SET007 Axioms: SET007+395.ax


%------------------------------------------------------------------------------
% File     : SET007+395 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subalgebras of Many Sorted Algebra.  Lattice of Subalgebras
% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   99 (   7 unit)
%            Number of atoms       :  764 (  56 equality)
%            Maximal formula depth :   18 (   9 average)
%            Number of connectives :  853 ( 188 ~  ;   0  |; 362  &)
%                                         (  26 <=>; 277 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   45 (   1 propositional; 0-4 arity)
%            Number of functors    :   48 (   1 constant; 0-6 arity)
%            Number of variables   :  321 (   0 singleton; 312 !;   9 ?)
%            Maximal term depth    :    7 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k2_pboole(A,B,C))
        & v2_relat_1(k2_pboole(A,B,C))
        & v1_funct_1(k2_pboole(A,B,C)) ) ) )).

fof(fc2_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k2_pboole(A,C,B))
        & v2_relat_1(k2_pboole(A,C,B))
        & v1_funct_1(k2_pboole(A,C,B)) ) ) )).

fof(fc3_msualg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( ~ v3_struct_0(g1_msualg_1(A,B,C,D))
        & v1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) )).

fof(rc1_msualg_2,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A)
      & v2_msualg_2(A) ) )).

fof(fc4_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msualg_2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_msualg_2(A,B,C)) ) )).

fof(fc5_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msualg_2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( v1_relat_1(k2_msualg_2(A,B))
        & v2_relat_1(k2_msualg_2(A,B))
        & ~ v3_relat_1(k2_msualg_2(A,B))
        & v1_funct_1(k2_msualg_2(A,B)) ) ) )).

fof(rc2_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_msualg_2(C,A,B)
          & v4_msualg_1(C,A) ) ) )).

fof(fc6_msualg_2,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) )
     => ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A)
        & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) )).

fof(rc3_msualg_2,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_2(C,A,B)
          & v4_msualg_1(C,A)
          & v5_msualg_1(C,A) ) ) )).

fof(fc7_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => ~ v1_xboole_0(k5_msualg_2(A,B,C)) ) )).

fof(fc8_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ~ v1_xboole_0(k6_msualg_2(A,B)) ) )).

fof(fc9_msualg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => ~ v1_xboole_0(k8_msualg_2(A,B,C,D)) ) )).

fof(fc10_msualg_2,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)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => ( v4_msualg_1(k12_msualg_2(A,B,C),A)
        & v5_msualg_1(k12_msualg_2(A,B,C),A) ) ) )).

fof(fc11_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ~ v1_xboole_0(k14_msualg_2(A,B)) ) )).

fof(fc12_msualg_2,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) )
     => ( ~ v3_struct_0(k17_msualg_2(A,B))
        & v3_lattices(k17_msualg_2(A,B))
        & v4_lattices(k17_msualg_2(A,B))
        & v5_lattices(k17_msualg_2(A,B))
        & v6_lattices(k17_msualg_2(A,B))
        & v7_lattices(k17_msualg_2(A,B))
        & v8_lattices(k17_msualg_2(A,B))
        & v9_lattices(k17_msualg_2(A,B))
        & v10_lattices(k17_msualg_2(A,B))
        & v13_lattices(k17_msualg_2(A,B))
        & v14_lattices(k17_msualg_2(A,B))
        & v15_lattices(k17_msualg_2(A,B)) ) ) )).

fof(t1_msualg_2,axiom,(
    $true )).

fof(t2_msualg_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_pboole(C,A)
             => ! [D] :
                  ( m2_finseq_2(D,A,k3_finseq_2(A))
                 => k4_card_3(k5_relat_1(D,k3_pboole(A,B,C))) = k3_xboole_0(k4_card_3(k5_relat_1(D,B)),k4_card_3(k5_relat_1(D,C))) ) ) ) ) )).

fof(d1_msualg_2,axiom,(
    $true )).

fof(d2_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_msualg_2(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
                & k1_funct_1(u2_msualg_1(A),C) = k1_xboole_0
                & k1_funct_1(u3_msualg_1(A),C) = B ) ) ) ) )).

fof(d3_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ( v2_msualg_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => v1_msualg_2(B,A) ) ) ) )).

fof(d5_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( C = k2_msualg_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k1_msualg_2(A,B,D) ) ) ) ) ) )).

fof(d6_msualg_2,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] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( r1_msualg_2(A,B,C,D)
                  <=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) ) ) ) ) ) )).

fof(d7_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( v3_msualg_2(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => r1_msualg_2(A,B,D,C) ) ) ) ) ) )).

fof(t3_msualg_2,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] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C))
                     => ( r2_pboole(u1_struct_0(A),D,E)
                       => r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B)) ) ) ) ) ) ) )).

fof(d8_msualg_2,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] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( r1_msualg_2(A,B,C,D)
                   => k3_msualg_2(A,B,C,D) = k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C)) ) ) ) ) ) )).

fof(d9_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] :
                  ( m3_pboole(D,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C))
                 => ( D = k4_msualg_2(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => k1_funct_1(D,E) = k3_msualg_2(A,B,E,C) ) ) ) ) ) ) )).

fof(t4_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
               => ( v3_msualg_2(C,A,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_msualg_1(A))
                     => k3_msualg_2(A,B,D,C) = k5_msualg_1(A,D,B) ) ) ) ) ) ) )).

fof(t5_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
               => r6_pboole(u1_msualg_1(A),k4_msualg_2(A,B,C),u5_msualg_1(A,B)) ) ) ) ) )).

fof(d10_msualg_2,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)
             => ( m1_msualg_2(C,A,B)
              <=> ( m4_pboole(u4_msualg_1(A,C),u1_struct_0(A),u4_msualg_1(A,B))
                  & ! [D] :
                      ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                     => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
                       => ( v3_msualg_2(D,A,B)
                          & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) ) )).

fof(t6_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => m1_msualg_2(B,A,B) ) ) )).

fof(t7_msualg_2,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] :
                  ( l3_msualg_1(D,A)
                 => ( ( m1_msualg_2(B,A,C)
                      & m1_msualg_2(C,A,D) )
                   => m1_msualg_2(B,A,D) ) ) ) ) ) )).

fof(t8_msualg_2,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)
             => ( ( v4_msualg_1(B,A)
                  & m1_msualg_2(B,A,C)
                  & v4_msualg_1(C,A)
                  & m1_msualg_2(C,A,B) )
               => B = C ) ) ) ) )).

fof(t9_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_2(C,A,B)
             => ! [D] :
                  ( m1_msualg_2(D,A,B)
                 => ( r2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                   => m1_msualg_2(C,A,D) ) ) ) ) ) )).

fof(t10_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v4_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                   => C = D ) ) ) ) ) )).

fof(t11_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_2(C,A,B)
             => m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)) ) ) ) )).

fof(t12_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msualg_2(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) )
             => ( v2_relat_1(k2_msualg_2(A,B))
                & m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)) ) ) ) ) )).

fof(t13_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msualg_2(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] :
                  ( ( v5_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => v2_relat_1(k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))) ) ) ) ) )).

fof(d11_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] :
                  ( D = k5_msualg_2(A,B,C)
                <=> ! [E] :
                      ( r2_hidden(E,D)
                    <=> ( r2_hidden(E,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B)))))
                        & m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B))
                        & ! [F] :
                            ( m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B))
                           => ( F = E
                             => ( v3_msualg_2(F,A,B)
                                & r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),F)
                                & r2_pboole(u1_struct_0(A),C,F) ) ) ) ) ) ) ) ) ) )).

fof(d12_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( C = k6_msualg_2(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ( r2_hidden(D,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B)))))
                    & m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                    & ! [E] :
                        ( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B))
                       => ( E = D
                         => v3_msualg_2(E,A,B) ) ) ) ) ) ) ) )).

fof(d13_msualg_2,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,k6_msualg_2(A,B))
             => k7_msualg_2(A,B,C) = C ) ) ) )).

fof(t14_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( r2_hidden(D,k5_msualg_2(A,B,C))
                  <=> ( v3_msualg_2(D,A,B)
                      & r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),D)
                      & r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ) )).

fof(t15_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( r2_hidden(C,k6_msualg_2(A,B))
              <=> v3_msualg_2(C,A,B) ) ) ) ) )).

fof(d14_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( E = k8_msualg_2(A,B,C,D)
                    <=> ! [F] :
                          ( r2_hidden(F,E)
                        <=> ? [G] :
                              ( m4_pboole(G,u1_struct_0(A),u4_msualg_1(A,B))
                              & r2_hidden(G,k5_msualg_2(A,B,C))
                              & F = k1_funct_1(G,D) ) ) ) ) ) ) ) )).

fof(d15_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( D = k9_msualg_2(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_funct_1(D,E) = k1_setfam_1(k8_msualg_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t16_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => r2_pboole(u1_struct_0(A),k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C),k9_msualg_2(A,B,C)) ) ) ) )).

fof(t17_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( v2_relat_1(k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C))
               => v2_relat_1(k9_msualg_2(A,B,C)) ) ) ) ) )).

fof(t18_msualg_2,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] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C))
                     => ( r2_hidden(E,k5_msualg_2(A,C,D))
                       => r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B)) ) ) ) ) ) ) )).

fof(t19_msualg_2,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] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C))
                     => ( r2_hidden(E,k5_msualg_2(A,C,D))
                       => r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),E),B)) ) ) ) ) ) ) )).

fof(t20_msualg_2,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] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
                 => r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k9_msualg_2(A,C,D)),B)) ) ) ) ) )).

fof(t21_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( v3_msualg_2(k9_msualg_2(A,B,C),A,B)
                & r2_pboole(u1_struct_0(A),C,k9_msualg_2(A,B,C)) ) ) ) ) )).

fof(d16_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( v3_msualg_2(C,A,B)
               => k10_msualg_2(A,B,C) = g3_msualg_1(A,C,k4_msualg_2(A,B,C)) ) ) ) ) )).

fof(d17_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_2(C,A,B)
             => ! [D] :
                  ( m1_msualg_2(D,A,B)
                 => ! [E] :
                      ( ( v4_msualg_1(E,A)
                        & m1_msualg_2(E,A,B) )
                     => ( E = k11_msualg_2(A,B,C,D)
                      <=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)))
                          & ! [F] :
                              ( m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B))
                             => ( r6_pboole(u1_struct_0(A),F,u4_msualg_1(A,E))
                               => ( v3_msualg_2(F,A,B)
                                  & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,E),k4_msualg_2(A,B,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(d18_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => ( D = k12_msualg_2(A,B,C)
                  <=> ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,D))
                      & ! [E] :
                          ( m1_msualg_2(E,A,B)
                         => ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,E))
                           => m1_msualg_2(D,A,E) ) ) ) ) ) ) ) ) )).

fof(t22_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
               => k12_msualg_2(A,B,C) = B ) ) ) ) )).

fof(t23_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v4_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
                   => k12_msualg_2(A,B,D) = C ) ) ) ) ) )).

fof(t24_msualg_2,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_2(C,A,B)
             => k11_msualg_2(A,B,k12_msualg_2(A,B,k2_msualg_2(A,B)),C) = k12_msualg_2(A,B,k2_msualg_2(A,B)) ) ) ) )).

fof(d19_msualg_2,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_2(C,A,B)
             => ! [D] :
                  ( m1_msualg_2(D,A,B)
                 => ! [E] :
                      ( ( v4_msualg_1(E,A)
                        & m1_msualg_2(E,A,B) )
                     => ( E = k13_msualg_2(A,B,C,D)
                      <=> ! [F] :
                            ( m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B))
                           => ( r6_pboole(u1_struct_0(A),F,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)))
                             => E = k12_msualg_2(A,B,F) ) ) ) ) ) ) ) ) )).

fof(t25_msualg_2,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_2(C,A,B)
             => ! [D] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ! [E] :
                      ( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B))
                     => ( r6_pboole(u1_struct_0(A),E,k2_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)))
                       => k13_msualg_2(A,B,k12_msualg_2(A,B,D),C) = k12_msualg_2(A,B,E) ) ) ) ) ) ) )).

fof(t26_msualg_2,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_2(C,A,B)
             => ! [D] :
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,B))
                   => k13_msualg_2(A,B,k12_msualg_2(A,B,D),C) = k12_msualg_2(A,B,D) ) ) ) ) ) )).

fof(t27_msualg_2,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_2(C,A,B)
             => ! [D] :
                  ( m1_msualg_2(D,A,B)
                 => k13_msualg_2(A,B,C,D) = k13_msualg_2(A,B,D,C) ) ) ) ) )).

fof(t28_msualg_2,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)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => k11_msualg_2(A,B,C,k13_msualg_2(A,B,C,D)) = C ) ) ) ) )).

fof(t29_msualg_2,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)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => k13_msualg_2(A,B,k11_msualg_2(A,B,C,D),D) = D ) ) ) ) )).

fof(d20_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( C = k14_msualg_2(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ( v4_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) ) ) ) ) ) )).

fof(d21_msualg_2,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
                & m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) )
             => ( C = k15_msualg_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k14_msualg_2(A,B))
                   => ! [E] :
                        ( m1_subset_1(E,k14_msualg_2(A,B))
                       => ! [F] :
                            ( ( v4_msualg_1(F,A)
                              & m1_msualg_2(F,A,B) )
                           => ! [G] :
                                ( ( v4_msualg_1(G,A)
                                  & m1_msualg_2(G,A,B) )
                               => ( ( D = F
                                    & E = G )
                                 => k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E) = k13_msualg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) )).

fof(d22_msualg_2,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
                & m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) )
             => ( C = k16_msualg_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k14_msualg_2(A,B))
                   => ! [E] :
                        ( m1_subset_1(E,k14_msualg_2(A,B))
                       => ! [F] :
                            ( ( v4_msualg_1(F,A)
                              & m1_msualg_2(F,A,B) )
                           => ! [G] :
                                ( ( v4_msualg_1(G,A)
                                  & m1_msualg_2(G,A,B) )
                               => ( ( D = F
                                    & E = G )
                                 => k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E) = k11_msualg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t30_msualg_2,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) )
         => v1_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).

fof(t31_msualg_2,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) )
         => v2_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).

fof(t32_msualg_2,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) )
         => v1_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).

fof(t33_msualg_2,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) )
         => v2_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).

fof(d23_msualg_2,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) )
         => k17_msualg_2(A,B) = g3_lattices(k14_msualg_2(A,B),k15_msualg_2(A,B),k16_msualg_2(A,B)) ) ) )).

fof(t34_msualg_2,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) )
         => v15_lattices(k17_msualg_2(A,B)) ) ) )).

fof(t35_msualg_2,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) )
         => k5_lattices(k17_msualg_2(A,B)) = k12_msualg_2(A,B,k2_msualg_2(A,B)) ) ) )).

fof(t36_msualg_2,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] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
               => k6_lattices(k17_msualg_2(A,B)) = k12_msualg_2(A,B,C) ) ) ) ) )).

fof(t37_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => k6_lattices(k17_msualg_2(A,B)) = B ) ) )).

fof(t38_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => m1_msualg_2(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A,B) ) ) )).

fof(t39_msualg_2,axiom,(
    $true )).

fof(t40_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => r2_hidden(u4_msualg_1(A,B),k5_msualg_2(A,B,C)) ) ) ) )).

fof(t41_msualg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => r1_tarski(k5_msualg_2(A,B,C),k6_msualg_2(A,B)) ) ) ) )).

fof(dt_m1_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_msualg_2(C,A,B)
         => l3_msualg_1(C,A) ) ) )).

fof(existence_m1_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ? [C] : m1_msualg_2(C,A,B) ) )).

fof(dt_k1_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_msualg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) ) )).

fof(dt_k2_msualg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) )).

fof(dt_k3_msualg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_msualg_1(A))
        & m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) )
     => ( v1_funct_1(k3_msualg_2(A,B,C,D))
        & v1_funct_2(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C))
        & m2_relset_1(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) ) ) )).

fof(dt_k4_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => m3_pboole(k4_msualg_2(A,B,C),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)) ) )).

fof(dt_k5_msualg_2,axiom,(
    $true )).

fof(dt_k6_msualg_2,axiom,(
    $true )).

fof(dt_k7_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k6_msualg_2(A,B)) )
     => m4_pboole(k7_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)) ) )).

fof(dt_k8_msualg_2,axiom,(
    $true )).

fof(dt_k9_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => m4_pboole(k9_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)) ) )).

fof(dt_k10_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => ( v4_msualg_1(k10_msualg_2(A,B,C),A)
        & m1_msualg_2(k10_msualg_2(A,B,C),A,B) ) ) )).

fof(dt_k11_msualg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m1_msualg_2(C,A,B)
        & m1_msualg_2(D,A,B) )
     => ( v4_msualg_1(k11_msualg_2(A,B,C,D),A)
        & m1_msualg_2(k11_msualg_2(A,B,C,D),A,B) ) ) )).

fof(dt_k12_msualg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => ( v4_msualg_1(k12_msualg_2(A,B,C),A)
        & m1_msualg_2(k12_msualg_2(A,B,C),A,B) ) ) )).

fof(dt_k13_msualg_2,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_msualg_2(C,A,B)
        & m1_msualg_2(D,A,B) )
     => ( v4_msualg_1(k13_msualg_2(A,B,C,D),A)
        & m1_msualg_2(k13_msualg_2(A,B,C,D),A,B) ) ) )).

fof(dt_k14_msualg_2,axiom,(
    $true )).

fof(dt_k15_msualg_2,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) )
     => ( v1_funct_1(k15_msualg_2(A,B))
        & v1_funct_2(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
        & m2_relset_1(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) ) ) )).

fof(dt_k16_msualg_2,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) )
     => ( v1_funct_1(k16_msualg_2(A,B))
        & v1_funct_2(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
        & m2_relset_1(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) ) ) )).

fof(dt_k17_msualg_2,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) )
     => ( ~ v3_struct_0(k17_msualg_2(A,B))
        & v3_lattices(k17_msualg_2(A,B))
        & v10_lattices(k17_msualg_2(A,B))
        & l3_lattices(k17_msualg_2(A,B)) ) ) )).

fof(d4_msualg_2,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_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C)))
                 => ( ( k1_funct_1(u4_msualg_1(A,B),C) != k1_xboole_0
                     => ( D = k1_msualg_2(A,B,C)
                      <=> ? [E] :
                            ( ~ v1_xboole_0(E)
                            & E = k1_funct_1(u4_msualg_1(A,B),C)
                            & D = a_4_0_msualg_2(A,B,C,E) ) ) )
                    & ( k1_funct_1(u4_msualg_1(A,B),C) = k1_xboole_0
                     => ( D = k1_msualg_2(A,B,C)
                      <=> D = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(fraenkel_a_4_0_msualg_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & l3_msualg_1(C,B)
        & m1_subset_1(D,u1_struct_0(B))
        & ~ v1_xboole_0(E) )
     => ( r2_hidden(A,a_4_0_msualg_2(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,E)
            & A = F
            & ? [G] :
                ( m1_subset_1(G,u1_msualg_1(B))
                & k1_funct_1(u2_msualg_1(B),G) = k1_xboole_0
                & k1_funct_1(u3_msualg_1(B),G) = D
                & r2_hidden(F,k2_relat_1(k5_msualg_1(B,G,C))) ) ) ) ) )).
%------------------------------------------------------------------------------