SET007 Axioms: SET007+469.ax


%------------------------------------------------------------------------------
% File     : SET007+469 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Trivial Many Sorted Algebras and Many Sorted Congruences
% 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_9 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   51 (   1 unit)
%            Number of atoms       :  433 (  21 equality)
%            Maximal formula depth :   19 (  10 average)
%            Number of connectives :  443 (  61 ~  ;   0  |; 188  &)
%                                         (   3 <=>; 191 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   42 (   0 propositional; 1-4 arity)
%            Number of functors    :   54 (   3 constant; 0-6 arity)
%            Number of variables   :  218 (   0 singleton; 206 !;  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_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ? [C] :
          ( m1_subset_1(C,k6_closure2(A,B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) )).

fof(rc2_msualg_9,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] :
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) )).

fof(cc1_msualg_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ! [D] :
          ( m1_subset_1(D,k3_msualg_1(A,C,B))
         => ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D) ) ) ) )).

fof(cc2_msualg_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(C,u1_struct_0(A))
        & m2_pralg_2(D,B,A) )
     => ! [E] :
          ( m1_subset_1(E,k1_funct_1(k11_pralg_2(B,A,D),C))
         => ( v1_relat_1(E)
            & v1_funct_1(E) ) ) ) )).

fof(fc1_msualg_9,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k13_msafree(A,B))
        & v2_relat_1(k13_msafree(A,B))
        & ~ v3_relat_1(k13_msafree(A,B))
        & v1_funct_1(k13_msafree(A,B))
        & v1_msafree(k13_msafree(A,B),A,k11_msafree(A,B)) ) ) )).

fof(fc2_msualg_9,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v4_msualg_1(k11_msafree(A,B),A)
        & v5_msualg_1(k11_msafree(A,B),A)
        & v2_msafree(k11_msafree(A,B),A) ) ) )).

fof(fc3_msualg_9,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)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A) )
     => ( v4_msualg_1(k9_pralg_2(A,B,C),A)
        & v5_msualg_1(k9_pralg_2(A,B,C),A) ) ) )).

fof(fc4_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ( v1_relat_1(u4_msualg_1(A,k8_msafree2(A)))
        & v2_relat_1(u4_msualg_1(A,k8_msafree2(A)))
        & ~ v3_relat_1(u4_msualg_1(A,k8_msafree2(A)))
        & v1_funct_1(u4_msualg_1(A,k8_msafree2(A)))
        & v1_pre_circ(u4_msualg_1(A,k8_msafree2(A)),u1_struct_0(A)) ) ) )).

fof(fc5_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ( v4_msualg_1(k8_msafree2(A),A)
        & v5_msualg_1(k8_msafree2(A),A)
        & v4_msafree2(k8_msafree2(A),A) ) ) )).

fof(t1_msualg_9,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( ( r2_hidden(A,k1_relat_1(D))
          & r2_hidden(k1_funct_1(D,A),k2_zfmisc_1(B,C)) )
       => k1_funct_1(D,A) = k4_tarski(k1_funct_1(k15_mcart_1(D),A),k1_funct_1(k16_mcart_1(D),A)) ) ) )).

fof(t2_msualg_9,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_tarski(B))
            & m2_relset_1(C,A,k1_tarski(B)) )
         => k2_relat_1(C) = k1_tarski(B) ) ) )).

fof(t3_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,A)
          & m2_relset_1(B,k5_numbers,A)
          & k2_relat_1(B) = A ) ) )).

fof(t4_msualg_9,axiom,(
    ! [A] : r1_tarski(k8_eqrel_1(A,k1_eqrel_1(A)),k1_tarski(A)) )).

fof(t5_msualg_9,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k8_eqrel_1(A,k1_eqrel_1(A)) = k1_tarski(A) ) )).

fof(t6_msualg_9,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_pboole(C,A)
      & r6_pboole(A,k1_pzfmisc1(A,C),k2_pre_circ(A,k1_tarski(B))) ) )).

fof(t7_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ? [C] :
          ( v2_relat_1(C)
          & m1_pboole(C,A)
          & r2_pboole(A,B,C) ) ) )).

fof(t8_msualg_9,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v1_pre_circ(C,A)
            & m4_pboole(C,A,B) )
         => ? [D] :
              ( v2_relat_1(D)
              & v1_pre_circ(D,A)
              & m4_pboole(D,A,B)
              & r2_pboole(A,C,D) ) ) ) )).

fof(t9_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,B,k1_pzfmisc1(A,C))
             => ! [E] :
                  ( m3_pboole(E,A,B,k1_pzfmisc1(A,C))
                 => r6_pboole(A,D,E) ) ) ) ) )).

fof(t10_msualg_9,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,B,k1_pzfmisc1(A,C))
             => v2_msualg_3(D,A,B,k1_pzfmisc1(A,C)) ) ) ) )).

fof(t11_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( m3_pboole(D,A,k1_pzfmisc1(A,B),C)
             => v1_msualg_3(D) ) ) ) )).

fof(t12_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v1_msualg_3(k15_msafree(A,B)) ) ) )).

fof(t13_msualg_9,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ? [C] :
          ( m3_pboole(C,A,k2_pre_circ(A,k5_numbers),B)
          & v2_msualg_3(C,A,k2_pre_circ(A,k5_numbers),B) ) ) )).

fof(t14_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_pralg_2(C,k4_card_3(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m1_pralg_2(D,k4_card_3(u4_msualg_1(A,B)))
                 => ( ! [E] : k1_funct_1(k3_pralg_3(u4_msualg_1(A,B),E),C) = k1_funct_1(k3_pralg_3(u4_msualg_1(A,B),E),D)
                   => r6_pboole(k1_pralg_2(k4_card_3(u4_msualg_1(A,B))),C,D) ) ) ) ) ) )).

fof(t15_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_pralg_2(D,B,A)
                 => ! [E] :
                      ( m1_pralg_2(E,k4_card_3(k10_pralg_2(B,A,C,D)))
                     => ! [F] :
                          ( m1_pralg_2(F,k4_card_3(k10_pralg_2(B,A,C,D)))
                         => ( ! [G] :
                                ( m1_subset_1(G,B)
                               => k1_funct_1(k3_pralg_3(k10_pralg_2(B,A,C,D),G),E) = k1_funct_1(k3_pralg_3(k10_pralg_2(B,A,C,D),G),F) )
                           => r6_pboole(k1_pralg_2(k4_card_3(k10_pralg_2(B,A,C,D))),E,F) ) ) ) ) ) ) ) )).

fof(t16_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                     => ( r1_msualg_3(A,C,D,E)
                       => ! [F] :
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                           => ( r6_pboole(u1_struct_0(A),E,F)
                             => r1_msualg_3(A,C,B,F) ) ) ) ) ) ) ) ) )).

fof(t17_msualg_9,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))
                 => ( r3_msualg_3(A,B,C,D)
                   => r6_msualg_3(A,B,k7_msualg_3(A,B,C,D)) ) ) ) ) ) )).

fof(t18_msualg_9,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))
                 => ( v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                   => ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,E,C))
                           => ? [G] :
                                ( m1_subset_1(G,k3_msualg_1(A,E,B))
                                & k6_msualg_3(A,B,C,E,D,G) = F ) ) ) ) ) ) ) ) )).

fof(t19_msualg_9,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_msualg_1(A))
             => ! [D] :
                  ( m1_subset_1(D,k3_msualg_1(A,C,B))
                 => r2_hidden(k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),D),k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C))) ) ) ) ) )).

fof(t20_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D))
                         => ( ( r2_msualg_3(A,B,C,E)
                              & r1_msualg_3(A,B,D,F) )
                           => ! [G] :
                                ( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                               => ( r6_pboole(u1_struct_0(A),k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,G),F)
                                 => r1_msualg_3(A,C,D,G) ) ) ) ) ) ) ) ) ) )).

fof(d1_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] :
                  ( m3_pboole(E,A,B,k11_pboole(A,C,D))
                 => ! [F] :
                      ( m3_pboole(F,A,B,C)
                     => ( F = k1_msualg_9(A,B,C,D,E)
                      <=> ! [G] :
                            ( r2_hidden(G,A)
                           => k1_funct_1(F,G) = k15_mcart_1(k1_funct_1(E,G)) ) ) ) ) ) ) ) )).

fof(d2_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] :
                  ( m3_pboole(E,A,B,k11_pboole(A,C,D))
                 => ! [F] :
                      ( m3_pboole(F,A,B,D)
                     => ( F = k2_msualg_9(A,B,C,D,E)
                      <=> ! [G] :
                            ( r2_hidden(G,A)
                           => k1_funct_1(F,G) = k16_mcart_1(k1_funct_1(E,G)) ) ) ) ) ) ) ) )).

fof(t21_msualg_9,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,A)
     => ! [D] :
          ( m3_pboole(D,A,C,k11_pboole(A,k2_pre_circ(A,k1_tarski(B)),k2_pre_circ(A,k1_tarski(B))))
         => r6_pboole(A,k1_msualg_9(A,C,k2_pre_circ(A,k1_tarski(B)),k2_pre_circ(A,k1_tarski(B)),D),k2_msualg_9(A,C,k2_pre_circ(A,k1_tarski(B)),k2_pre_circ(A,k1_tarski(B)),D)) ) ) )).

fof(t22_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] :
                  ( m3_pboole(E,A,B,k11_pboole(A,C,D))
                 => ( v2_msualg_3(E,A,B,k11_pboole(A,C,D))
                   => v2_msualg_3(k1_msualg_9(A,B,C,D,E),A,B,C) ) ) ) ) ) )).

fof(t23_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] :
                  ( m3_pboole(E,A,B,k11_pboole(A,C,D))
                 => ( v2_msualg_3(E,A,B,k11_pboole(A,C,D))
                   => v2_msualg_3(k2_msualg_9(A,B,C,D,E),A,B,D) ) ) ) ) ) )).

fof(t24_msualg_9,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] :
                  ( ( v2_relat_1(E)
                    & m1_pboole(E,A) )
                 => ! [F] :
                      ( m3_pboole(F,A,B,k11_pboole(A,D,E))
                     => ( r1_pboole(A,C,k1_mssubfam(A,F))
                       => ! [G] :
                            ( r2_hidden(G,A)
                           => k1_funct_1(k1_closure1(A,F,C),G) = k4_tarski(k1_funct_1(k1_closure1(A,k1_msualg_9(A,B,D,E,F),C),G),k1_funct_1(k1_closure1(A,k2_msualg_9(A,B,D,E,F),C),G)) ) ) ) ) ) ) ) )).

fof(t25_msualg_9,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] :
              ( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k8_msafree2(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,k3_msualg_1(A,D,B))
                     => ( k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k8_msafree2(A)),C,k2_msualg_1(A,D)),k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),E)) = np__0
                        & k8_funct_2(k3_msualg_1(A,D,k8_msafree2(A)),k4_msualg_1(A,D,k8_msafree2(A)),k5_msualg_1(A,D,k8_msafree2(A)),k6_msualg_3(A,B,k8_msafree2(A),D,C,E)) = np__0 ) ) ) ) ) ) )).

fof(t26_msualg_9,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] :
              ( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k8_msafree2(A)))
             => r2_msualg_3(A,B,k8_msafree2(A),C) ) ) ) )).

fof(t27_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( ? [C] :
                ( m1_pboole(C,u1_struct_0(A))
                & r6_pboole(u1_struct_0(A),u4_msualg_1(A,B),k1_pzfmisc1(u1_struct_0(A),C)) )
           => r6_msualg_3(A,B,k8_msafree2(A)) ) ) ) )).

fof(t28_msualg_9,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)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => m4_pboole(C,u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))) ) ) ) )).

fof(t29_msualg_9,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,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))))
                 => ( C = D
                   => ( v3_msualg_4(k6_mssubfam(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),k5_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),D)),A,B)
                      & v4_msualg_4(k6_mssubfam(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),k5_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),D)),A,B)
                      & m1_msualg_4(k6_mssubfam(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),k5_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),D)),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ) )).

fof(t30_msualg_9,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)
                & v4_msualg_4(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),C,k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))
               => r6_pboole(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),k1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ) ) )).

fof(t31_msualg_9,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)
                   => r6_pboole(u1_struct_0(A),k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C),k16_msualg_4(A,B,k18_msualg_4(A,B,C,D)),k20_msualg_4(A,B,C,D)),D) ) ) ) ) ) )).

fof(t32_msualg_9,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)
                & v4_msualg_4(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,k14_msualg_4(A,B,C)),D))
                     => ? [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                          & E = k3_msualg_4(A,B,C,D,F) ) ) ) ) ) ) )).

fof(t33_msualg_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( 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)) )
             => ! [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)
                   => ! [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),k2_msualg_4(A,B,C,E))
                                 => ( r1_tarski(k3_msualg_4(A,B,C,E,F),k3_msualg_4(A,B,D,E,G))
                                    & ( v5_msualg_1(B,A)
                                     => r1_tarski(k3_msualg_4(A,B,C,E,G),k3_msualg_4(A,B,D,E,F)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t34_msualg_9,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)
                & v4_msualg_4(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))
                         => ( k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),k16_msualg_4(A,B,C),D),E) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),k16_msualg_4(A,B,C),D),F)
                          <=> r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,C,D)) ) ) ) ) ) ) ) )).

fof(t35_msualg_9,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)
                & v4_msualg_4(C,A,B)
                & 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)
                    & v4_msualg_4(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)))
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F))
                               => ! [H] :
                                    ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F))
                                   => ( G = k3_msualg_4(A,B,C,F,H)
                                     => k8_funct_2(k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,D)),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)),E,F),G) = k3_msualg_4(A,B,D,F,H) ) ) ) )
                       => r6_pboole(u1_struct_0(A),k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)),k16_msualg_4(A,B,C),E),k16_msualg_4(A,B,D)) ) ) ) ) ) ) )).

fof(t36_msualg_9,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)
                & v4_msualg_4(C,A,B)
                & 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)
                    & v4_msualg_4(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)))
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F))
                               => ! [H] :
                                    ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F))
                                   => ( G = k3_msualg_4(A,B,C,F,H)
                                     => k8_funct_2(k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,D)),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)),E,F),G) = k3_msualg_4(A,B,D,F,H) ) ) ) )
                       => r2_msualg_3(A,k14_msualg_4(A,B,C),k14_msualg_4(A,B,D),E) ) ) ) ) ) ) )).

fof(t37_msualg_9,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] :
                        ( ( v3_msualg_4(E,A,B)
                          & v4_msualg_4(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),E,k18_msualg_4(A,B,C,D))
                            & ! [F] :
                                ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,E)),u4_msualg_1(A,C))
                               => ~ ( r1_msualg_3(A,k14_msualg_4(A,B,E),C,F)
                                    & r6_pboole(u1_struct_0(A),D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,E)),u4_msualg_1(A,C),k16_msualg_4(A,B,E),F)) ) ) ) ) ) ) ) ) ) )).

fof(s1_msualg_9,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s1_msualg_9)
       => ? [B] : p1_s1_msualg_9(A,B) )
   => ? [A] :
        ( m1_pboole(A,f1_s1_msualg_9)
        & ! [B] :
            ( m1_subset_1(B,f1_s1_msualg_9)
           => p1_s1_msualg_9(B,k1_funct_1(A,B)) ) ) )).

fof(dt_k1_msualg_9,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & v2_relat_1(D)
        & m1_pboole(D,A)
        & m3_pboole(E,A,B,k11_pboole(A,C,D)) )
     => m3_pboole(k1_msualg_9(A,B,C,D,E),A,B,C) ) )).

fof(dt_k2_msualg_9,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & v2_relat_1(D)
        & m1_pboole(D,A)
        & m3_pboole(E,A,B,k11_pboole(A,C,D)) )
     => m3_pboole(k2_msualg_9(A,B,C,D,E),A,B,D) ) )).
%------------------------------------------------------------------------------