SET007 Axioms: SET007+384.ax


%------------------------------------------------------------------------------
% File     : SET007+384 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Product of Family of Universal Algebras
% 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    : pralg_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   0 unit)
%            Number of atoms       :  675 (  87 equality)
%            Maximal formula depth :   29 (   9 average)
%            Number of connectives :  708 ( 115 ~  ;   0  |; 364  &)
%                                         (  22 <=>; 207 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   40 (   0 propositional; 1-3 arity)
%            Number of functors    :   61 (   3 constant; 0-4 arity)
%            Number of variables   :  252 (   0 singleton; 245 !;   7 ?)
%            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(fc1_pralg_1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ( ~ v1_xboole_0(k7_pralg_1(A))
        & v1_relat_1(k7_pralg_1(A))
        & v1_funct_1(k7_pralg_1(A))
        & v1_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0))
        & v2_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)) ) ) )).

fof(rc1_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_finseq_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B) ) ) )).

fof(rc2_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k3_finseq_2(A))
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B) ) ) )).

fof(rc3_pralg_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_pralg_1(A) ) )).

fof(cc1_pralg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_pralg_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) )).

fof(rc4_pralg_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B) ) )).

fof(rc5_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_pralg_1(B)
          & v2_pralg_1(B)
          & v3_pralg_1(B) ) ) )).

fof(fc2_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k12_pralg_1(A,B))
        & v2_relat_1(k12_pralg_1(A,B))
        & ~ v3_relat_1(k12_pralg_1(A,B))
        & v1_funct_1(k12_pralg_1(A,B)) ) ) )).

fof(fc3_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( ~ v1_xboole_0(k4_card_3(B))
        & v1_fraenkel(k4_card_3(B)) ) ) )).

fof(rc6_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] :
          ( m1_pralg_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funcop_1(C)
          & v4_pralg_1(C) ) ) )).

fof(t1_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k4_finseq_2(C,A) = k4_finseq_2(D,B)
                   => C = D ) ) ) ) ) )).

fof(d1_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ( D = k1_pralg_1(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(C)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => k1_funct_1(D,E) = k1_mcart_1(k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).

fof(d2_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m2_finseq_1(D,B)
                 => ( D = k2_pralg_1(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(C)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => k1_funct_1(D,E) = k2_mcart_1(k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).

fof(d3_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_funct_1(C)
                & v1_unialg_1(C,A)
                & v2_unialg_1(C,A)
                & m2_relset_1(C,k3_finseq_2(A),A) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_funct_1(D)
                    & v1_unialg_1(D,B)
                    & v2_unialg_1(D,B)
                    & m2_relset_1(D,k3_finseq_2(B),B) )
                 => ( k2_unialg_1(A,C) = k2_unialg_1(B,D)
                   => ! [E] :
                        ( ( ~ v1_xboole_0(E)
                          & v1_funct_1(E)
                          & v1_unialg_1(E,k2_zfmisc_1(A,B))
                          & v2_unialg_1(E,k2_zfmisc_1(A,B))
                          & m2_relset_1(E,k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) )
                       => ( E = k3_pralg_1(A,B,C,D)
                        <=> ( k1_relat_1(E) = k4_finseq_2(k2_unialg_1(A,C),k2_zfmisc_1(A,B))
                            & ! [F] :
                                ( m2_finseq_1(F,k2_zfmisc_1(A,B))
                               => ( r2_hidden(F,k1_relat_1(E))
                                 => k1_funct_1(E,F) = k4_tarski(k1_funct_1(C,k1_pralg_1(A,B,F)),k1_funct_1(D,k2_pralg_1(A,B,F))) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ! [C] :
                ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))))
               => ( C = k4_pralg_1(A,B)
                <=> ( k3_finseq_1(C) = k3_finseq_1(u1_unialg_1(A))
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( r2_hidden(D,k4_finseq_1(C))
                         => ! [E] :
                              ( ( ~ v1_xboole_0(E)
                                & v1_funct_1(E)
                                & v1_unialg_1(E,u1_struct_0(A))
                                & v2_unialg_1(E,u1_struct_0(A))
                                & m2_relset_1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) )
                             => ! [F] :
                                  ( ( ~ v1_xboole_0(F)
                                    & v1_funct_1(F)
                                    & v1_unialg_1(F,u1_struct_0(B))
                                    & v2_unialg_1(F,u1_struct_0(B))
                                    & m2_relset_1(F,k3_finseq_2(u1_struct_0(B)),u1_struct_0(B)) )
                                 => ( ( E = k1_funct_1(u1_unialg_1(A),D)
                                      & F = k1_funct_1(u1_unialg_1(B),D) )
                                   => k1_funct_1(C,D) = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),E,F) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t2_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ( ~ v3_struct_0(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))
              & v3_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))
              & v6_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))
              & v7_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))
              & v8_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))
              & l1_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) ) ) ) ) )).

fof(d5_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k5_pralg_1(A,B) = g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)) ) ) ) )).

fof(d6_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))
                & m2_relset_1(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) )
             => ( C = k6_pralg_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k2_zfmisc_1(A,B))
                   => k8_funct_2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A),C,D) = k1_domain_1(B,A,k3_domain_1(A,B,D),k2_domain_1(A,B,D)) ) ) ) ) ) )).

fof(t3_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => k9_funcop_1(k2_zfmisc_1(A,B),B,A,k6_pralg_1(A,B)) = k2_zfmisc_1(B,A) ) ) )).

fof(t4_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => v2_funct_1(k6_pralg_1(A,B)) ) ) )).

fof(t5_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ( v1_funct_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)))
              & v1_funct_2(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A)))
              & m2_relset_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A))) ) ) ) ) )).

fof(t6_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ! [C] :
                ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
               => ! [D] :
                    ( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
                   => ! [E] :
                        ( m2_unialg_2(E,u1_struct_0(k5_pralg_1(A,B)),k1_unialg_2(k5_pralg_1(A,B)))
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ( C = k1_funct_1(u1_unialg_1(A),F)
                                & D = k1_funct_1(u1_unialg_1(B),F)
                                & E = k1_funct_1(u1_unialg_1(k5_pralg_1(A,B)),F)
                                & r2_hidden(F,k4_finseq_1(u1_unialg_1(A))) )
                             => ( k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(A),C)
                                & k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(B),D)
                                & E = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),C,D) ) ) ) ) ) ) ) ) ) )).

fof(t7_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => r1_unialg_2(k5_pralg_1(A,B),A) ) ) ) )).

fof(t8_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_unialg_1(D)
                    & v7_unialg_1(D)
                    & v8_unialg_1(D)
                    & l1_unialg_1(D) )
                 => ( ( m3_unialg_2(A,B)
                      & m3_unialg_2(C,D)
                      & r1_unialg_2(B,D) )
                   => m3_unialg_2(k5_pralg_1(A,C),k5_pralg_1(B,D)) ) ) ) ) ) )).

fof(d7_pralg_1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) )
         => ( B = k7_pralg_1(A)
          <=> ( k1_relat_1(B) = k1_tarski(k2_finseq_2(A,k1_xboole_0))
              & k2_relat_1(B) = k1_tarski(k1_xboole_0) ) ) ) ) )).

fof(t9_pralg_1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k2_unialg_1(k1_tarski(k1_xboole_0),k7_pralg_1(A)) = A ) )).

fof(d8_pralg_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)))
         => ( B = k8_pralg_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( D = k1_funct_1(A,C)
                         => k1_funct_1(B,C) = k7_pralg_1(D) ) ) ) ) ) ) ) ) )).

fof(t10_pralg_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ( v4_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0))
        & v5_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0))
        & v2_relat_1(k8_pralg_1(A)) ) ) )).

fof(t11_pralg_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ( A != k1_xboole_0
       => ( ~ v3_struct_0(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))
          & v3_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))
          & v6_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))
          & v7_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))
          & v8_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))
          & l1_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) ) ) ) )).

fof(d9_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,k5_numbers) )
     => k9_pralg_1(A) = g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)) ) )).

fof(d10_pralg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_pralg_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => ( ~ v3_struct_0(k1_funct_1(A,B))
              & v6_unialg_1(k1_funct_1(A,B))
              & v7_unialg_1(k1_funct_1(A,B))
              & v8_unialg_1(k1_funct_1(A,B))
              & l1_unialg_1(k1_funct_1(A,B)) ) ) ) ) )).

fof(d11_pralg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_pralg_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => l1_struct_0(k1_funct_1(A,B)) ) ) ) )).

fof(d12_pralg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v3_pralg_1(A)
      <=> ! [B,C] :
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A)) )
           => ! [D] :
                ( ( ~ v3_struct_0(D)
                  & v6_unialg_1(D)
                  & v7_unialg_1(D)
                  & v8_unialg_1(D)
                  & l1_unialg_1(D) )
               => ! [E] :
                    ( ( ~ v3_struct_0(E)
                      & v6_unialg_1(E)
                      & v7_unialg_1(E)
                      & v8_unialg_1(E)
                      & l1_unialg_1(E) )
                   => ( ( D = k1_funct_1(A,B)
                        & E = k1_funct_1(A,C) )
                     => k3_unialg_1(D) = k3_unialg_1(E) ) ) ) ) ) ) )).

fof(d13_pralg_1,axiom,(
    ! [A,B] :
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( m1_pboole(C,A)
         => ( C = k12_pralg_1(A,B)
          <=> ! [D] :
                ~ ( r2_hidden(D,A)
                  & ! [E] :
                      ( l1_struct_0(E)
                     => ~ ( E = k1_funct_1(B,D)
                          & k1_funct_1(C,D) = u1_struct_0(E) ) ) ) ) ) ) )).

fof(d14_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_pralg_1(B)
            & v3_pralg_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,k5_numbers)
             => ( C = k13_pralg_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => C = k3_unialg_1(k11_pralg_1(A,B,D)) ) ) ) ) ) )).

fof(d15_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( v1_funcop_1(C)
                & m1_pboole(C,A) )
             => ( m1_pralg_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ( ~ v1_xboole_0(k1_funct_1(C,D))
                      & v1_funct_1(k1_funct_1(C,D))
                      & v1_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D))
                      & v2_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D))
                      & m2_relset_1(k1_funct_1(C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d16_pralg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_pralg_1(A)
      <=> ! [B,C] :
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A)) )
           => ! [D] :
                ( ( v1_relat_1(D)
                  & v1_funct_1(D) )
               => ! [E] :
                    ( ( v1_relat_1(E)
                      & v1_funct_1(E) )
                   => ( ( k1_funct_1(A,B) = D
                        & k1_funct_1(A,C) = E )
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => ! [H] :
                                  ( ~ v1_xboole_0(H)
                                 => ! [I] :
                                      ( ~ v1_xboole_0(I)
                                     => ( ( k1_relat_1(D) = k4_finseq_2(F,H)
                                          & k1_relat_1(E) = k4_finseq_2(G,I) )
                                       => ! [J] :
                                            ( ( ~ v1_xboole_0(J)
                                              & v1_funct_1(J)
                                              & v1_unialg_1(J,H)
                                              & v2_unialg_1(J,H)
                                              & m2_relset_1(J,k3_finseq_2(H),H) )
                                           => ! [K] :
                                                ( ( ~ v1_xboole_0(K)
                                                  & v1_funct_1(K)
                                                  & v1_unialg_1(K,I)
                                                  & v2_unialg_1(K,I)
                                                  & m2_relset_1(K,k3_finseq_2(I),I) )
                                               => ( ( D = J
                                                    & E = K )
                                                 => k2_unialg_1(H,J) = k2_unialg_1(I,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_pralg_1(C,A,B)
             => ( v4_pralg_1(C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => k2_unialg_1(k1_funct_1(B,D),k14_pralg_1(A,B,C,D)) = k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) ) ) ) ) ) ) )).

fof(d17_pralg_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k15_pralg_1(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(A)
                  & ! [D] :
                      ( r2_hidden(D,k1_relat_1(A))
                     => k1_funct_1(C,D) = k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d18_pralg_1,axiom,(
    ! [A,B] :
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k16_pralg_1(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => ! [F] :
                        ( ( v1_relat_1(F)
                          & v1_funct_1(F) )
                       => ( F = k1_funct_1(B,E)
                         => k1_funct_1(D,E) = k1_funct_1(F,k1_funct_1(C,E)) ) ) ) ) ) ) ) )).

fof(d19_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( v4_pralg_1(C)
                & m1_pralg_1(C,A,B) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( D = k20_pralg_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => D = k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) ) ) ) ) ) ) )).

fof(d20_pralg_1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( C = k21_pralg_1(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_subset_1(k1_funct_1(B,D)) ) ) ) ) )).

fof(d21_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( v4_pralg_1(C)
                & m1_pralg_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_funct_1(D)
                    & v1_unialg_1(D,k4_card_3(B))
                    & v2_unialg_1(D,k4_card_3(B))
                    & m2_relset_1(D,k3_finseq_2(k4_card_3(B)),k4_card_3(B)) )
                 => ( D = k22_pralg_1(A,B,C)
                  <=> ( k1_relat_1(D) = k4_finseq_2(k20_pralg_1(A,B,C),k4_card_3(B))
                      & ! [E] :
                          ( m2_finseq_2(E,k4_card_3(B),k3_finseq_2(k4_card_3(B)))
                         => ( r2_hidden(E,k1_relat_1(D))
                           => ( ( k4_finseq_1(E) = k1_xboole_0
                               => k1_funct_1(D,E) = k16_pralg_1(A,C,k21_pralg_1(A,B)) )
                              & ( k4_finseq_1(E) != k1_xboole_0
                               => ! [F] :
                                    ( ~ v1_xboole_0(F)
                                   => ! [G] :
                                        ( m1_pboole(G,k2_zfmisc_1(A,F))
                                       => ( ( F = k4_finseq_1(E)
                                            & G = k18_pralg_1(k4_finseq_1(E),A,k17_pralg_1(A,B,E)) )
                                         => k1_funct_1(D,E) = k16_pralg_1(A,C,k19_pralg_1(A,F,G)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d22_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_pralg_1(B)
            & v3_pralg_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( v4_ordinal2(C)
             => ( r2_hidden(C,k4_finseq_1(k13_pralg_1(A,B)))
               => ! [D] :
                    ( ( v4_pralg_1(D)
                      & m1_pralg_1(D,A,k12_pralg_1(A,B)) )
                   => ( D = k23_pralg_1(A,B,C)
                    <=> ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m2_unialg_2(F,u1_struct_0(k11_pralg_1(A,B,E)),k1_unialg_2(k11_pralg_1(A,B,E)))
                             => ( k1_funct_1(u1_unialg_1(k11_pralg_1(A,B,E)),C) = F
                               => k14_pralg_1(A,k12_pralg_1(A,B),D,E) = F ) ) ) ) ) ) ) ) ) )).

fof(d23_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_pralg_1(B)
            & v3_pralg_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B))))
             => ( C = k24_pralg_1(A,B)
              <=> ( k3_finseq_1(C) = k3_finseq_1(k13_pralg_1(A,B))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(C))
                       => k1_funct_1(C,D) = k22_pralg_1(A,k12_pralg_1(A,B),k23_pralg_1(A,B,D)) ) ) ) ) ) ) ) )).

fof(d24_pralg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_pralg_1(B)
            & v3_pralg_1(B)
            & m1_pboole(B,A) )
         => k25_pralg_1(A,B) = g1_unialg_1(k4_card_3(k12_pralg_1(A,B)),k24_pralg_1(A,B)) ) ) )).

fof(dt_m1_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( m1_pralg_1(C,A,B)
         => ( v1_funcop_1(C)
            & m1_pboole(C,A) ) ) ) )).

fof(existence_m1_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : m1_pralg_1(C,A,B) ) )).

fof(dt_k1_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => m2_finseq_1(k1_pralg_1(A,B,C),A) ) )).

fof(redefinition_k1_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => k1_pralg_1(A,B,C) = k15_mcart_1(C) ) )).

fof(dt_k2_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => m2_finseq_1(k2_pralg_1(A,B,C),B) ) )).

fof(redefinition_k2_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_1(C,k2_zfmisc_1(A,B)) )
     => k2_pralg_1(A,B,C) = k16_mcart_1(C) ) )).

fof(dt_k3_pralg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(C)
        & v1_unialg_1(C,A)
        & v2_unialg_1(C,A)
        & m1_relset_1(C,k3_finseq_2(A),A)
        & ~ v1_xboole_0(D)
        & v1_funct_1(D)
        & v1_unialg_1(D,B)
        & v2_unialg_1(D,B)
        & m1_relset_1(D,k3_finseq_2(B),B) )
     => ( ~ v1_xboole_0(k3_pralg_1(A,B,C,D))
        & v1_funct_1(k3_pralg_1(A,B,C,D))
        & v1_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B))
        & v2_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B))
        & m2_relset_1(k3_pralg_1(A,B,C,D),k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) ) ) )).

fof(dt_k4_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => m2_finseq_1(k4_pralg_1(A,B),k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) )).

fof(dt_k5_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => ( ~ v3_struct_0(k5_pralg_1(A,B))
        & v3_unialg_1(k5_pralg_1(A,B))
        & v6_unialg_1(k5_pralg_1(A,B))
        & v7_unialg_1(k5_pralg_1(A,B))
        & v8_unialg_1(k5_pralg_1(A,B))
        & l1_unialg_1(k5_pralg_1(A,B)) ) ) )).

fof(dt_k6_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( v1_funct_1(k6_pralg_1(A,B))
        & v1_funct_2(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))
        & m2_relset_1(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) ) ) )).

fof(dt_k7_pralg_1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ( v1_funct_1(k7_pralg_1(A))
        & m2_relset_1(k7_pralg_1(A),k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) ) ) )).

fof(dt_k8_pralg_1,axiom,(
    ! [A] :
      ( m1_finseq_1(A,k5_numbers)
     => m2_finseq_1(k8_pralg_1(A),k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))) ) )).

fof(dt_k9_pralg_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( ~ v3_struct_0(k9_pralg_1(A))
        & v3_unialg_1(k9_pralg_1(A))
        & v6_unialg_1(k9_pralg_1(A))
        & v7_unialg_1(k9_pralg_1(A))
        & v8_unialg_1(k9_pralg_1(A))
        & l1_unialg_1(k9_pralg_1(A)) ) ) )).

fof(dt_k10_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_pralg_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => l1_struct_0(k10_pralg_1(A,B,C)) ) )).

fof(redefinition_k10_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_pralg_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k10_pralg_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k11_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k11_pralg_1(A,B,C))
        & v6_unialg_1(k11_pralg_1(A,B,C))
        & v7_unialg_1(k11_pralg_1(A,B,C))
        & v8_unialg_1(k11_pralg_1(A,B,C))
        & l1_unialg_1(k11_pralg_1(A,B,C)) ) ) )).

fof(redefinition_k11_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k11_pralg_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k12_pralg_1,axiom,(
    ! [A,B] :
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k12_pralg_1(A,B),A) ) )).

fof(dt_k13_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & v3_pralg_1(B)
        & m1_pboole(B,A) )
     => m2_finseq_1(k13_pralg_1(A,B),k5_numbers) ) )).

fof(dt_k14_pralg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_pralg_1(C,A,B)
        & m1_subset_1(D,A) )
     => ( ~ v1_xboole_0(k14_pralg_1(A,B,C,D))
        & v1_funct_1(k14_pralg_1(A,B,C,D))
        & v1_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D))
        & v2_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D))
        & m2_relset_1(k14_pralg_1(A,B,C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) ) ) )).

fof(redefinition_k14_pralg_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_pralg_1(C,A,B)
        & m1_subset_1(D,A) )
     => k14_pralg_1(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k15_pralg_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k15_pralg_1(A,B))
        & v1_funct_1(k15_pralg_1(A,B)) ) ) )).

fof(dt_k16_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k16_pralg_1(A,B,C),A) ) )).

fof(redefinition_k16_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k16_pralg_1(A,B,C) = k15_pralg_1(B,C) ) )).

fof(dt_k17_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_finseq_1(C,k4_card_3(B)) )
     => m1_pboole(k17_pralg_1(A,B,C),k2_zfmisc_1(k4_finseq_1(C),A)) ) )).

fof(redefinition_k17_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_finseq_1(C,k4_card_3(B)) )
     => k17_pralg_1(A,B,C) = k4_funct_5(C) ) )).

fof(dt_k18_pralg_1,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,k2_zfmisc_1(A,B))
     => m1_pboole(k18_pralg_1(A,B,C),k2_zfmisc_1(B,A)) ) )).

fof(redefinition_k18_pralg_1,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,k2_zfmisc_1(A,B))
     => k18_pralg_1(A,B,C) = k2_funct_4(C) ) )).

fof(dt_k19_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m1_pboole(C,k2_zfmisc_1(A,B)) )
     => m1_pboole(k19_pralg_1(A,B,C),A) ) )).

fof(redefinition_k19_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m1_pboole(C,k2_zfmisc_1(A,B)) )
     => k19_pralg_1(A,B,C) = k3_funct_5(C) ) )).

fof(dt_k20_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & v4_pralg_1(C)
        & m1_pralg_1(C,A,B) )
     => m2_subset_1(k20_pralg_1(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k21_pralg_1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => m1_pboole(k21_pralg_1(A,B),A) ) )).

fof(dt_k22_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & v4_pralg_1(C)
        & m1_pralg_1(C,A,B) )
     => ( ~ v1_xboole_0(k22_pralg_1(A,B,C))
        & v1_funct_1(k22_pralg_1(A,B,C))
        & v1_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B))
        & v2_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B))
        & m2_relset_1(k22_pralg_1(A,B,C),k3_finseq_2(k4_card_3(B)),k4_card_3(B)) ) ) )).

fof(dt_k23_pralg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & v3_pralg_1(B)
        & m1_pboole(B,A)
        & v4_ordinal2(C) )
     => ( v4_pralg_1(k23_pralg_1(A,B,C))
        & m1_pralg_1(k23_pralg_1(A,B,C),A,k12_pralg_1(A,B)) ) ) )).

fof(dt_k24_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & v3_pralg_1(B)
        & m1_pboole(B,A) )
     => m2_finseq_1(k24_pralg_1(A,B),k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))) ) )).

fof(dt_k25_pralg_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_pralg_1(B)
        & v3_pralg_1(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k25_pralg_1(A,B))
        & v3_unialg_1(k25_pralg_1(A,B))
        & v6_unialg_1(k25_pralg_1(A,B))
        & v7_unialg_1(k25_pralg_1(A,B))
        & v8_unialg_1(k25_pralg_1(A,B))
        & l1_unialg_1(k25_pralg_1(A,B)) ) ) )).
%------------------------------------------------------------------------------