SET007 Axioms: SET007+441.ax


%------------------------------------------------------------------------------
% File     : SET007+441 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Minimal Signature for Partial Algebra
% 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    : pua2mss1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  102 (   4 unit)
%            Number of atoms       :  686 (  67 equality)
%            Maximal formula depth :   22 (   9 average)
%            Number of connectives :  653 (  69 ~  ;   2  |; 302  &)
%                                         (  31 <=>; 249 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   53 (   1 propositional; 0-4 arity)
%            Number of functors    :   79 (  16 constant; 0-6 arity)
%            Number of variables   :  323 (   0 singleton; 295 !;  28 ?)
%            Maximal term depth    :    7 (   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(rc1_pua2mss1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] :
          ( m1_relset_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C) ) ) )).

fof(cc1_pua2mss1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( m1_finseq_1(B,A)
         => v2_relat_1(B) ) ) )).

fof(rc2_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v4_unialg_1(B,A)
          & v5_unialg_1(B,A) ) ) )).

fof(cc2_pua2mss1,axiom,(
    ! [A] :
      ( l1_unialg_1(A)
     => ( v8_unialg_1(A)
       => ~ v3_struct_0(A) ) ) )).

fof(cc3_pua2mss1,axiom,(
    ! [A,B] :
      ( m2_pua2mss1(B,A)
     => ( v2_relat_1(B)
        & v2_funct_1(B) ) ) )).

fof(cc4_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_pua2mss1(B,A)
         => ( ~ v1_xboole_0(B)
            & v2_relat_1(B)
            & v2_funct_1(B) ) ) ) )).

fof(fc1_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(k7_pua2mss1(A))
        & v1_relat_2(k7_pua2mss1(A))
        & v3_relat_2(k7_pua2mss1(A))
        & v8_relat_2(k7_pua2mss1(A))
        & v1_partfun1(k7_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(fc2_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(k10_pua2mss1(A))
        & v1_relat_2(k10_pua2mss1(A))
        & v3_relat_2(k10_pua2mss1(A))
        & v8_relat_2(k10_pua2mss1(A))
        & v1_partfun1(k10_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(fc3_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A) )
     => ( ~ v3_struct_0(k12_pua2mss1(A,B))
        & v1_msualg_1(k12_pua2mss1(A,B))
        & ~ v2_msualg_1(k12_pua2mss1(A,B)) ) ) )).

fof(t1_pua2mss1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(k4_card_3(A),k4_card_3(B))
           => ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) )).

fof(t2_pua2mss1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( k4_card_3(A) = k4_card_3(B)
           => A = B ) ) ) )).

fof(d1_pua2mss1,axiom,(
    ! [A] :
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_finseq_1(u1_unialg_1(A)))
         => k2_pua2mss1(A,B) = k1_funct_1(u1_unialg_1(A),B) ) ) )).

fof(t3_pua2mss1,axiom,(
    ! [A,B] :
      ( m1_eqrel_1(B,A)
     => ! [C,D,E] :
          ( ( r2_hidden(C,D)
            & r2_hidden(D,B)
            & r2_hidden(C,E)
            & r2_hidden(E,B) )
         => D = E ) ) )).

fof(t4_pua2mss1,axiom,(
    ! [A,B] :
      ( r1_setfam_1(A,B)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => ? [D] :
              ( m2_finseq_1(D,B)
              & r1_tarski(k4_card_3(C),k4_card_3(D)) ) ) ) )).

fof(t5_pua2mss1,axiom,(
    ! [A,B] :
      ( m1_eqrel_1(B,A)
     => ! [C] :
          ( m1_eqrel_1(C,A)
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,C)
                & m2_relset_1(D,B,C) )
             => ( ! [E] :
                    ( r2_hidden(E,B)
                   => r1_tarski(E,k1_funct_1(D,E)) )
               => ! [E] :
                    ( m2_finseq_1(E,B)
                   => ! [F] :
                        ( m2_finseq_1(F,C)
                       => ( r1_tarski(k4_card_3(E),k4_card_3(F))
                        <=> k1_partfun1(k5_numbers,B,B,C,E,D) = F ) ) ) ) ) ) ) )).

fof(t6_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ~ ( r1_tarski(k2_relat_1(B),k3_tarski(A))
          & ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ~ ( k1_relat_1(C) = k1_relat_1(B)
                  & r1_tarski(k2_relat_1(C),A)
                  & r2_hidden(B,k4_card_3(C)) ) ) ) ) )).

fof(t7_pua2mss1,axiom,(
    ! [A,B] :
      ( m1_eqrel_1(B,A)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => ? [D] :
              ( m2_finseq_1(D,B)
              & r2_hidden(C,k4_card_3(D)) ) ) ) )).

fof(d2_pua2mss1,axiom,(
    ! [A] : k3_pua2mss1(A) = k8_eqrel_1(A,k6_partfun1(A)) )).

fof(t14_pua2mss1,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,k3_pua2mss1(A))
     => ? [C] :
          ( m2_finseq_1(C,A)
          & k4_card_3(B) = k1_tarski(C) ) ) )).

fof(d3_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m2_pua2mss1(B,A)
      <=> ( m1_eqrel_1(k2_relat_1(B),A)
          & v2_funct_1(B) ) ) ) )).

fof(d4_pua2mss1,axiom,(
    ! [A,B] :
      ( m2_pua2mss1(B,A)
     => ! [C] :
          ( r2_hidden(C,A)
         => ! [D] :
              ( D = k6_pua2mss1(A,B,C)
            <=> ( r2_hidden(D,k1_relat_1(B))
                & r2_hidden(C,k1_funct_1(B,D)) ) ) ) ) )).

fof(t15_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v2_relat_1(B)
        & v1_funct_1(B) )
     => ( ( k3_card_3(B) = A
          & ! [C,D] :
              ( ( r2_hidden(C,k1_relat_1(B))
                & r2_hidden(D,k1_relat_1(B)) )
             => ( C = D
                | r1_xboole_0(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) )
       => m2_pua2mss1(B,A) ) ) )).

fof(t16_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_eqrel_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,C)
                    & m2_relset_1(D,A,C) )
                 => ( ( r1_tarski(C,k2_relat_1(D))
                      & v2_funct_1(D) )
                   => m2_pua2mss1(D,B) ) ) ) ) ) )).

fof(d5_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k7_pua2mss1(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> ! [E] :
                          ( m1_pua2mss1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
                         => ! [F] :
                              ( ( v1_relat_1(F)
                                & v1_funct_1(F)
                                & v1_finseq_1(F) )
                             => ! [G] :
                                  ( ( v1_relat_1(G)
                                    & v1_funct_1(G)
                                    & v1_finseq_1(G) )
                                 => ( r2_hidden(k7_finseq_1(k7_finseq_1(F,k12_finseq_1(u1_struct_0(A),C)),G),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),E))
                                  <=> r2_hidden(k7_finseq_1(k7_finseq_1(F,k12_finseq_1(u1_struct_0(A),D)),G),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),E)) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => ( C = k8_pua2mss1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(k4_tarski(D,E),C)
                        <=> ( r2_hidden(k4_tarski(D,E),B)
                            & ! [F] :
                                ( m1_pua2mss1(F,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
                               => ! [G] :
                                    ( ( v1_relat_1(G)
                                      & v1_funct_1(G)
                                      & v1_finseq_1(G) )
                                   => ! [H] :
                                        ( ( v1_relat_1(H)
                                          & v1_funct_1(H)
                                          & v1_finseq_1(H) )
                                       => ( ( r2_hidden(k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),D)),H),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),F))
                                            & r2_hidden(k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),E)),H),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),F)) )
                                         => r2_hidden(k4_tarski(k1_funct_1(F,k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),D)),H)),k1_funct_1(F,k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),E)),H))),B) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
                 => ( D = k9_pua2mss1(A,B,C)
                  <=> ? [E] :
                        ( m1_pboole(E,k5_numbers)
                        & D = k1_funct_1(E,C)
                        & k1_funct_1(E,np__0) = B
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( m2_relset_1(G,u1_struct_0(A),u1_struct_0(A))
                               => ( G = k1_funct_1(E,F)
                                 => k1_funct_1(E,k1_nat_1(F,np__1)) = k8_pua2mss1(A,G) ) ) ) ) ) ) ) ) ) )).

fof(t17_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( k9_pua2mss1(A,B,np__0) = B
            & k9_pua2mss1(A,B,np__1) = k8_pua2mss1(A,B) ) ) ) )).

fof(t18_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => k9_pua2mss1(A,C,k1_nat_1(B,np__1)) = k8_pua2mss1(A,k9_pua2mss1(A,C,B)) ) ) ) )).

fof(t19_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
                 => k9_pua2mss1(A,D,k1_nat_1(B,C)) = k9_pua2mss1(A,k9_pua2mss1(A,D,B),C) ) ) ) ) )).

fof(t20_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r1_tarski(B,k7_pua2mss1(A))
           => ( v1_partfun1(k8_pua2mss1(A,B),u1_struct_0(A),u1_struct_0(A))
              & v3_relat_2(k8_pua2mss1(A,B))
              & v8_relat_2(k8_pua2mss1(A,B)) ) ) ) ) )).

fof(t21_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => r1_tarski(k8_pua2mss1(A,B),B) ) ) )).

fof(t22_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r1_tarski(B,k7_pua2mss1(A))
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( v1_partfun1(k9_pua2mss1(A,B,C),u1_struct_0(A),u1_struct_0(A))
                  & v3_relat_2(k9_pua2mss1(A,B,C))
                  & v8_relat_2(k9_pua2mss1(A,B,C)) ) ) ) ) ) )).

fof(d8_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k10_pua2mss1(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => r2_hidden(k4_tarski(C,D),k9_pua2mss1(A,k7_pua2mss1(A),E)) ) ) ) ) ) ) ) )).

fof(t23_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r1_tarski(k10_pua2mss1(A),k7_pua2mss1(A)) ) )).

fof(d9_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( r1_pua2mss1(A,B,C)
              <=> ! [D] :
                    ( m2_finseq_1(D,C)
                   => ? [E] :
                        ( m2_subset_1(E,k1_zfmisc_1(A),C)
                        & r1_tarski(k9_relat_1(B,k4_card_3(D)),E) ) ) ) ) ) ) )).

fof(d10_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( r2_pua2mss1(A,B,C)
              <=> ( r1_pua2mss1(A,B,C)
                  & ! [D] :
                      ( m2_finseq_1(D,C)
                     => ( ~ r1_xboole_0(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B))
                       => r1_tarski(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B)) ) ) ) ) ) ) ) )).

fof(t24_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_pua2mss1(B,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
         => r2_pua2mss1(u1_struct_0(A),B,k3_pua2mss1(u1_struct_0(A))) ) ) )).

fof(t25_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_pua2mss1(B,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
         => r2_pua2mss1(u1_struct_0(A),B,k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))) ) ) )).

fof(d11_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_eqrel_1(B,u1_struct_0(A))
         => ( m3_pua2mss1(B,A)
          <=> ! [C] :
                ( m1_pua2mss1(C,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
               => r2_pua2mss1(u1_struct_0(A),C,B) ) ) ) ) )).

fof(d12_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_pua2mss1(B,u1_struct_0(A))
         => ( m4_pua2mss1(B,A)
          <=> m3_pua2mss1(k4_pua2mss1(u1_struct_0(A),B),A) ) ) ) )).

fof(t26_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m3_pua2mss1(k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A)),A) ) )).

fof(t27_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F,G] :
                          ( r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(F)),E),k4_card_3(C))
                         => ( ! [H] :
                                ( m2_subset_1(H,k1_zfmisc_1(A),B)
                               => ~ ( r2_hidden(F,H)
                                    & r2_hidden(G,H) ) )
                            | r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(G)),E),k4_card_3(C)) ) ) ) ) ) ) ) )).

fof(t28_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_pua2mss1(B,A)
         => r1_setfam_1(B,k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))) ) ) )).

fof(d13_pua2mss1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( l1_msualg_1(B)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                  <=> ( k1_relat_1(C) = u1_struct_0(A)
                      & k1_relat_1(D) = u1_msualg_1(A)
                      & r1_tarski(k2_relat_1(C),u1_struct_0(B))
                      & r1_tarski(k2_relat_1(D),u1_msualg_1(B))
                      & k5_relat_1(u3_msualg_1(A),C) = k5_relat_1(D,u3_msualg_1(B))
                      & ! [E,F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ( ( r2_hidden(E,u1_msualg_1(A))
                              & F = k1_funct_1(u2_msualg_1(A),E) )
                           => k5_relat_1(F,C) = k1_funct_1(u2_msualg_1(B),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).

fof(t29_pua2mss1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) )).

fof(t30_pua2mss1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( l1_msualg_1(B)
         => ! [C] :
              ( l1_msualg_1(C)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ( ( r3_pua2mss1(A,B,D,F)
                                  & r3_pua2mss1(B,C,E,G) )
                               => r3_pua2mss1(A,C,k5_relat_1(D,E),k5_relat_1(F,G)) ) ) ) ) ) ) ) ) )).

fof(d14_pua2mss1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( l1_msualg_1(B)
         => ( r4_pua2mss1(A,B)
          <=> ? [C] :
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & ? [D] :
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & r3_pua2mss1(B,A,C,D)
                    & k2_relat_1(C) = u1_struct_0(A)
                    & k2_relat_1(D) = u1_msualg_1(A) ) ) ) ) ) )).

fof(t31_pua2mss1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( l1_msualg_1(B)
         => ! [C] :
              ( l1_msualg_1(C)
             => ( ( r4_pua2mss1(A,B)
                  & r4_pua2mss1(B,C) )
               => r4_pua2mss1(A,C) ) ) ) ) )).

fof(d16_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,B)
             => ! [D] :
                  ( m2_pua2mss1(D,u1_msualg_1(B))
                 => ( r6_pua2mss1(A,B,C,D)
                  <=> ( m4_pua2mss1(u4_msualg_1(B,C),A)
                      & k1_relat_1(D) = k4_finseq_1(u1_unialg_1(A))
                      & ! [E] :
                          ( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
                         => m2_pua2mss1(k7_relat_1(u5_msualg_1(B,C),k1_funct_1(D,E)),k2_pua2mss1(A,E)) ) ) ) ) ) ) ) )).

fof(d17_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ( r7_pua2mss1(A,B)
          <=> ? [C] :
                ( l3_msualg_1(C,B)
                & ? [D] :
                    ( m2_pua2mss1(D,u1_msualg_1(B))
                    & r6_pua2mss1(A,B,C,D) ) ) ) ) ) )).

fof(t32_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_pua2mss1(B,A)
         => r7_pua2mss1(A,k12_pua2mss1(A,B)) ) ) )).

fof(t33_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( l3_msualg_1(C,B)
             => ! [D] :
                  ( m2_pua2mss1(D,u1_msualg_1(B))
                 => ( r6_pua2mss1(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
                       => ! [F] :
                            ( m2_finseq_1(F,k2_relat_1(u4_msualg_1(B,C)))
                           => ~ ( r1_tarski(k4_card_3(F),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,E)))
                                & ! [G] :
                                    ( m1_subset_1(G,u1_msualg_1(B))
                                   => ~ ( k5_relat_1(k1_msualg_1(B,G),u4_msualg_1(B,C)) = F
                                        & r2_hidden(G,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ) ) )).

fof(t34_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_pua2mss1(B,A)
         => ( B = k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & ~ v2_msualg_1(C)
                  & l1_msualg_1(C) )
               => ( r7_pua2mss1(A,C)
                 => r5_pua2mss1(k12_pua2mss1(A,B),C) ) ) ) ) ) )).

fof(s1_pua2mss1,axiom,(
    ? [A] :
      ( m2_relset_1(A,f1_s1_pua2mss1,f2_s1_pua2mss1)
      & ? [B] :
          ( m1_pboole(B,k5_numbers)
          & A = k1_funct_1(B,f3_s1_pua2mss1)
          & k1_funct_1(B,np__0) = f4_s1_pua2mss1
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_relset_1(D,f1_s1_pua2mss1,f2_s1_pua2mss1)
                 => ( D = k1_funct_1(B,C)
                   => k1_funct_1(B,k1_nat_1(C,np__1)) = f5_s1_pua2mss1(D,C) ) ) ) ) ) )).

fof(s2_pua2mss1,axiom,(
    ! [A] :
      ( m2_relset_1(A,f1_s2_pua2mss1,f2_s2_pua2mss1)
     => ! [B] :
          ( m2_relset_1(B,f1_s2_pua2mss1,f2_s2_pua2mss1)
         => ( ( ! [C] :
                  ( m1_subset_1(C,f1_s2_pua2mss1)
                 => ! [D] :
                      ( m1_subset_1(D,f2_s2_pua2mss1)
                     => ( r2_hidden(k4_tarski(C,D),A)
                      <=> p1_s2_pua2mss1(C,D) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s2_pua2mss1)
                 => ! [D] :
                      ( m1_subset_1(D,f2_s2_pua2mss1)
                     => ( r2_hidden(k4_tarski(C,D),B)
                      <=> p1_s2_pua2mss1(C,D) ) ) ) )
           => A = B ) ) ) )).

fof(s3_pua2mss1,axiom,(
    ! [A] :
      ( m2_relset_1(A,f1_s3_pua2mss1,f2_s3_pua2mss1)
     => ! [B] :
          ( m2_relset_1(B,f1_s3_pua2mss1,f2_s3_pua2mss1)
         => ~ ( ? [C] :
                  ( m1_pboole(C,k5_numbers)
                  & A = k1_funct_1(C,f3_s3_pua2mss1)
                  & k1_funct_1(C,np__0) = f4_s3_pua2mss1
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_relset_1(E,f1_s3_pua2mss1,f2_s3_pua2mss1)
                         => ( E = k1_funct_1(C,D)
                           => k1_funct_1(C,k1_nat_1(D,np__1)) = f5_s3_pua2mss1(E,D) ) ) ) )
              & ? [C] :
                  ( m1_pboole(C,k5_numbers)
                  & B = k1_funct_1(C,f3_s3_pua2mss1)
                  & k1_funct_1(C,np__0) = f4_s3_pua2mss1
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_relset_1(E,f1_s3_pua2mss1,f2_s3_pua2mss1)
                         => ( E = k1_funct_1(C,D)
                           => k1_funct_1(C,k1_nat_1(D,np__1)) = f5_s3_pua2mss1(E,D) ) ) ) )
              & A != B ) ) ) )).

fof(s4_pua2mss1,axiom,
    ( ( p1_s4_pua2mss1(f1_s4_pua2mss1)
      & k3_finseq_1(f1_s4_pua2mss1) = k3_finseq_1(f2_s4_pua2mss1)
      & ! [A] :
          ( ( v1_relat_1(A)
            & v1_funct_1(A)
            & v1_finseq_1(A) )
         => ! [B] :
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ! [C,D] :
                  ( ( p1_s4_pua2mss1(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(C)),B))
                    & p2_s4_pua2mss1(C,D) )
                 => p1_s4_pua2mss1(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(D)),B)) ) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k4_finseq_1(f1_s4_pua2mss1))
           => p2_s4_pua2mss1(k1_funct_1(f1_s4_pua2mss1,A),k1_funct_1(f2_s4_pua2mss1,A)) ) ) )
   => p1_s4_pua2mss1(f2_s4_pua2mss1) )).

fof(dt_m1_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
     => ! [D] :
          ( m1_pua2mss1(D,A,B,C)
         => ( v1_funct_1(D)
            & m2_relset_1(D,A,B) ) ) ) )).

fof(existence_m1_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
     => ? [D] : m1_pua2mss1(D,A,B,C) ) )).

fof(redefinition_m1_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
     => ! [D] :
          ( m1_pua2mss1(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) )).

fof(dt_m2_pua2mss1,axiom,(
    ! [A,B] :
      ( m2_pua2mss1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) )).

fof(existence_m2_pua2mss1,axiom,(
    ! [A] :
    ? [B] : m2_pua2mss1(B,A) )).

fof(dt_m3_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_pua2mss1(B,A)
         => m1_eqrel_1(B,u1_struct_0(A)) ) ) )).

fof(existence_m3_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m3_pua2mss1(B,A) ) )).

fof(dt_m4_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m4_pua2mss1(B,A)
         => m2_pua2mss1(B,u1_struct_0(A)) ) ) )).

fof(existence_m4_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m4_pua2mss1(B,A) ) )).

fof(reflexivity_r5_pua2mss1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => r5_pua2mss1(A,A) ) )).

fof(redefinition_r5_pua2mss1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ( r5_pua2mss1(A,B)
      <=> r4_pua2mss1(A,B) ) ) )).

fof(dt_k1_pua2mss1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
     => m1_subset_1(k1_pua2mss1(A,B),k1_zfmisc_1(k4_partfun1(k3_finseq_2(A),A))) ) )).

fof(redefinition_k1_pua2mss1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
     => k1_pua2mss1(A,B) = k2_relat_1(B) ) )).

fof(dt_k2_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A)
        & m1_subset_1(B,k4_finseq_1(u1_unialg_1(A))) )
     => m1_pua2mss1(k2_pua2mss1(A,B),k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A))) ) )).

fof(dt_k3_pua2mss1,axiom,(
    ! [A] : m1_eqrel_1(k3_pua2mss1(A),A) )).

fof(dt_k4_pua2mss1,axiom,(
    ! [A,B] :
      ( m2_pua2mss1(B,A)
     => m1_eqrel_1(k4_pua2mss1(A,B),A) ) )).

fof(redefinition_k4_pua2mss1,axiom,(
    ! [A,B] :
      ( m2_pua2mss1(B,A)
     => k4_pua2mss1(A,B) = k2_relat_1(B) ) )).

fof(dt_k5_pua2mss1,axiom,(
    ! [A,B] :
      ( m1_eqrel_1(B,A)
     => m2_pua2mss1(k5_pua2mss1(A,B),A) ) )).

fof(redefinition_k5_pua2mss1,axiom,(
    ! [A,B] :
      ( m1_eqrel_1(B,A)
     => k5_pua2mss1(A,B) = k6_relat_1(B) ) )).

fof(dt_k6_pua2mss1,axiom,(
    $true )).

fof(dt_k7_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m2_relset_1(k7_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k8_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => m2_relset_1(k8_pua2mss1(A,B),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k9_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,k5_numbers) )
     => m2_relset_1(k9_pua2mss1(A,B,C),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k10_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m2_relset_1(k10_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k11_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m4_pua2mss1(B,A) )
     => m3_pua2mss1(k11_pua2mss1(A,B),A) ) )).

fof(redefinition_k11_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m4_pua2mss1(B,A) )
     => k11_pua2mss1(A,B) = k2_relat_1(B) ) )).

fof(dt_k12_pua2mss1,axiom,(
    ! [A,B] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A) )
     => ( v1_msualg_1(k12_pua2mss1(A,B))
        & l1_msualg_1(k12_pua2mss1(A,B)) ) ) )).

fof(dt_k13_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => m1_subset_1(k13_pua2mss1(A,B,C),k4_finseq_1(u1_unialg_1(A))) ) )).

fof(redefinition_k13_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => k13_pua2mss1(A,B,C) = k1_mcart_1(C) ) )).

fof(dt_k14_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => m2_finseq_2(k14_pua2mss1(A,B,C),B,k3_finseq_2(B)) ) )).

fof(redefinition_k14_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_pua2mss1(B,A)
        & m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
     => k14_pua2mss1(A,B,C) = k2_mcart_1(C) ) )).

fof(t8_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,B)
                 => m1_eqrel_1(a_4_0_pua2mss1(A,B,C,D),k2_zfmisc_1(A,B)) ) ) ) ) )).

fof(t9_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => m1_eqrel_1(a_2_0_pua2mss1(A,B),k3_finseq_2(A)) ) ) )).

fof(t10_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => m1_eqrel_1(a_3_0_pua2mss1(A,B,C),k4_finseq_2(B,A)) ) ) ) )).

fof(t11_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( r1_tarski(B,A)
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => m1_eqrel_1(a_3_1_pua2mss1(A,B,C),B) ) ) ) )).

fof(t12_pua2mss1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( m1_eqrel_1(B,k1_relat_1(A))
         => m1_eqrel_1(a_2_1_pua2mss1(A,B),A) ) ) )).

fof(t13_pua2mss1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k3_pua2mss1(A) = a_1_0_pua2mss1(A) ) )).

fof(d15_pua2mss1,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_pua2mss1(B,A)
         => ! [C] :
              ( ( v1_msualg_1(C)
                & l1_msualg_1(C) )
             => ( C = k12_pua2mss1(A,B)
              <=> ( u1_struct_0(C) = B
                  & u1_msualg_1(C) = a_2_2_pua2mss1(A,B)
                  & ! [D] :
                      ( m1_subset_1(D,k4_finseq_1(u1_unialg_1(A)))
                     => ! [E] :
                          ( m2_finseq_2(E,B,k3_finseq_2(B))
                         => ( ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,D)))
                           => ( k1_funct_1(u2_msualg_1(C),k4_tarski(D,E)) = E
                              & r1_tarski(k9_relat_1(k2_pua2mss1(A,D),k4_card_3(E)),k1_funct_1(u3_msualg_1(C),k4_tarski(D,E))) ) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_4_0_pua2mss1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_eqrel_1(D,B)
        & m1_eqrel_1(E,C) )
     => ( r2_hidden(A,a_4_0_pua2mss1(B,C,D,E))
      <=> ? [F,G] :
            ( m2_subset_1(F,k1_zfmisc_1(B),D)
            & m2_subset_1(G,k1_zfmisc_1(C),E)
            & A = k12_mcart_1(B,C,F,G) ) ) ) )).

fof(fraenkel_a_2_0_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m1_eqrel_1(C,B) )
     => ( r2_hidden(A,a_2_0_pua2mss1(B,C))
      <=> ? [D] :
            ( m2_finseq_2(D,C,k3_finseq_2(C))
            & A = k4_card_3(D) ) ) ) )).

fof(fraenkel_a_3_0_pua2mss1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & m1_eqrel_1(D,B) )
     => ( r2_hidden(A,a_3_0_pua2mss1(B,C,D))
      <=> ? [E] :
            ( m2_finseq_2(E,D,k4_finseq_2(C,D))
            & A = k4_card_3(E) ) ) ) )).

fof(fraenkel_a_3_1_pua2mss1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & m1_eqrel_1(D,B) )
     => ( r2_hidden(A,a_3_1_pua2mss1(B,C,D))
      <=> ? [E] :
            ( m2_subset_1(E,k1_zfmisc_1(B),D)
            & A = k3_xboole_0(E,C)
            & ~ r1_xboole_0(E,C) ) ) ) )).

fof(fraenkel_a_2_1_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & m1_eqrel_1(C,k1_relat_1(B)) )
     => ( r2_hidden(A,a_2_1_pua2mss1(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_zfmisc_1(k1_relat_1(B)),C)
            & A = k7_relat_1(B,D) ) ) ) )).

fof(fraenkel_a_1_0_pua2mss1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_pua2mss1(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k1_tarski(C) ) ) ) )).

fof(fraenkel_a_2_2_pua2mss1,axiom,(
    ! [A,B,C] :
      ( ( v6_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B)
        & m3_pua2mss1(C,B) )
     => ( r2_hidden(A,a_2_2_pua2mss1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k4_finseq_1(u1_unialg_1(B)))
            & m2_finseq_2(E,C,k3_finseq_2(C))
            & A = k4_tarski(D,E)
            & ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,D))) ) ) ) )).
%------------------------------------------------------------------------------