SET007 Axioms: SET007+397.ax


%------------------------------------------------------------------------------
% File     : SET007+397 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Homomorphisms of Many Sorted 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    : msualg_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   52 (   2 unit)
%            Number of atoms       :  474 (  29 equality)
%            Maximal formula depth :   22 (  12 average)
%            Number of connectives :  503 (  81 ~  ;   0  |; 207  &)
%                                         (  16 <=>; 199 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   1 propositional; 0-4 arity)
%            Number of functors    :   28 (   3 constant; 0-6 arity)
%            Number of variables   :  237 (   0 singleton; 235 !;   2 ?)
%            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(rc1_msualg_3,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B)
      & v1_msualg_3(B) ) )).

fof(fc1_msualg_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ( ~ v1_xboole_0(k3_msualg_1(A,C,B))
        & v1_fraenkel(k3_msualg_1(A,C,B)) ) ) )).

fof(d1_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m3_pboole(C,A,B,B)
         => ( C = k2_msualg_3(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) )).

fof(d2_msualg_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_msualg_3(A)
      <=> ! [B,C] :
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r2_hidden(B,k1_relat_1(A))
                & k1_funct_1(A,B) = C )
             => v2_funct_1(C) ) ) ) ) )).

fof(t1_msualg_3,axiom,(
    ! [A,B] :
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ( v1_msualg_3(B)
      <=> ! [C] :
            ( r2_hidden(C,A)
           => v2_funct_1(k1_funct_1(B,C)) ) ) ) )).

fof(d3_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,B,C)
             => ( v2_msualg_3(D,A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k2_relat_1(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) )).

fof(t2_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m3_pboole(E,A,B,C)
                 => ! [F] :
                      ( m3_pboole(F,A,C,D)
                     => ( k1_relat_1(k13_pboole(E,F)) = A
                        & ! [G] :
                            ( r2_hidden(G,A)
                           => k1_funct_1(k13_pboole(E,F),G) = k5_relat_1(k1_funct_1(E,G),k1_funct_1(F,G)) ) ) ) ) ) ) ) )).

fof(t3_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,B,C)
             => k13_pboole(k2_msualg_3(A,B),D) = D ) ) ) )).

fof(t4_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,B,C)
             => k13_pboole(D,k2_msualg_3(A,C)) = D ) ) ) )).

fof(d4_msualg_3,axiom,(
    $true )).

fof(d5_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,B,C)
             => ( ( v1_msualg_3(D)
                  & v2_msualg_3(D,A,B,C) )
               => ! [E] :
                    ( m3_pboole(E,A,C,B)
                   => ( E = k4_msualg_3(A,B,C,D)
                    <=> ! [F] :
                          ( r2_hidden(F,A)
                         => k1_funct_1(E,F) = k2_funct_1(k1_funct_1(D,F)) ) ) ) ) ) ) ) )).

fof(t5_msualg_3,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( m3_pboole(D,A,B,C)
             => ! [E] :
                  ( m3_pboole(E,A,C,B)
                 => ( ( v1_msualg_3(D)
                      & v2_msualg_3(D,A,B,C)
                      & r6_pboole(A,E,k4_msualg_3(A,B,C,D)) )
                   => ( r6_pboole(A,k3_msualg_3(A,C,B,C,E,D),k2_msualg_3(A,C))
                      & r6_pboole(A,k3_msualg_3(A,B,C,B,D,E),k2_msualg_3(A,B)) ) ) ) ) ) ) )).

fof(t6_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,B,C))
                   => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B))
                      & ! [E] :
                          ( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C))))
                         => r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) )).

fof(d6_msualg_3,axiom,(
    $true )).

fof(d7_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ~ ( k3_msualg_1(A,D,B) != k1_xboole_0
                              & k3_msualg_1(A,D,C) != k1_xboole_0
                              & k5_msualg_3(A,B,C,D,E,F) != k1_funct_1(k3_pralg_2(k5_relat_1(k1_msualg_1(A,D),E)),F) ) ) ) ) ) ) ) )).

fof(d8_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ! [G] :
                              ( m1_subset_1(G,k3_msualg_1(A,D,C))
                             => ( G = k6_msualg_3(A,B,C,D,E,F)
                              <=> ! [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ( r2_hidden(H,k1_relat_1(F))
                                     => k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),H)),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t7_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ( k3_msualg_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( m1_subset_1(D,k3_msualg_1(A,B,C))
                   => D = k5_msualg_3(A,C,C,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)),D) ) ) ) ) ) )).

fof(t8_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( ( v5_msualg_1(E,A)
                        & l3_msualg_1(E,A) )
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ! [G] :
                              ( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
                             => ! [H] :
                                  ( m1_subset_1(H,k3_msualg_1(A,B,C))
                                 => k6_msualg_3(A,C,E,B,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D),u4_msualg_1(A,E),F,G),H) = k6_msualg_3(A,D,E,B,G,k6_msualg_3(A,C,D,B,F,H)) ) ) ) ) ) ) ) ) )).

fof(d9_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k3_msualg_1(A,E,B) != k1_xboole_0
                         => ! [F] :
                              ( m1_subset_1(F,k3_msualg_1(A,E,B))
                             => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,B),F)) = k1_funct_1(k5_msualg_1(A,E,C),k5_msualg_3(A,B,C,E,D,F)) ) ) ) ) ) ) ) ) )).

fof(t9_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => r1_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B))) ) ) )).

fof(t10_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r1_msualg_3(A,B,C,E)
                              & r1_msualg_3(A,C,D,F) )
                           => r1_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) )).

fof(d10_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r2_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) ) ) ) ) ) )).

fof(t11_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r2_msualg_3(A,B,C,E)
                              & r2_msualg_3(A,C,D,F) )
                           => r2_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) )).

fof(d11_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r3_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v1_msualg_3(D) ) ) ) ) ) ) )).

fof(t12_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r3_msualg_3(A,B,C,E)
                              & r3_msualg_3(A,C,D,F) )
                           => r3_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) )).

fof(d12_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r4_msualg_3(A,B,C,D)
                  <=> ( r2_msualg_3(A,B,C,D)
                      & r3_msualg_3(A,B,C,D) ) ) ) ) ) ) )).

fof(t13_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r4_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                      & v1_msualg_3(D) ) ) ) ) ) ) )).

fof(t14_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                     => ( ( r4_msualg_3(A,B,C,D)
                          & r6_pboole(u1_struct_0(A),E,k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D)) )
                       => r4_msualg_3(A,C,B,E) ) ) ) ) ) ) )).

fof(t15_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r4_msualg_3(A,B,C,E)
                              & r4_msualg_3(A,C,D,F) )
                           => r4_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) )).

fof(d13_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ( r5_msualg_3(A,B,C)
              <=> ? [D] :
                    ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                    & r4_msualg_3(A,B,C,D) ) ) ) ) ) )).

fof(t16_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( r4_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)))
            & r5_msualg_3(A,B,B) ) ) ) )).

fof(t17_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ( r6_msualg_3(A,B,C)
               => r6_msualg_3(A,C,B) ) ) ) ) )).

fof(t18_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( ( r6_msualg_3(A,B,C)
                      & r6_msualg_3(A,C,D) )
                   => r6_msualg_3(A,B,D) ) ) ) ) ) )).

fof(d14_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => ! [E] :
                        ( ( v4_msualg_1(E,A)
                          & v5_msualg_1(E,A)
                          & m1_msualg_2(E,A,C) )
                       => ( E = k7_msualg_3(A,B,C,D)
                        <=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k14_pboole(u1_struct_0(A),u4_msualg_1(A,B),D)) ) ) ) ) ) ) ) )).

fof(t19_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v4_msualg_1(C,A)
                & v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => ( r2_msualg_3(A,B,C,D)
                    <=> k7_msualg_3(A,B,C,D) = C ) ) ) ) ) ) )).

fof(t20_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
                     => ( ( r6_pboole(u1_struct_0(A),D,E)
                          & r1_msualg_3(A,B,C,D) )
                       => r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E) ) ) ) ) ) ) )).

fof(t21_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ~ ( r1_msualg_3(A,B,C,D)
                      & ! [E] :
                          ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
                         => ~ ( r6_pboole(u1_struct_0(A),D,E)
                              & r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E) ) ) ) ) ) ) ) )).

fof(t22_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                 => ( r6_pboole(u1_struct_0(A),D,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)))
                   => r3_msualg_3(A,C,B,D) ) ) ) ) ) )).

fof(t23_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ~ ( r1_msualg_3(A,B,C,D)
                      & ! [E] :
                          ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
                         => ! [F] :
                              ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k7_msualg_3(A,B,C,D)),u4_msualg_1(A,C))
                             => ~ ( r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E)
                                  & r3_msualg_3(A,k7_msualg_3(A,B,C,D),C,F)
                                  & r6_pboole(u1_struct_0(A),D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)),u4_msualg_1(A,C),E,F)) ) ) ) ) ) ) ) ) )).

fof(t24_msualg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ! [H] :
                                  ( ( v1_relat_1(H)
                                    & v1_funct_1(H) )
                                 => ( ( F = G
                                      & r2_hidden(F,k3_msualg_1(A,D,B))
                                      & r2_hidden(H,k3_msualg_1(A,D,C)) )
                                   => ( H = k5_msualg_3(A,B,C,D,E,F)
                                    <=> ! [I] :
                                          ( m2_subset_1(I,k1_numbers,k5_numbers)
                                         => ( r2_hidden(I,k1_relat_1(G))
                                           => k1_funct_1(H,I) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),I)),k1_funct_1(G,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(reflexivity_r6_msualg_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & l3_msualg_1(C,A) )
     => r6_msualg_3(A,B,B) ) )).

fof(redefinition_r6_msualg_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & l3_msualg_1(C,A) )
     => ( r6_msualg_3(A,B,C)
      <=> r5_msualg_3(A,B,C) ) ) )).

fof(dt_k1_msualg_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k1_msualg_3(A,B,C,D,E))
        & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E))
        & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) )).

fof(redefinition_k1_msualg_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C)
        & m1_subset_1(E,A) )
     => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) )).

fof(dt_k2_msualg_3,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => m3_pboole(k2_msualg_3(A,B),A,B,B) ) )).

fof(dt_k3_msualg_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & v2_relat_1(D)
        & m1_pboole(D,A)
        & m3_pboole(E,A,B,C)
        & m3_pboole(F,A,C,D) )
     => m3_pboole(k3_msualg_3(A,B,C,D,E,F),A,B,D) ) )).

fof(redefinition_k3_msualg_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & v2_relat_1(D)
        & m1_pboole(D,A)
        & m3_pboole(E,A,B,C)
        & m3_pboole(F,A,C,D) )
     => k3_msualg_3(A,B,C,D,E,F) = k13_pboole(E,F) ) )).

fof(dt_k4_msualg_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C) )
     => m3_pboole(k4_msualg_3(A,B,C,D),A,C,B) ) )).

fof(dt_k5_msualg_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & l3_msualg_1(C,A)
        & m1_subset_1(D,u1_msualg_1(A))
        & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(F,k3_msualg_1(A,D,B)) )
     => m1_subset_1(k5_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) )).

fof(dt_k6_msualg_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m1_subset_1(D,u1_msualg_1(A))
        & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(F,k3_msualg_1(A,D,B)) )
     => m1_subset_1(k6_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) )).

fof(redefinition_k6_msualg_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m1_subset_1(D,u1_msualg_1(A))
        & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(F,k3_msualg_1(A,D,B)) )
     => k6_msualg_3(A,B,C,D,E,F) = k5_msualg_3(A,B,C,D,E,F) ) )).

fof(dt_k7_msualg_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
     => ( v4_msualg_1(k7_msualg_3(A,B,C,D),A)
        & v5_msualg_1(k7_msualg_3(A,B,C,D),A)
        & m1_msualg_2(k7_msualg_3(A,B,C,D),A,C) ) ) )).
%------------------------------------------------------------------------------