% Mizar problem: t5_msualg_5,msualg_5,522,10 
fof(t5_msualg_5,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ! [C] : 
              ( ( v2_msualg_4(C,A,B)
                & m1_msualg_4(C,A,B,B) )
             => r6_pboole(A,k3_msualg_5(A,B,C),C) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_msualg_4,cc1_partfun1,cc1_pboole,cc1_relset_1,cc2_pboole,d3_msualg_4,d3_msualg_5,dt_k1_funct_1,dt_k1_msualg_4,dt_k1_msualg_5,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_msualg_5,dt_m1_msualg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_msualg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_subset_1,fc2_finseq_1,fc2_pboole,fc4_subset_1,rc1_finseq_1,rc1_msualg_4,rc1_msualg_5,rc1_partfun1,rc1_pboole,rc1_subset_1,rc2_partfun1,rc2_pboole,rc2_subset_1,rc3_finseq_1,rc3_pboole,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_msualg_4,redefinition_m2_relset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r6_pboole,symmetry_r6_pboole,t1_subset,t2_subset,t3_msualg_5,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(msualg_5,t5_msualg_5)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m1_msualg_4(D,A,B,C)
         => v1_msualg_4(D) ) ) ),
    file(msualg_4,cc1_msualg_4),
    []).

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(d3_msualg_4,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_msualg_4(C,A,B,B)
         => ( v2_msualg_4(C,A,B)
          <=> ! [D,E] : 
                ( m2_relset_1(E,k1_funct_1(B,D),k1_funct_1(B,D))
               => ( ( r2_hidden(D,A)
                    & k1_funct_1(C,D) = E )
                 => ( v3_relat_2(E)
                    & v8_relat_2(E)
                    & v1_partfun1(E,k1_funct_1(B,D),k1_funct_1(B,D))
                    & m2_relset_1(E,k1_funct_1(B,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(msualg_4,d3_msualg_4),
    []).

fof(d3_msualg_5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ! [C] : 
              ( m1_msualg_4(C,A,B,B)
             => ! [D] : 
                  ( ( v2_msualg_4(D,A,B)
                    & m1_msualg_4(D,A,B,B) )
                 => ( D = k3_msualg_5(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k1_msualg_4(A,B,B,D,E) = k1_msualg_5(k1_funct_1(B,E),k1_msualg_4(A,B,B,C,E)) ) ) ) ) ) ) ),
    file(msualg_5,d3_msualg_5),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_msualg_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_msualg_4(D,A,B,C)
        & m1_subset_1(E,A) )
     => m2_relset_1(k1_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ),
    file(msualg_4,k1_msualg_4),
    []).

fof(dt_k1_msualg_5,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_partfun1(k1_msualg_5(A,B),A,A)
        & v3_relat_2(k1_msualg_5(A,B))
        & v8_relat_2(k1_msualg_5(A,B))
        & m2_relset_1(k1_msualg_5(A,B),A,A) ) ) ),
    file(msualg_5,k1_msualg_5),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_msualg_5,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_msualg_4(C,A,B,B) )
     => ( v2_msualg_4(k3_msualg_5(A,B,C),A,B)
        & m1_msualg_4(k3_msualg_5(A,B,C),A,B,B) ) ) ),
    file(msualg_5,k3_msualg_5),
    []).

fof(dt_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m1_msualg_4(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(msualg_4,m1_msualg_4),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m1_msualg_4(D,A,B,C) ) ),
    file(msualg_4,m1_msualg_4),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_msualg_4,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_msualg_4(B) ) ),
    file(msualg_4,rc1_msualg_4),
    []).

fof(rc1_msualg_5,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_msualg_4(C,A,B,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v2_msualg_4(C,A,B) ) ) ),
    file(msualg_5,rc1_msualg_5),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k1_msualg_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_msualg_4(D,A,B,C)
        & m1_subset_1(E,A) )
     => k1_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ),
    file(msualg_4,k1_msualg_4),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_msualg_5,axiom,(
    ! [A,B] : 
      ( ( v1_partfun1(B,A,A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & m2_relset_1(B,A,A) )
     => k1_msualg_5(A,B) = B ) ),
    file(msualg_5,t3_msualg_5),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).