SET007 Axioms: SET007+566.ax


%------------------------------------------------------------------------------
% File     : SET007+566 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Correspondence Between Lattices of Subalgebras
% Version  : [Urb08] axioms.
% English  : The Correspondence Between Lattices of Subalgebras of Universal
%            Algebras and Many Sorted Algebras},

% 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    : mssublat [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   38 (   4 unit)
%            Number of atoms       :  401 (  45 equality)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :  420 (  57 ~  ;   0  |; 244  &)
%                                         (   3 <=>; 116 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   0 propositional; 1-3 arity)
%            Number of functors    :   48 (   7 constant; 0-4 arity)
%            Number of variables   :   92 (   0 singleton;  92 !;   0 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v2_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & ~ v1_xboole_0(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A))
        & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A))
        & v1_funcop_1(u1_unialg_1(A)) ) ) )).

fof(fc2_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ( ~ v3_struct_0(k7_msualg_1(A))
        & v3_realset2(k7_msualg_1(A))
        & v1_msualg_1(k7_msualg_1(A))
        & ~ v2_msualg_1(k7_msualg_1(A))
        & v6_msualg_1(k7_msualg_1(A))
        & v2_msualg_2(k7_msualg_1(A)) ) ) )).

fof(fc3_mssublat,axiom,(
    ! [A] :
      ( ( v7_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v7_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) )).

fof(fc4_mssublat,axiom,(
    ! [A] :
      ( ( v6_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v6_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) )).

fof(fc5_mssublat,axiom,(
    ! [A] :
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v8_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) )).

fof(fc6_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ( ~ v3_struct_0(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v6_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v7_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v8_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
        & v2_unialg_2(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) )).

fof(t1_mssublat,axiom,(
    ! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__0) = k1_xboole_0 )).

fof(t2_mssublat,axiom,(
    ! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__1) = k9_finseq_1(A) )).

fof(t3_mssublat,axiom,(
    ! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__2) = k10_finseq_1(A,A) )).

fof(t4_mssublat,axiom,(
    ! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__3) = k11_finseq_1(A,A,A) )).

fof(t5_mssublat,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k1_tarski(np__0))
         => ( B = k2_finseq_2(A,np__0)
          <=> k3_finseq_1(B) = A ) ) ) )).

fof(t6_mssublat,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( B = k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(np__0)),k9_pboole(np__0),A)
           => k3_finseq_1(B) = A ) ) ) )).

fof(t7_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => k7_msualg_1(A) = k7_msualg_1(B) ) ) ) )).

fof(t8_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => ! [C] :
                ( m4_pboole(C,u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B)))
               => ( C = u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_msualg_1(k7_msualg_1(B)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_msualg_1(k7_msualg_1(A)))
                         => ( E = D
                           => k5_msualg_1(k7_msualg_1(A),E,k10_msualg_1(A)) = k2_partfun1(k3_msualg_1(k7_msualg_1(B),D,k10_msualg_1(B)),k4_msualg_1(k7_msualg_1(B),D,k10_msualg_1(B)),k5_msualg_1(k7_msualg_1(B),D,k10_msualg_1(B)),k3_msualg_1(k7_msualg_1(A),E,k10_msualg_1(A))) ) ) ) ) ) ) ) ) )).

fof(t9_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => m4_pboole(u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B))) ) ) ) )).

fof(t10_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => ! [C] :
                ( m4_pboole(C,u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B)))
               => ( C = u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))
                 => v3_msualg_2(C,k7_msualg_1(B),k10_msualg_1(B)) ) ) ) ) ) )).

fof(t11_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => ! [C] :
                ( m4_pboole(C,u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B)))
               => ( C = u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))
                 => u5_msualg_1(k7_msualg_1(A),k10_msualg_1(A)) = k4_msualg_2(k7_msualg_1(B),k10_msualg_1(B),C) ) ) ) ) ) )).

fof(t12_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)) ) ) ) )).

fof(t13_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
           => m1_subset_1(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ) )).

fof(t14_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
               => ( C = u1_struct_0(A)
                 => v1_unialg_2(C,B) ) ) ) ) ) )).

fof(t15_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
               => ( C = u1_struct_0(A)
                 => u1_unialg_1(A) = k3_unialg_2(B,C) ) ) ) ) ) )).

fof(t16_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
           => m3_unialg_2(A,B) ) ) ) )).

fof(t17_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => m1_subset_1(u1_struct_0(k13_msualg_1(A,C)),k1_zfmisc_1(u1_struct_0(k13_msualg_1(A,B)))) ) ) ) )).

fof(t18_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k13_msualg_1(A,B)))) )
                 => ( D = u1_struct_0(k13_msualg_1(A,C))
                   => v1_unialg_2(D,k13_msualg_1(A,B)) ) ) ) ) ) )).

fof(t19_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k13_msualg_1(A,B)))) )
                 => ( D = u1_struct_0(k13_msualg_1(A,C))
                   => u1_unialg_1(k13_msualg_1(A,C)) = k3_unialg_2(k13_msualg_1(A,B),D) ) ) ) ) ) )).

fof(t20_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => m3_unialg_2(k13_msualg_1(A,C),k13_msualg_1(A,B)) ) ) ) )).

fof(t21_mssublat,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(B,A,C)
              <=> m1_msualg_2(B,A,g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C))) ) ) ) ) )).

fof(t22_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( k6_msualg_1(A) = k6_msualg_1(B)
          <=> k7_msualg_1(A) = k7_msualg_1(B) ) ) ) )).

fof(t23_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ( u1_struct_0(A) = k1_tarski(np__0)
           => k7_msualg_1(k13_msualg_1(A,B)) = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ) )).

fof(t24_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_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) )
             => ( ( u1_struct_0(A) = k1_tarski(np__0)
                  & k13_msualg_1(A,B) = k13_msualg_1(A,C) )
               => g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C)) ) ) ) ) )).

fof(t25_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ( u1_struct_0(A) = k1_tarski(np__0)
           => u4_msualg_1(A,B) = u4_msualg_1(k7_msualg_1(k13_msualg_1(A,B)),k10_msualg_1(k13_msualg_1(A,B))) ) ) ) )).

fof(t26_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ( u1_struct_0(A) = k1_tarski(np__0)
           => k10_msualg_1(k13_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ) )).

fof(t27_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,k7_msualg_1(A))
            & v5_msualg_1(B,k7_msualg_1(A))
            & m1_msualg_2(B,k7_msualg_1(A),k10_msualg_1(A)) )
         => ( u1_struct_0(k7_msualg_1(A)) = k1_tarski(np__0)
           => m3_unialg_2(k13_msualg_1(k7_msualg_1(A),B),A) ) ) ) )).

fof(t28_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & v8_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & v8_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ! [D] :
                  ( ( v4_msualg_1(D,k7_msualg_1(A))
                    & v5_msualg_1(D,k7_msualg_1(A))
                    & m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
                 => ! [E] :
                      ( ( v4_msualg_1(E,k7_msualg_1(A))
                        & v5_msualg_1(E,k7_msualg_1(A))
                        & m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
                     => ( ( D = k10_msualg_1(B)
                          & E = k10_msualg_1(C) )
                       => k2_pboole(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),D),u4_msualg_1(k7_msualg_1(A),E)) = k3_cqc_lang(np__0,k2_xboole_0(u1_struct_0(B),u1_struct_0(C))) ) ) ) ) ) ) )).

fof(t29_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & v8_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & v8_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ! [D] :
                  ( ( v4_msualg_1(D,k7_msualg_1(A))
                    & v5_msualg_1(D,k7_msualg_1(A))
                    & m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
                 => ! [E] :
                      ( ( v4_msualg_1(E,k7_msualg_1(A))
                        & v5_msualg_1(E,k7_msualg_1(A))
                        & m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
                     => ( ( D = k10_msualg_1(B)
                          & E = k10_msualg_1(C) )
                       => k3_pboole(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),D),u4_msualg_1(k7_msualg_1(A),E)) = k3_cqc_lang(np__0,k3_xboole_0(u1_struct_0(B),u1_struct_0(C))) ) ) ) ) ) ) )).

fof(t30_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_unialg_1(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & v8_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & v8_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ! [D] :
                  ( ( v4_msualg_1(D,k7_msualg_1(A))
                    & v5_msualg_1(D,k7_msualg_1(A))
                    & m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
                 => ! [E] :
                      ( ( v4_msualg_1(E,k7_msualg_1(A))
                        & v5_msualg_1(E,k7_msualg_1(A))
                        & m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
                     => ( ( D = k10_msualg_1(B)
                          & E = k10_msualg_1(C) )
                       => k10_msualg_1(k8_unialg_2(A,B,C)) = k13_msualg_2(k7_msualg_1(A),k10_msualg_1(A),D,E) ) ) ) ) ) ) )).

fof(t31_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & v8_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & v8_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ! [D] :
                  ( ( v4_msualg_1(D,k7_msualg_1(A))
                    & v5_msualg_1(D,k7_msualg_1(A))
                    & m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
                 => ! [E] :
                      ( ( v4_msualg_1(E,k7_msualg_1(A))
                        & v5_msualg_1(E,k7_msualg_1(A))
                        & m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
                     => ( ( D = k10_msualg_1(B)
                          & E = k10_msualg_1(C) )
                       => k10_msualg_1(k5_unialg_2(A,B,C)) = k11_msualg_2(k7_msualg_1(A),k10_msualg_1(A),D,E) ) ) ) ) ) ) )).

fof(t32_mssublat,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => r1_filter_1(k12_unialg_2(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))),k17_msualg_2(k7_msualg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))),k10_msualg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))))) ) )).
%------------------------------------------------------------------------------