof(d14_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))))
                    & m2_relset_1(D,u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B)))) )
                 => ( D = k12_catalg_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(k3_catalg_1(u1_cat_1(A))))
                       => k8_funct_2(u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))),D,E) = k4_tarski(k1_mcart_1(E),k5_relat_1(k2_mcart_1(E),k12_cat_1(A,B,C))) ) ) ) ) ) ) )).

fof(t30_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => k8_funct_2(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))),k11_catalg_1(A,B,C),k9_catalg_1(u1_cat_1(A),D,E)) = k9_catalg_1(u1_cat_1(B),k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ) ) ) ) )).

fof(t31_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))),k12_catalg_1(A,B,C),k8_catalg_1(u1_cat_1(A),D)) = k8_catalg_1(u1_cat_1(B),k13_cat_1(A,B,C,D)) ) ) ) ) )).

fof(t32_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => k8_funct_2(u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))),k12_catalg_1(A,B,C),k10_catalg_1(u1_cat_1(A),D,E,F)) = k10_catalg_1(u1_cat_1(B),k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E),k13_cat_1(A,B,C,F)) ) ) ) ) ) ) )).

fof(t33_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => r3_pua2mss1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)) ) ) ) )).

fof(t34_catalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( l3_msualg_1(B,k3_catalg_1(A))
         => ! [C] :
              ( m1_subset_1(C,A)
             => k3_msualg_1(k3_catalg_1(A),k8_catalg_1(A,C),B) = k1_tarski(k1_xboole_0) ) ) ) )).

fof(d15_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,k3_catalg_1(u1_cat_1(A)))
            & l3_msualg_1(B,k3_catalg_1(u1_cat_1(A))) )
         => ( B = k13_catalg_1(A)
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => k1_funct_1(u4_msualg_1(k3_catalg_1(u1_cat_1(A)),B),k9_catalg_1(u1_cat_1(A),C,D)) = k6_cat_1(A,C,D) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k8_catalg_1(u1_cat_1(A),C),B),k1_xboole_0) = k10_cat_1(A,C) )
              & ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ( ( k2_cat_1(A,F) = C
                                      & k3_cat_1(A,F) = D
                                      & k2_cat_1(A,G) = D
                                      & k3_cat_1(A,G) = E )
                                   => k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),C,D,E),B),k2_finseq_4(u2_cat_1(A),G,F)) = k4_cat_1(A,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_catalg_1,axiom,(
    $true )).

fof(t36_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k4_msualg_1(k3_catalg_1(u1_cat_1(A)),k8_catalg_1(u1_cat_1(A),B),k13_catalg_1(A)) = k6_cat_1(A,B,B) ) ) )).

fof(t37_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ( k3_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)) = k4_card_3(k2_finseq_4(k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,C,D),k6_cat_1(A,B,C)))
                    & k4_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)) = k6_cat_1(A,B,D) ) ) ) ) ) )).

fof(t38_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => m3_pboole(k1_catalg_1(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),C),u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)))) ) ) ) )).

fof(t39_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( r2_hidden(E,k3_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)))
                    <=> ? [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                          & ? [G] :
                              ( m1_subset_1(G,u2_cat_1(A))
                              & E = k2_finseq_4(u2_cat_1(A),F,G)
                              & k2_cat_1(A,G) = B
                              & k3_cat_1(A,G) = C
                              & k2_cat_1(A,F) = C
                              & k3_cat_1(A,F) = D ) ) ) ) ) ) ) )).

fof(t40_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u2_cat_1(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u2_cat_1(A))
                                 => ( ( r2_hidden(G,k6_cat_1(A,D,E))
                                      & r2_hidden(H,k6_cat_1(A,E,F)) )
                                   => ! [I] :
                                        ( m1_subset_1(I,k3_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),D,E,F),k13_catalg_1(A)))
                                       => ( I = k2_finseq_4(u2_cat_1(A),H,G)
                                         => ! [J] :
                                              ( m3_pboole(J,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C))))
                                             => ( r6_pboole(u1_struct_0(k3_catalg_1(u1_cat_1(A))),J,k1_catalg_1(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),C))
                                               => k5_msualg_3(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)),k10_catalg_1(u1_cat_1(A),D,E,F),J,I) = k2_finseq_4(u2_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,H),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_catalg_1,axiom,(
    $true )).

fof(t42_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ( ( r2_hidden(E,k6_cat_1(A,B,C))
                              & r2_hidden(F,k6_cat_1(A,C,D)) )
                           => k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),F,E)) = k4_cat_1(A,E,F) ) ) ) ) ) ) ) )).

fof(t43_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u2_cat_1(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u2_cat_1(A))
                                 => ( ( r2_hidden(F,k6_cat_1(A,B,C))
                                      & r2_hidden(G,k6_cat_1(A,C,D))
                                      & r2_hidden(H,k6_cat_1(A,D,E)) )
                                   => k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,D,E),k13_catalg_1(A)),k10_finseq_1(H,k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),G,F)))) = k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,E),k13_catalg_1(A)),k10_finseq_1(k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),C,D,E),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),H,G)),F)) ) ) ) ) ) ) ) ) ) )).

fof(t44_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                   => ( k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,C),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),k10_cat_1(A,C),D)) = D
                      & k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,B,C),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),D,k10_cat_1(A,B))) = D ) ) ) ) ) ) )).

fof(t45_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ? [D] :
                  ( m3_pboole(D,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C))))
                  & r6_pboole(u1_struct_0(k3_catalg_1(u1_cat_1(A))),D,k1_catalg_1(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),C))
                  & r1_msualg_3(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)),D) ) ) ) ) )).

fof(s1_catalg_1,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s1_catalg_1)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_catalg_1)
             => r1_tarski(f3_s1_catalg_1(A,B),f2_s1_catalg_1) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_catalg_1)
         => r2_hidden(f5_s1_catalg_1(A),f3_s1_catalg_1(A,A)) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_catalg_1)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_catalg_1)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_catalg_1)
                 => ! [D] :
                      ( m1_subset_1(D,f2_s1_catalg_1)
                     => ! [E] :
                          ( m1_subset_1(E,f2_s1_catalg_1)
                         => ( ( r2_hidden(D,f3_s1_catalg_1(A,B))
                              & r2_hidden(E,f3_s1_catalg_1(B,C)) )
                           => r2_hidden(f4_s1_catalg_1(A,B,C,E,D),f3_s1_catalg_1(A,C)) ) ) ) ) ) ) )
   => ? [A] :
        ( v4_msualg_1(A,k3_catalg_1(f1_s1_catalg_1))
        & l3_msualg_1(A,k3_catalg_1(f1_s1_catalg_1))
        & ! [B] :
            ( m1_subset_1(B,f1_s1_catalg_1)
           => ! [C] :
                ( m1_subset_1(C,f1_s1_catalg_1)
               => k1_funct_1(u4_msualg_1(k3_catalg_1(f1_s1_catalg_1),A),k9_catalg_1(f1_s1_catalg_1,B,C)) = f3_s1_catalg_1(B,C) ) )
        & ! [B] :
            ( m1_subset_1(B,f1_s1_catalg_1)
           => k1_funct_1(k5_msualg_1(k3_catalg_1(f1_s1_catalg_1),k8_catalg_1(f1_s1_catalg_1,B),A),k1_xboole_0) = f5_s1_catalg_1(B) )
        & ! [B] :
            ( m1_subset_1(B,f1_s1_catalg_1)
           => ! [C] :
                ( m1_subset_1(C,f1_s1_catalg_1)
               => ! [D] :
                    ( m1_subset_1(D,f1_s1_catalg_1)
                   => ! [E] :
                        ( m1_subset_1(E,f2_s1_catalg_1)
                       => ! [F] :
                            ( m1_subset_1(F,f2_s1_catalg_1)
                           => ( ( r2_hidden(E,f3_s1_catalg_1(B,C))
                                & r2_hidden(F,f3_s1_catalg_1(C,D)) )
                             => k1_funct_1(k5_msualg_1(k3_catalg_1(f1_s1_catalg_1),k10_catalg_1(f1_s1_catalg_1,B,C,D),A),k2_finseq_4(f2_s1_catalg_1,F,E)) = f4_s1_catalg_1(B,C,D,F,E) ) ) ) ) ) ) ) )).

fof(dt_m1_catalg_1,axiom,(
    ! [A,B] :
      ( m1_catalg_1(B,A)
     => ( v1_instalg1(B)
        & l1_msualg_1(B) ) ) )).

fof(existence_m1_catalg_1,axiom,(
    ! [A] :
    ? [B] : m1_catalg_1(B,A) )).

fof(dt_k1_catalg_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_funcop_1(k1_catalg_1(A,B,C))
        & m1_pboole(k1_catalg_1(A,B,C),A) ) ) )).

fof(dt_k2_catalg_1,axiom,(
    ! [A] :
      ( v1_msualg_1(k2_catalg_1(A))
      & l1_msualg_1(k2_catalg_1(A)) ) )).

fof(dt_k3_catalg_1,axiom,(
    ! [A] :
      ( v1_msualg_1(k3_catalg_1(A))
      & m1_catalg_1(k3_catalg_1(A),A) ) )).

fof(redefinition_k3_catalg_1,axiom,(
    ! [A] : k3_catalg_1(A) = k2_catalg_1(A) )).

fof(dt_k4_catalg_1,axiom,(
    $true )).

fof(dt_k5_catalg_1,axiom,(
    $true )).

fof(dt_k6_catalg_1,axiom,(
    $true )).

fof(dt_k7_catalg_1,axiom,(
    $true )).

fof(dt_k8_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k8_catalg_1(A,B),u1_msualg_1(k3_catalg_1(A))) ) )).

fof(redefinition_k8_catalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k8_catalg_1(A,B) = k5_catalg_1(B) ) )).

fof(dt_k9_catalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k9_catalg_1(A,B,C),u1_struct_0(k3_catalg_1(A))) ) )).

fof(redefinition_k9_catalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k9_catalg_1(A,B,C) = k6_catalg_1(B,C) ) )).

fof(dt_k10_catalg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => m1_subset_1(k10_catalg_1(A,B,C,D),u1_msualg_1(k3_catalg_1(A))) ) )).

fof(redefinition_k10_catalg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => k10_catalg_1(A,B,C,D) = k7_catalg_1(B,C,D) ) )).

fof(dt_k11_catalg_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => ( v1_funct_1(k11_catalg_1(A,B,C))
        & v1_funct_2(k11_catalg_1(A,B,C),u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))))
        & m2_relset_1(k11_catalg_1(A,B,C),u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B)))) ) ) )).

fof(dt_k12_catalg_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => ( v1_funct_1(k12_catalg_1(A,B,C))
        & v1_funct_2(k12_catalg_1(A,B,C),u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))))
        & m2_relset_1(k12_catalg_1(A,B,C),u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B)))) ) ) )).

fof(dt_k13_catalg_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v4_msualg_1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A)))
        & l3_msualg_1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A))) ) ) )).
%------------------------------------------------------------------------------