SET007 Axioms: SET007+393.ax


%------------------------------------------------------------------------------
% File     : SET007+393 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Many Sorted Algebras
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : msualg_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   83 (  13 unit)
%            Number of atoms       :  436 (  40 equality)
%            Maximal formula depth :   14 (   6 average)
%            Number of connectives :  437 (  84 ~  ;   0  |; 242  &)
%                                         (   5 <=>; 106 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   1 propositional; 0-4 arity)
%            Number of functors    :   48 (   4 constant; 0-6 arity)
%            Number of variables   :  151 (   0 singleton; 139 !;  12 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_msualg_1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & v1_msualg_1(A) ) )).

fof(rc2_msualg_1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & v2_msualg_1(A) ) )).

fof(rc3_msualg_1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A) ) )).

fof(rc4_msualg_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] :
          ( l2_msualg_1(B,A)
          & v3_msualg_1(B,A) ) ) )).

fof(rc5_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A) ) ) )).

fof(rc6_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A)
          & v5_msualg_1(B,A) ) ) )).

fof(rc7_msualg_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] :
          ( l2_msualg_1(B,A)
          & v3_msualg_1(B,A)
          & v5_msualg_1(B,A) ) ) )).

fof(fc1_msualg_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & v5_msualg_1(B,A)
        & l2_msualg_1(B,A) )
     => ( v1_relat_1(u4_msualg_1(A,B))
        & v2_relat_1(u4_msualg_1(A,B))
        & v1_funct_1(u4_msualg_1(A,B)) ) ) )).

fof(cc1_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
         => ~ v1_xboole_0(C) ) ) )).

fof(cc2_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))))
         => ~ v1_xboole_0(C) ) ) )).

fof(rc8_msualg_1,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A)
      & v6_msualg_1(A) ) )).

fof(fc2_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(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)) ) ) )).

fof(fc3_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A))
        & v5_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) ) ) )).

fof(fc4_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ~ v1_xboole_0(k11_msualg_1(A,B)) ) )).

fof(d1_msualg_1,axiom,(
    $true )).

fof(d2_msualg_1,axiom,(
    $true )).

fof(d3_msualg_1,axiom,(
    $true )).

fof(d4_msualg_1,axiom,(
    $true )).

fof(d5_msualg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
      <=> u1_msualg_1(A) = k1_xboole_0 ) ) )).

fof(d6_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B) ) ) )).

fof(d7_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) )).

fof(d8_msualg_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l2_msualg_1(B,A)
         => ( v5_msualg_1(B,A)
          <=> v2_relat_1(u4_msualg_1(A,B)) ) ) ) )).

fof(d9_msualg_1,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_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),u4_msualg_1(A,C))),B) ) ) ) )).

fof(d10_msualg_1,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)
             => k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) )).

fof(d11_msualg_1,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)
             => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) )).

fof(t1_msualg_1,axiom,(
    $true )).

fof(t2_msualg_1,axiom,(
    $true )).

fof(t3_msualg_1,axiom,(
    $true )).

fof(t4_msualg_1,axiom,(
    $true )).

fof(t5_msualg_1,axiom,(
    $true )).

fof(t6_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ~ v1_xboole_0(k5_msualg_1(A,B,C)) ) ) ) )).

fof(t7_msualg_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
                    & v1_funct_2(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C)
                    & m2_relset_1(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) ) ) ) ) ) )).

fof(t8_msualg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & ~ v1_xboole_0(B)
            & v1_unialg_1(B,A)
            & v2_unialg_1(B,A)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => k1_relat_1(B) = k1_funct_2(k2_finseq_1(k2_unialg_1(A,B)),A) ) ) )).

fof(t9_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ~ v1_xboole_0(k3_unialg_1(A)) ) )).

fof(d12_msualg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v6_msualg_1(A)
      <=> ? [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & u1_msualg_1(A) = k2_finseq_1(B) ) ) ) )).

fof(t10_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ( v3_realset2(A)
       => ! [B] :
            ( l3_msualg_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
               => ! [D] :
                    ( m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B)))
                   => C = D ) ) ) ) ) )).

fof(d13_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_realset2(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & v6_msualg_1(B)
            & l1_msualg_1(B) )
         => ( B = k7_msualg_1(A)
          <=> ( u1_struct_0(B) = k1_tarski(np__0)
              & u1_msualg_1(B) = k4_finseq_1(k6_msualg_1(A))
              & u2_msualg_1(B) = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0))
              & u3_msualg_1(B) = k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0) ) ) ) ) )).

fof(d14_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k8_msualg_1(A) = k10_pboole(k1_tarski(np__0),u1_struct_0(A)) ) )).

fof(d15_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k9_msualg_1(A) = u1_unialg_1(A) ) )).

fof(d16_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k10_msualg_1(A) = g3_msualg_1(k7_msualg_1(A),k8_msualg_1(A),k9_msualg_1(A)) ) )).

fof(d17_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( C = k11_msualg_1(A,B)
            <=> m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) ) ) ) )).

fof(t11_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => k3_msualg_1(A,B,C) = k4_finseq_2(k3_finseq_1(k1_msualg_1(A,B)),k11_msualg_1(A,C)) ) ) ) )).

fof(t12_msualg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) ) )).

fof(t13_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => r1_tarski(k3_msualg_1(A,B,C),k3_finseq_2(k11_msualg_1(A,C))) ) ) ) )).

fof(t14_msualg_1,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) )
         => m2_finseq_1(u5_msualg_1(A,B),k4_partfun1(k3_finseq_2(k11_msualg_1(A,B)),k11_msualg_1(A,B))) ) ) )).

fof(d18_msualg_1,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) )
         => k12_msualg_1(A,B) = u5_msualg_1(A,B) ) ) )).

fof(d19_msualg_1,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) )
         => k13_msualg_1(A,B) = g1_unialg_1(k11_msualg_1(A,B),k12_msualg_1(A,B)) ) ) )).

fof(t15_msualg_1,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) )
     => A = k13_msualg_1(k7_msualg_1(A),k10_msualg_1(A)) ) )).

fof(t16_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0)))
            & m2_relset_1(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0))) )
         => ( B = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0))
           => k7_msualg_1(A) = g1_msualg_1(k1_tarski(np__0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0)) ) ) ) )).

fof(dt_l1_msualg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) )).

fof(dt_l2_msualg_1,axiom,(
    $true )).

fof(existence_l2_msualg_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] : l2_msualg_1(B,A) ) )).

fof(dt_l3_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => l2_msualg_1(B,A) ) ) )).

fof(existence_l3_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : l3_msualg_1(B,A) ) )).

fof(abstractness_v1_msualg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v1_msualg_1(A)
       => A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) )).

fof(abstractness_v3_msualg_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A) )
     => ( v3_msualg_1(B,A)
       => B = g2_msualg_1(A,u4_msualg_1(A,B)) ) ) )).

fof(abstractness_v4_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ( v4_msualg_1(B,A)
       => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) )).

fof(dt_k1_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) )).

fof(dt_k2_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) )).

fof(dt_k3_msualg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & l3_msualg_1(C,A) )
     => m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) )).

fof(dt_k4_msualg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & l3_msualg_1(C,A) )
     => m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) )).

fof(dt_k5_msualg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & l3_msualg_1(C,A) )
     => ( v1_funct_1(k5_msualg_1(A,B,C))
        & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C))
        & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) )).

fof(dt_k6_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m2_finseq_1(k6_msualg_1(A),k5_numbers) ) )).

fof(redefinition_k6_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k6_msualg_1(A) = k3_unialg_1(A) ) )).

fof(dt_k7_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_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))
        & l1_msualg_1(k7_msualg_1(A)) ) ) )).

fof(dt_k8_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v2_relat_1(k8_msualg_1(A))
        & m1_pboole(k8_msualg_1(A),u1_struct_0(k7_msualg_1(A))) ) ) )).

fof(dt_k9_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m3_pboole(k9_msualg_1(A),u1_msualg_1(k7_msualg_1(A)),k8_pboole(u1_msualg_1(k7_msualg_1(A)),k3_finseq_2(u1_struct_0(k7_msualg_1(A))),u2_msualg_1(k7_msualg_1(A)),k6_pboole(u1_struct_0(k7_msualg_1(A)),k8_msualg_1(A))),k8_pboole(u1_msualg_1(k7_msualg_1(A)),u1_struct_0(k7_msualg_1(A)),u3_msualg_1(k7_msualg_1(A)),k8_msualg_1(A))) ) )).

fof(dt_k10_msualg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A))
        & l3_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) ) ) )).

fof(dt_k11_msualg_1,axiom,(
    $true )).

fof(dt_k12_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => m2_finseq_1(k12_msualg_1(A,B),k4_partfun1(k13_finseq_1(k11_msualg_1(A,B)),k11_msualg_1(A,B))) ) )).

fof(dt_k13_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( ~ v3_struct_0(k13_msualg_1(A,B))
        & v3_unialg_1(k13_msualg_1(A,B))
        & v6_unialg_1(k13_msualg_1(A,B))
        & v7_unialg_1(k13_msualg_1(A,B))
        & v8_unialg_1(k13_msualg_1(A,B))
        & l1_unialg_1(k13_msualg_1(A,B)) ) ) )).

fof(dt_u1_msualg_1,axiom,(
    $true )).

fof(dt_u2_msualg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v1_funct_1(u2_msualg_1(A))
        & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)))
        & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) )).

fof(dt_u3_msualg_1,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v1_funct_1(u3_msualg_1(A))
        & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A))
        & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) )).

fof(dt_u4_msualg_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A) )
     => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) )).

fof(dt_u5_msualg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => m3_pboole(u5_msualg_1(A,B),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),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) )).

fof(dt_g1_msualg_1,axiom,(
    ! [A,B,C,D] :
      ( ( 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) )
     => ( v1_msualg_1(g1_msualg_1(A,B,C,D))
        & l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) )).

fof(free_g1_msualg_1,axiom,(
    ! [A,B,C,D] :
      ( ( 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) )
     => ! [E,F,G,H] :
          ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).

fof(dt_g2_msualg_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v3_msualg_1(g2_msualg_1(A,B),A)
        & l2_msualg_1(g2_msualg_1(A,B),A) ) ) )).

fof(free_g2_msualg_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C,D] :
          ( g2_msualg_1(A,B) = g2_msualg_1(C,D)
         => ( A = C
            & B = D ) ) ) )).

fof(dt_g3_msualg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(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),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ( v4_msualg_1(g3_msualg_1(A,B,C),A)
        & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) )).

fof(free_g3_msualg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(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),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ! [D,E,F] :
          ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------