SET007 Axioms: SET007+456.ax


%------------------------------------------------------------------------------
% File     : SET007+456 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Translations, Endomorphisms, and Stable Equational Theories
% 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_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  101 (   0 unit)
%            Number of atoms       : 1188 (  73 equality)
%            Maximal formula depth :   36 (  13 average)
%            Number of connectives : 1291 ( 204 ~  ;   0  |; 562  &)
%                                         (  30 <=>; 495 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   0 propositional; 1-5 arity)
%            Number of functors    :   56 (  14 constant; 0-6 arity)
%            Number of variables   :  519 (   0 singleton; 487 !;  32 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v5_msualg_1(B,A)
           => v1_msualg_6(B,A) ) ) ) )).

fof(rc1_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( l3_msualg_1(B,A)
          & v5_msualg_1(B,A)
          & v1_msualg_6(B,A) ) ) )).

fof(cc2_msualg_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
         => ( ( v3_msualg_4(C,A,B)
              & v3_msualg_6(C,A,B) )
           => ( v1_msualg_4(C)
              & v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B))
              & v3_msualg_4(C,A,B)
              & v2_msualg_6(C,A,B) ) ) ) ) )).

fof(cc3_msualg_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
         => ( ( v3_msualg_4(C,A,B)
              & v2_msualg_6(C,A,B) )
           => ( v1_msualg_4(C)
              & v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B))
              & v3_msualg_4(C,A,B)
              & v3_msualg_6(C,A,B) ) ) ) ) )).

fof(fc1_msualg_6,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k6_relat_1(A))
        & v1_relat_1(k6_relat_1(A))
        & v1_funct_1(k6_relat_1(A))
        & v1_relat_2(k6_relat_1(A))
        & v3_relat_2(k6_relat_1(A))
        & v4_relat_2(k6_relat_1(A))
        & v8_relat_2(k6_relat_1(A)) ) ) )).

fof(cc4_msualg_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
         => ( v3_msualg_4(C,A,B)
           => ( v2_relat_1(C)
              & ~ v3_relat_1(C)
              & v1_msualg_4(C) ) ) ) ) )).

fof(rc2_msualg_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & ~ v3_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B))
          & v3_msualg_4(C,A,B)
          & v2_msualg_6(C,A,B)
          & v3_msualg_6(C,A,B)
          & v4_msualg_6(C,A,B) ) ) )).

fof(fc2_msualg_6,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)
        & v2_relat_1(C)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v1_relat_1(k6_msualg_6(A,B,C))
        & v2_relat_1(k6_msualg_6(A,B,C))
        & ~ v3_relat_1(k6_msualg_6(A,B,C))
        & v1_funct_1(k6_msualg_6(A,B,C))
        & v1_msualg_4(k6_msualg_6(A,B,C))
        & v3_msualg_6(k6_msualg_6(A,B,C),A,B) ) ) )).

fof(fc3_msualg_6,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)
        & v2_relat_1(C)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v1_relat_1(k7_msualg_6(A,B,C))
        & v2_relat_1(k7_msualg_6(A,B,C))
        & ~ v3_relat_1(k7_msualg_6(A,B,C))
        & v1_funct_1(k7_msualg_6(A,B,C))
        & v1_msualg_4(k7_msualg_6(A,B,C))
        & v4_msualg_6(k7_msualg_6(A,B,C),A,B) ) ) )).

fof(fc4_msualg_6,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)
        & v2_relat_1(C)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v1_relat_1(k8_msualg_6(A,B,C))
        & v2_relat_1(k8_msualg_6(A,B,C))
        & ~ v3_relat_1(k8_msualg_6(A,B,C))
        & v1_funct_1(k8_msualg_6(A,B,C))
        & v1_msualg_4(k8_msualg_6(A,B,C))
        & v3_msualg_6(k8_msualg_6(A,B,C),A,B)
        & v4_msualg_6(k8_msualg_6(A,B,C),A,B) ) ) )).

fof(fc5_msualg_6,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)
        & v4_msualg_6(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v1_relat_1(k9_msualg_6(A,B,C))
        & v2_relat_1(k9_msualg_6(A,B,C))
        & ~ v3_relat_1(k9_msualg_6(A,B,C))
        & v1_funct_1(k9_msualg_6(A,B,C))
        & v1_msualg_4(k9_msualg_6(A,B,C))
        & v2_msualg_4(k9_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B))
        & v3_msualg_4(k9_msualg_6(A,B,C),A,B)
        & v4_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) )).

fof(fc6_msualg_6,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)
        & v3_msualg_6(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v1_relat_1(k9_msualg_6(A,B,C))
        & v2_relat_1(k9_msualg_6(A,B,C))
        & ~ v3_relat_1(k9_msualg_6(A,B,C))
        & v1_funct_1(k9_msualg_6(A,B,C))
        & v1_msualg_4(k9_msualg_6(A,B,C))
        & v2_msualg_4(k9_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B))
        & v3_msualg_4(k9_msualg_6(A,B,C),A,B)
        & v2_msualg_6(k9_msualg_6(A,B,C),A,B)
        & v3_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) )).

fof(t1_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( r2_hidden(D,k3_msualg_1(A,C,B))
                 => ( v1_relat_1(D)
                    & v1_funct_1(D) ) ) ) ) ) )).

fof(t2_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,C,B))
                   => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,C))
                      & ! [E] :
                          ( r2_hidden(E,k4_finseq_1(k1_msualg_1(A,C)))
                         => r2_hidden(k1_funct_1(D,E),k1_funct_1(u4_msualg_1(A,B),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) )).

fof(d1_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v1_msualg_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
               => ~ ( k3_msualg_1(A,C,B) != k1_xboole_0
                    & k4_msualg_1(A,C,B) = k1_xboole_0 ) ) ) ) ) )).

fof(t3_msualg_6,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] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( r2_hidden(D,k4_finseq_1(k1_msualg_1(A,B)))
                        & k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),D)) = k1_xboole_0 ) ) ) ) ) ) )).

fof(d2_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( m1_msualg_6(C,A,B)
              <=> r1_msualg_3(A,B,B,C) ) ) ) ) )).

fof(t4_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => m1_msualg_6(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),A,B) ) ) )).

fof(t5_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_msualg_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,k3_msualg_1(A,E,B))
                         => ( r2_hidden(F,k3_msualg_1(A,E,B))
                           => k5_msualg_3(A,B,B,E,D,k5_msualg_3(A,B,B,E,C,F)) = k5_msualg_3(A,B,B,E,k1_msualg_6(u1_struct_0(A),u4_msualg_1(A,B),C,D),F) ) ) ) ) ) ) ) )).

fof(t6_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_6(C,A,B)
             => ! [D] :
                  ( m1_msualg_6(D,A,B)
                 => m1_msualg_6(k1_msualg_6(u1_struct_0(A),u4_msualg_1(A,B),C,D),A,B) ) ) ) ) )).

fof(d3_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k3_msualg_6(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_subset_1(E,u1_msualg_1(A))
                          & k2_msualg_1(A,E) = D
                          & ? [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                              & r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E)))
                              & k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F) = C ) ) ) ) ) ) ) ) )).

fof(t7_msualg_6,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))
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),E)))
                           => r2_hidden(k2_funct_7(D,E,F),k3_msualg_1(A,B,C)) ) ) ) ) ) ) ) )).

fof(t8_msualg_6,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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_msualg_1(A))
                     => ~ ( k3_msualg_1(A,E,B) != k1_xboole_0
                          & k3_msualg_1(A,E,C) != k1_xboole_0
                          & ? [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                              & r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E)))
                              & ~ ! [G] :
                                    ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F)))
                                   => r2_hidden(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F)),G),k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F))) ) ) ) ) ) ) ) ) )).

fof(t9_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(C,k4_finseq_1(k1_msualg_1(A,B)))
               => ! [D] :
                    ( l3_msualg_1(D,A)
                   => ! [E] :
                        ( l3_msualg_1(E,A)
                       => ! [F] :
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
                           => ! [G] :
                                ( m1_subset_1(G,k3_msualg_1(A,B,D))
                               => ! [H] :
                                    ( m1_subset_1(H,k3_msualg_1(A,B,D))
                                   => ( ( r2_hidden(G,k3_msualg_1(A,B,D))
                                        & r2_hidden(k5_msualg_3(A,D,E,B,F,G),k3_msualg_1(A,B,E)) )
                                     => ! [I] :
                                          ( ( v1_relat_1(I)
                                            & v1_funct_1(I) )
                                         => ! [J] :
                                              ( ( v1_relat_1(J)
                                                & v1_funct_1(J) )
                                             => ! [K] :
                                                  ( ( v1_relat_1(K)
                                                    & v1_funct_1(K) )
                                                 => ( ( I = G
                                                      & J = k5_msualg_3(A,D,E,B,F,G)
                                                      & K = k5_msualg_3(A,D,E,B,F,H) )
                                                   => ! [L] :
                                                        ( m1_subset_1(L,k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)))
                                                       => ( H = k2_funct_7(I,C,L)
                                                         => ( k1_funct_1(K,C) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E),F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)),L)
                                                            & k5_msualg_3(A,D,E,B,F,H) = k2_funct_7(J,C,k1_funct_1(K,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ( F = k4_msualg_6(A,B,C,D,E)
                          <=> ( k1_relat_1(F) = k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C))
                              & ! [G] :
                                  ( r2_hidden(G,k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)))
                                 => k1_funct_1(F,G) = k1_funct_1(k5_msualg_1(A,B,D),k2_funct_7(E,C,G)) ) ) ) ) ) ) ) ) ) )).

fof(t10_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(C,k4_finseq_1(k1_msualg_1(A,B)))
               => ! [D] :
                    ( ( v1_msualg_6(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( ( v1_relat_1(E)
                          & v1_funct_1(E) )
                       => ( r2_hidden(E,k3_msualg_1(A,B,D))
                         => ( v1_funct_1(k4_msualg_6(A,B,C,D,E))
                            & v1_funct_2(k4_msualg_6(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)),k1_funct_1(u4_msualg_1(A,D),k2_msualg_1(A,B)))
                            & m2_relset_1(k4_msualg_6(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)),k1_funct_1(u4_msualg_1(A,D),k2_msualg_1(A,B))) ) ) ) ) ) ) ) ) )).

fof(d5_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r1_msualg_6(A,B,C,D,E)
                      <=> ? [F] :
                            ( m1_subset_1(F,u1_msualg_1(A))
                            & k2_msualg_1(A,F) = C
                            & ? [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                                & r2_hidden(G,k4_finseq_1(k1_msualg_1(A,F)))
                                & k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G) = B
                                & ? [H] :
                                    ( v1_relat_1(H)
                                    & v1_funct_1(H)
                                    & r2_hidden(H,k3_msualg_1(A,F,D))
                                    & E = k4_msualg_6(A,F,G,D,H) ) ) ) ) ) ) ) ) ) )).

fof(t11_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_msualg_6(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r1_msualg_6(A,B,C,D,E)
                       => ( v1_funct_1(E)
                          & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,D),B),k1_funct_1(u4_msualg_1(A,D),C))
                          & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,D),B),k1_funct_1(u4_msualg_1(A,D),C))
                          & k1_funct_1(u4_msualg_1(A,D),B) != k1_xboole_0
                          & k1_funct_1(u4_msualg_1(A,D),C) != k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t12_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( l3_msualg_1(D,A)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r1_msualg_6(A,B,C,D,E)
                       => r2_hidden(k4_tarski(B,C),k3_msualg_6(A)) ) ) ) ) ) ) )).

fof(t13_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ~ ( r2_hidden(k4_tarski(B,C),k3_msualg_6(A))
                      & ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ~ r1_msualg_6(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t14_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v1_msualg_6(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_rewrite1(k3_msualg_6(A),C,D)
                   => ! [E] :
                        ( m1_rewrite1(E,k3_msualg_6(A))
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F)
                              & v1_finseq_1(F)
                              & v1_funcop_1(F) )
                           => ( ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(F),np__1)
                                & C = k1_funct_1(E,np__1)
                                & D = k1_funct_1(E,k3_finseq_1(E))
                                & ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ! [H] :
                                        ( ( v1_relat_1(H)
                                          & v1_funct_1(H) )
                                       => ! [I] :
                                            ( m1_subset_1(I,u1_struct_0(A))
                                           => ! [J] :
                                                ( m1_subset_1(J,u1_struct_0(A))
                                               => ( ( r2_hidden(G,k4_finseq_1(F))
                                                    & H = k1_funct_1(F,G)
                                                    & I = k1_funct_1(E,G)
                                                    & J = k1_funct_1(E,k1_nat_1(G,np__1)) )
                                                 => r1_msualg_6(A,I,J,B,H) ) ) ) ) ) )
                             => ( v1_funct_1(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F))
                                & v1_funct_2(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
                                & m2_relset_1(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
                                & ( F != k1_xboole_0
                                 => ( k1_funct_1(u4_msualg_1(A,B),C) != k1_xboole_0
                                    & k1_funct_1(u4_msualg_1(A,B),D) != k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_rewrite1(k3_msualg_6(A),C,D)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
                          & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) )
                       => ( m2_msualg_6(E,A,B,C,D)
                        <=> ? [F] :
                              ( m1_rewrite1(F,k3_msualg_6(A))
                              & ? [G] :
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & v1_finseq_1(G)
                                  & v1_funcop_1(G)
                                  & E = k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),G)
                                  & k3_finseq_1(F) = k1_nat_1(k3_finseq_1(G),np__1)
                                  & C = k1_funct_1(F,np__1)
                                  & D = k1_funct_1(F,k3_finseq_1(F))
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ! [I] :
                                          ( ( v1_relat_1(I)
                                            & v1_funct_1(I) )
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ! [K] :
                                                  ( m1_subset_1(K,u1_struct_0(A))
                                                 => ( ( r2_hidden(H,k4_finseq_1(G))
                                                      & I = k1_funct_1(G,H)
                                                      & J = k1_funct_1(F,H)
                                                      & K = k1_funct_1(F,k1_nat_1(H,np__1)) )
                                                   => r1_msualg_6(A,J,K,B,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_rewrite1(k3_msualg_6(A),C,D)
                   => ! [E] :
                        ( m1_rewrite1(E,k3_msualg_6(A))
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F)
                              & v1_finseq_1(F)
                              & v1_funcop_1(F) )
                           => ( ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(F),np__1)
                                & C = k1_funct_1(E,np__1)
                                & D = k1_funct_1(E,k3_finseq_1(E))
                                & ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ! [H] :
                                        ( ( v1_relat_1(H)
                                          & v1_funct_1(H) )
                                       => ! [I] :
                                            ( m1_subset_1(I,u1_struct_0(A))
                                           => ! [J] :
                                                ( m1_subset_1(J,u1_struct_0(A))
                                               => ( ( r2_hidden(G,k4_finseq_1(F))
                                                    & H = k1_funct_1(F,G)
                                                    & I = k1_funct_1(E,G)
                                                    & J = k1_funct_1(E,k1_nat_1(G,np__1)) )
                                                 => r1_msualg_6(A,I,J,B,H) ) ) ) ) ) )
                             => m2_msualg_6(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F),A,B,C,D) ) ) ) ) ) ) ) ) )).

fof(t16_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => m2_msualg_6(k6_partfun1(k1_funct_1(u4_msualg_1(A,B),C)),A,B,C,C) ) ) ) )).

fof(t17_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r1_msualg_6(A,C,D,B,E)
                       => ( r1_rewrite1(k3_msualg_6(A),C,D)
                          & m2_msualg_6(E,A,B,C,D) ) ) ) ) ) ) ) )).

fof(t18_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_rewrite1(k3_msualg_6(A),C,D)
                          & r1_rewrite1(k3_msualg_6(A),D,E) )
                       => ! [F] :
                            ( m2_msualg_6(F,A,B,C,D)
                           => ! [G] :
                                ( m2_msualg_6(G,A,B,D,E)
                               => m2_msualg_6(k7_funct_2(k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),F,G),A,B,C,E) ) ) ) ) ) ) ) ) )).

fof(t19_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_rewrite1(k3_msualg_6(A),C,D)
                       => ! [F] :
                            ( m2_msualg_6(F,A,B,C,D)
                           => ! [G] :
                                ( ( v1_relat_1(G)
                                  & v1_funct_1(G) )
                               => ( r1_msualg_6(A,D,E,B,G)
                                 => m2_msualg_6(k5_relat_1(F,G),A,B,C,E) ) ) ) ) ) ) ) ) ) )).

fof(t20_msualg_6,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_rewrite1(k3_msualg_6(A),D,E)
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F) )
                           => ( r1_msualg_6(A,C,D,B,F)
                             => ! [G] :
                                  ( m2_msualg_6(G,A,B,D,E)
                                 => m2_msualg_6(k5_relat_1(F,G),A,B,C,E) ) ) ) ) ) ) ) ) ) )).

fof(t21_msualg_6,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] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E)))
                             => ! [G] :
                                  ( m1_subset_1(G,k3_msualg_1(A,E,B))
                                 => k5_relat_1(k4_msualg_6(A,E,F,B,G),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E))) = k5_relat_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F)),k4_msualg_6(A,E,F,C,k6_msualg_3(A,B,C,E,D,G))) ) ) ) ) ) ) ) ) ) )).

fof(t22_msualg_6,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] :
              ( m1_msualg_6(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r2_hidden(E,k4_finseq_1(k1_msualg_1(A,D)))
                       => ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,D,B))
                           => k5_relat_1(k4_msualg_6(A,D,E,B,F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k2_msualg_1(A,D))) = k5_relat_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),E)),k4_msualg_6(A,D,E,B,k6_msualg_3(A,B,B,D,C,F))) ) ) ) ) ) ) ) )).

fof(t23_msualg_6,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] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( ( v1_relat_1(G)
                                  & v1_funct_1(G) )
                               => ~ ( r1_msualg_6(A,E,F,B,G)
                                    & ! [H] :
                                        ( ( v1_funct_1(H)
                                          & v1_funct_2(H,k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F))
                                          & m2_relset_1(H,k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F)) )
                                       => ~ ( r1_msualg_6(A,E,F,C,H)
                                            & k7_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) = k5_relat_1(G,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_msualg_6,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] :
              ( m1_msualg_6(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ~ ( r1_msualg_6(A,D,E,B,F)
                              & ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E))
                                    & m2_relset_1(G,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E)) )
                                 => ~ ( r1_msualg_6(A,D,E,B,G)
                                      & k7_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),G) = k5_relat_1(F,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) )).

fof(t25_msualg_6,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] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r1_rewrite1(k3_msualg_6(A),E,F)
                             => ! [G] :
                                  ( m2_msualg_6(G,A,B,E,F)
                                 => ? [H] :
                                      ( m2_msualg_6(H,A,C,E,F)
                                      & k7_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) = k7_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),F),k1_funct_1(u4_msualg_1(A,C),F),G,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_msualg_6,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] :
              ( m1_msualg_6(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_rewrite1(k3_msualg_6(A),D,E)
                       => ! [F] :
                            ( m2_msualg_6(F,A,B,D,E)
                           => ? [G] :
                                ( m2_msualg_6(G,A,B,D,E)
                                & k7_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),G) = k7_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E),F,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) )).

fof(d7_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( v2_msualg_6(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] :
                        ( ( v1_relat_1(E)
                          & v1_funct_1(E) )
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F) )
                           => ( ( r2_hidden(E,k3_msualg_1(A,D,B))
                                & r2_hidden(F,k3_msualg_1(A,D,B))
                                & ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,D)))
                                     => r2_hidden(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),G))) ) ) )
                             => r2_hidden(k4_tarski(k1_funct_1(k5_msualg_1(A,D,B),E),k1_funct_1(k5_msualg_1(A,D,B),F)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k2_msualg_1(A,D))) ) ) ) ) ) ) ) ) )).

fof(d8_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( v3_msualg_6(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( ( v1_relat_1(F)
                              & v1_funct_1(F) )
                           => ( r1_msualg_6(A,D,E,B,F)
                             => ! [G,H] :
                                  ( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D))
                                 => r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,H)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) )).

fof(d9_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( v4_msualg_6(C,A,B)
              <=> ! [D] :
                    ( m1_msualg_6(D,A,B)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F,G] :
                            ( r2_hidden(k4_tarski(F,G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E))
                           => r2_hidden(k4_tarski(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E),F),k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E),G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) )).

fof(t27_msualg_6,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] :
              ( ( v3_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ( v2_msualg_6(C,A,B)
              <=> ( v3_msualg_4(C,A,B)
                  & v4_msualg_4(C,A,B)
                  & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) )).

fof(t28_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( v3_msualg_6(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r1_rewrite1(k3_msualg_6(A),D,E)
                         => ! [F] :
                              ( m2_msualg_6(F,A,B,D,E)
                             => ! [G,H] :
                                  ( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D))
                                 => r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,H)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) )).

fof(d10_msualg_6,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_msualg_4(C,A,B,B)
         => ( C = k5_msualg_6(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) )).

fof(d11_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( ( v3_msualg_6(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ( D = k6_msualg_6(A,B,C)
                  <=> ( r2_pboole(u1_struct_0(A),C,D)
                      & ! [E] :
                          ( ( v3_msualg_6(E,A,B)
                            & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                         => ( r2_pboole(u1_struct_0(A),C,E)
                           => r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) )).

fof(t29_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k6_msualg_6(A,B,C),D))
                          <=> ? [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                                & ? [H] :
                                    ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),G))
                                    & ? [I] :
                                        ( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,B),G))
                                        & ? [J] :
                                            ( m2_msualg_6(J,A,B,G,D)
                                            & r1_rewrite1(k3_msualg_6(A),G,D)
                                            & r2_hidden(k4_tarski(H,I),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,G))
                                            & E = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),J,H)
                                            & F = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),J,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t30_msualg_6,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_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => v4_msualg_6(k6_msualg_6(A,B,C),A,B) ) ) ) )).

fof(d12_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( ( v4_msualg_6(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ( D = k7_msualg_6(A,B,C)
                  <=> ( r2_pboole(u1_struct_0(A),C,D)
                      & ! [E] :
                          ( ( v4_msualg_6(E,A,B)
                            & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                         => ( r2_pboole(u1_struct_0(A),C,E)
                           => r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) )).

fof(t31_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k7_msualg_6(A,B,C),D))
                          <=> ? [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),D))
                                & ? [H] :
                                    ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),D))
                                    & ? [I] :
                                        ( m1_msualg_6(I,A,B)
                                        & r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D))
                                        & E = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),I,D),G)
                                        & F = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),I,D),H) ) ) ) ) ) ) ) ) ) ) )).

fof(t32_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => v4_msualg_6(k6_msualg_6(A,B,k7_msualg_6(A,B,C)),A,B) ) ) ) )).

fof(d13_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( ( v3_msualg_6(D,A,B)
                    & v4_msualg_6(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ( D = k8_msualg_6(A,B,C)
                  <=> ( r2_pboole(u1_struct_0(A),C,D)
                      & ! [E] :
                          ( ( v3_msualg_6(E,A,B)
                            & v4_msualg_6(E,A,B)
                            & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                         => ( r2_pboole(u1_struct_0(A),C,E)
                           => r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) )).

fof(t33_msualg_6,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] :
              ( ( v3_msualg_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => r6_pboole(u1_struct_0(A),k6_msualg_6(A,B,C),C) ) ) ) )).

fof(t34_msualg_6,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_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => r6_pboole(u1_struct_0(A),k7_msualg_6(A,B,C),C) ) ) ) )).

fof(t35_msualg_6,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] :
              ( ( v3_msualg_6(C,A,B)
                & v4_msualg_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => r6_pboole(u1_struct_0(A),k8_msualg_6(A,B,C),C) ) ) ) )).

fof(t36_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( r2_pboole(u1_struct_0(A),k7_msualg_6(A,B,C),k8_msualg_6(A,B,C))
                & r2_pboole(u1_struct_0(A),k6_msualg_6(A,B,C),k8_msualg_6(A,B,C))
                & r2_pboole(u1_struct_0(A),k7_msualg_6(A,B,k6_msualg_6(A,B,C)),k8_msualg_6(A,B,C)) ) ) ) ) )).

fof(t37_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => r6_pboole(u1_struct_0(A),k6_msualg_6(A,B,k7_msualg_6(A,B,C)),k8_msualg_6(A,B,C)) ) ) ) )).

fof(t38_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k8_msualg_6(A,B,C),D))
                          <=> ? [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                                & r1_rewrite1(k3_msualg_6(A),G,D)
                                & ? [H] :
                                    ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),G))
                                    & ? [I] :
                                        ( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,B),G))
                                        & ? [J] :
                                            ( m1_msualg_6(J,A,B)
                                            & ? [K] :
                                                ( m2_msualg_6(K,A,B,G,D)
                                                & r2_hidden(k4_tarski(H,I),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,G))
                                                & E = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),K,k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),G),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),J,G),H))
                                                & F = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),K,k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),G),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),J,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_msualg_6,axiom,(
    ! [A,B] :
      ( m2_relset_1(B,A,A)
     => ! [C] :
          ( m2_relset_1(C,A,A)
         => ( ! [D,E] :
                ( ( r2_hidden(D,A)
                  & r2_hidden(E,A) )
               => ( r2_hidden(k4_tarski(D,E),C)
                <=> r2_rewrite1(B,D,E) ) )
           => ( v1_partfun1(C,A,A)
              & v3_relat_2(C)
              & v8_relat_2(C) ) ) ) ) )).

fof(t40_msualg_6,axiom,(
    ! [A,B] :
      ( m2_relset_1(B,A,A)
     => ! [C] :
          ( ( v1_partfun1(C,A,A)
            & v3_relat_2(C)
            & v8_relat_2(C)
            & m2_relset_1(C,A,A) )
         => ( r1_tarski(B,C)
           => ! [D,E] :
                ( ( r2_hidden(D,A)
                  & r2_hidden(E,A)
                  & r2_rewrite1(B,D,E) )
               => r2_hidden(k4_tarski(D,E),C) ) ) ) ) )).

fof(t41_msualg_6,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( r2_hidden(k4_tarski(C,D),k1_msualg_5(A,B))
                  <=> r2_rewrite1(B,C,D) ) ) ) ) ) )).

fof(t42_msualg_6,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_msualg_4(C,A,B,B)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(B,D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(B,D))
                         => ( r2_hidden(k4_tarski(E,F),k1_msualg_4(A,B,B,k3_msualg_5(A,B,C),D))
                          <=> r2_rewrite1(k1_msualg_4(A,B,B,C,D),E,F) ) ) ) ) ) ) ) )).

fof(d14_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => k9_msualg_6(A,B,C) = k3_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),C) ) ) ) )).

fof(t43_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => r2_pboole(u1_struct_0(A),C,k9_msualg_6(A,B,C)) ) ) ) )).

fof(t44_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( ( v3_msualg_4(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ( r2_pboole(u1_struct_0(A),C,D)
                   => r2_pboole(u1_struct_0(A),k9_msualg_6(A,B,C),D) ) ) ) ) ) )).

fof(t45_msualg_6,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_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),E,F)
                           => ! [G] :
                                ( m1_msualg_6(G,A,B)
                               => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),G,D),E),k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),G,D),F)) ) ) ) ) ) ) ) ) )).

fof(t46_msualg_6,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_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => v4_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) ) )).

fof(t47_msualg_6,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] :
              ( ( v3_msualg_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ! [G] :
                              ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),D))
                             => ( r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),F,G)
                               => ! [H] :
                                    ( ( v1_relat_1(H)
                                      & v1_funct_1(H) )
                                   => ( r1_msualg_6(A,D,E,B,H)
                                     => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t48_msualg_6,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] :
              ( ( v3_msualg_6(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => v3_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) ) )).

fof(t49_msualg_6,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_msualg_4(C,A,B,B)
             => ! [D] :
                  ( m1_msualg_4(D,A,B,B)
                 => ( ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,k1_funct_1(B,E))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(B,E))
                               => ( r2_hidden(k4_tarski(F,G),k1_msualg_4(A,B,B,D,E))
                                <=> r2_rewrite1(k1_msualg_4(A,B,B,C,E),F,G) ) ) ) )
                   => v2_msualg_4(D,A,B) ) ) ) ) ) )).

fof(t50_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
                 => ( ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),E))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
                               => ( r2_hidden(k4_tarski(F,G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E))
                                <=> r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k8_msualg_6(A,B,C),E),F,G) ) ) ) )
                   => ( v3_msualg_4(D,A,B)
                      & v3_msualg_6(D,A,B)
                      & v4_msualg_6(D,A,B)
                      & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ) )).

fof(t51_msualg_6,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_msualg_4(C,A,B,B)
             => ! [D] :
                  ( ( v2_msualg_4(D,A,B)
                    & m1_msualg_4(D,A,B,B) )
                 => ( r2_pboole(A,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,k1_funct_1(B,E))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(B,E))
                               => ( r2_rewrite1(k1_msualg_4(A,B,B,C,E),F,G)
                                 => r2_hidden(k4_tarski(F,G),k1_msualg_4(A,B,B,D,E)) ) ) ) ) ) ) ) ) ) )).

fof(d15_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( ( v3_msualg_4(D,A,B)
                    & v3_msualg_6(D,A,B)
                    & v4_msualg_6(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ( D = k10_msualg_6(A,B,C)
                  <=> ( r2_pboole(u1_struct_0(A),C,D)
                      & ! [E] :
                          ( ( v3_msualg_4(E,A,B)
                            & v3_msualg_6(E,A,B)
                            & v4_msualg_6(E,A,B)
                            & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                         => ( r2_pboole(u1_struct_0(A),C,E)
                           => r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) )).

fof(t52_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( r2_pboole(u1_struct_0(A),k9_msualg_6(A,B,C),k10_msualg_6(A,B,C))
                & r2_pboole(u1_struct_0(A),k6_msualg_6(A,B,C),k10_msualg_6(A,B,C))
                & r2_pboole(u1_struct_0(A),k7_msualg_6(A,B,C),k10_msualg_6(A,B,C))
                & r2_pboole(u1_struct_0(A),k8_msualg_6(A,B,C),k10_msualg_6(A,B,C)) ) ) ) ) )).

fof(t53_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,k10_msualg_6(A,B,C),D))
                          <=> r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k8_msualg_6(A,B,C),D),E,F) ) ) ) ) ) ) ) )).

fof(t54_msualg_6,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => r6_pboole(u1_struct_0(A),k10_msualg_6(A,B,C),k9_msualg_6(A,B,k8_msualg_6(A,B,C))) ) ) ) )).

fof(s1_msualg_6,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_msualg_6))
         => p1_s1_msualg_6(k6_partfun1(k1_funct_1(u4_msualg_1(f1_s1_msualg_6,f2_s1_msualg_6),A)),A,A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_msualg_6))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s1_msualg_6))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s1_msualg_6))
                 => ( r1_rewrite1(k3_msualg_6(f1_s1_msualg_6),A,B)
                   => ! [D] :
                        ( m2_msualg_6(D,f1_s1_msualg_6,f2_s1_msualg_6,A,B)
                       => ( p1_s1_msualg_6(D,A,B)
                         => ! [E] :
                              ( ( v1_relat_1(E)
                                & v1_funct_1(E) )
                             => ( r1_msualg_6(f1_s1_msualg_6,B,C,f2_s1_msualg_6,E)
                               => p1_s1_msualg_6(k5_relat_1(D,E),A,C) ) ) ) ) ) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,u1_struct_0(f1_s1_msualg_6))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s1_msualg_6))
           => ( r1_rewrite1(k3_msualg_6(f1_s1_msualg_6),A,B)
             => ! [C] :
                  ( m2_msualg_6(C,f1_s1_msualg_6,f2_s1_msualg_6,A,B)
                 => p1_s1_msualg_6(C,A,B) ) ) ) ) )).

fof(s2_msualg_6,axiom,(
    ? [A] :
      ( m1_msualg_4(A,f1_s2_msualg_6,f2_s2_msualg_6,f2_s2_msualg_6)
      & ! [B] :
          ( m1_subset_1(B,f1_s2_msualg_6)
         => ! [C] :
              ( m1_subset_1(C,k1_funct_1(f2_s2_msualg_6,B))
             => ! [D] :
                  ( m1_subset_1(D,k1_funct_1(f2_s2_msualg_6,B))
                 => ( r2_hidden(k4_tarski(C,D),k1_msualg_4(f1_s2_msualg_6,f2_s2_msualg_6,f2_s2_msualg_6,A,B))
                  <=> p1_s2_msualg_6(B,C,D) ) ) ) ) ) )).

fof(s3_msualg_6,axiom,
    ( ! [A] :
        ( r2_hidden(A,f1_s3_msualg_6)
       => m2_relset_1(f3_s3_msualg_6(A),k1_funct_1(f2_s3_msualg_6,A),k1_funct_1(f2_s3_msualg_6,A)) )
   => ( ? [A] :
          ( m1_msualg_4(A,f1_s3_msualg_6,f2_s3_msualg_6,f2_s3_msualg_6)
          & ! [B] :
              ( r2_hidden(B,f1_s3_msualg_6)
             => k1_funct_1(A,B) = f3_s3_msualg_6(B) ) )
      & ! [A] :
          ( m1_msualg_4(A,f1_s3_msualg_6,f2_s3_msualg_6,f2_s3_msualg_6)
         => ! [B] :
              ( m1_msualg_4(B,f1_s3_msualg_6,f2_s3_msualg_6,f2_s3_msualg_6)
             => ( ( ! [C] :
                      ( r2_hidden(C,f1_s3_msualg_6)
                     => k1_funct_1(A,C) = f3_s3_msualg_6(C) )
                  & ! [C] :
                      ( r2_hidden(C,f1_s3_msualg_6)
                     => k1_funct_1(B,C) = f3_s3_msualg_6(C) ) )
               => r6_pboole(f1_s3_msualg_6,A,B) ) ) ) ) )).

fof(s4_msualg_6,axiom,
    ( ( ! [A] :
          ( m1_msualg_4(A,u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6))
         => ( p2_s4_msualg_6(A)
          <=> ! [B] :
                ( m1_subset_1(B,u1_struct_0(f1_s4_msualg_6))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(f1_s4_msualg_6))
                   => ! [D] :
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C))
                          & m2_relset_1(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C)) )
                       => ( p1_s4_msualg_6(D,B,C)
                         => ! [E,F] :
                              ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A,B))
                             => r2_hidden(k4_tarski(k1_funct_1(D,E),k1_funct_1(D,F)),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A,C)) ) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_msualg_6))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s4_msualg_6))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s4_msualg_6))
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B))
                        & m2_relset_1(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B)) )
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C))
                            & m2_relset_1(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C)) )
                         => ( ( p1_s4_msualg_6(D,A,B)
                              & p1_s4_msualg_6(E,B,C) )
                           => p1_s4_msualg_6(k7_funct_2(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C),D,E),A,C) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_msualg_6))
         => p1_s4_msualg_6(k6_partfun1(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A)),A,A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_msualg_6))
         => ! [B] :
              ( m1_subset_1(B,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
             => ! [C] :
                  ( m1_subset_1(C,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
                 => ( r2_hidden(k4_tarski(B,C),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),f4_s4_msualg_6,A))
                  <=> ? [D] :
                        ( m1_subset_1(D,u1_struct_0(f1_s4_msualg_6))
                        & ? [E] :
                            ( v1_funct_1(E)
                            & v1_funct_2(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
                            & m2_relset_1(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
                            & ? [F] :
                                ( m1_subset_1(F,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D))
                                & ? [G] :
                                    ( m1_subset_1(G,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D))
                                    & p1_s4_msualg_6(E,D,A)
                                    & r2_hidden(k4_tarski(F,G),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),f3_s4_msualg_6,D))
                                    & B = k8_funct_2(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),E,F)
                                    & C = k8_funct_2(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),E,G) ) ) ) ) ) ) ) ) )
   => ( p2_s4_msualg_6(f4_s4_msualg_6)
      & r2_pboole(u1_struct_0(f1_s4_msualg_6),f3_s4_msualg_6,f4_s4_msualg_6)
      & ! [A] :
          ( m1_msualg_4(A,u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6))
         => ( ( p2_s4_msualg_6(A)
              & r2_pboole(u1_struct_0(f1_s4_msualg_6),f3_s4_msualg_6,A) )
           => r2_pboole(u1_struct_0(f1_s4_msualg_6),f4_s4_msualg_6,A) ) ) ) )).

fof(dt_m1_msualg_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_msualg_6(C,A,B)
         => m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(existence_m1_msualg_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ? [C] : m1_msualg_6(C,A,B) ) )).

fof(dt_m2_msualg_6,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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => ! [E] :
          ( m2_msualg_6(E,A,B,C,D)
         => ( v1_funct_1(E)
            & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
            & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ) )).

fof(existence_m2_msualg_6,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)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => ? [E] : m2_msualg_6(E,A,B,C,D) ) )).

fof(dt_k1_msualg_6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(B,A)
        & m3_pboole(C,A,B,B)
        & m3_pboole(D,A,B,B) )
     => m3_pboole(k1_msualg_6(A,B,C,D),A,B,B) ) )).

fof(redefinition_k1_msualg_6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(B,A)
        & m3_pboole(C,A,B,B)
        & m3_pboole(D,A,B,B) )
     => k1_msualg_6(A,B,C,D) = k13_pboole(C,D) ) )).

fof(dt_k2_msualg_6,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m1_msualg_6(C,A,B)
        & m1_msualg_6(D,A,B) )
     => m1_msualg_6(k2_msualg_6(A,B,C,D),A,B) ) )).

fof(redefinition_k2_msualg_6,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m1_msualg_6(C,A,B)
        & m1_msualg_6(D,A,B) )
     => k2_msualg_6(A,B,C,D) = k13_pboole(C,D) ) )).

fof(dt_k3_msualg_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => m2_relset_1(k3_msualg_6(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k4_msualg_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & m1_subset_1(C,k5_numbers)
        & l3_msualg_1(D,A)
        & v1_relat_1(E)
        & v1_funct_1(E) )
     => ( v1_relat_1(k4_msualg_6(A,B,C,D,E))
        & v1_funct_1(k4_msualg_6(A,B,C,D,E)) ) ) )).

fof(dt_k5_msualg_6,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => m1_msualg_4(k5_msualg_6(A,B),A,B,B) ) )).

fof(dt_k6_msualg_6,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_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v3_msualg_6(k6_msualg_6(A,B,C),A,B)
        & m1_msualg_4(k6_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k7_msualg_6,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_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v4_msualg_6(k7_msualg_6(A,B,C),A,B)
        & m1_msualg_4(k7_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k8_msualg_6,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_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v3_msualg_6(k8_msualg_6(A,B,C),A,B)
        & v4_msualg_6(k8_msualg_6(A,B,C),A,B)
        & m1_msualg_4(k8_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k9_msualg_6,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_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v3_msualg_4(k9_msualg_6(A,B,C),A,B)
        & m1_msualg_4(k9_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k10_msualg_6,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_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v3_msualg_4(k10_msualg_6(A,B,C),A,B)
        & v3_msualg_6(k10_msualg_6(A,B,C),A,B)
        & v4_msualg_6(k10_msualg_6(A,B,C),A,B)
        & m1_msualg_4(k10_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).
%------------------------------------------------------------------------------