% Mizar problem: t26_mssubfam,mssubfam,648,14 
fof(t26_mssubfam,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ~ ( v1_pre_circ(B,A)
                  & r2_pboole(A,B,k11_pboole(A,C,D))
                  & ! [E] : 
                      ( m1_pboole(E,A)
                     => ! [F] : 
                          ( m1_pboole(F,A)
                         => ~ ( v1_pre_circ(E,A)
                              & r2_pboole(A,E,C)
                              & v1_pre_circ(F,A)
                              & r2_pboole(A,F,D)
                              & r2_pboole(A,B,k11_pboole(A,E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_mssubfam,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,cc2_pboole,d21_pboole,d3_pre_circ,d5_pboole,dt_k11_pboole,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_subset_1,existence_m1_pboole,existence_m1_subset_1,fc12_relat_1,fc14_finset_1,fc2_pboole,fc4_relat_1,fc7_mssubfam,rc1_finset_1,rc1_funct_1,rc1_pboole,rc1_relat_1,rc2_funct_1,rc2_pboole,rc2_pre_circ,rc2_relat_1,rc3_finset_1,rc3_funct_1,rc3_pboole,rc3_relat_1,rc4_finset_1,rc4_funct_1,rc5_funct_1,reflexivity_r1_tarski,reflexivity_r2_pboole,s3_pboole__e4_41__mssubfam,s3_pboole__e7_41__mssubfam,t13_cqc_the1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(mssubfam,t26_mssubfam)]).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
       => v1_pre_circ(B,A) ) ) ),
    file(mssubfam,cc1_mssubfam),
    []).

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_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_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(d21_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k11_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d21_pboole),
    []).

fof(d3_pre_circ,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_pre_circ(B,A)
      <=> ! [C] : 
            ( r2_hidden(C,A)
           => v1_finset_1(k1_funct_1(B,C)) ) ) ) ),
    file(pre_circ,d3_pre_circ),
    []).

fof(d5_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    []).

fof(dt_k11_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k11_pboole(A,B,C),A) ) ),
    file(pboole,k11_pboole),
    []).

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

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_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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

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

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

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_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_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc7_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A)
        & v1_pre_circ(C,A)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k11_pboole(A,B,C))
        & v1_funct_1(k11_pboole(A,B,C))
        & v1_pre_circ(k11_pboole(A,B,C),A) ) ) ),
    file(mssubfam,fc7_mssubfam),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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_pre_circ,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B)
      & v1_pre_circ(B,A) ) ),
    file(pre_circ,rc2_pre_circ),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_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(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

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

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    []).

fof(s3_pboole__e4_41__mssubfam,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_pboole(D,A) )
     => ( ! [E] : ~ ( r2_hidden(E,A)
            & ! [F] : ~ ? [G] : 
                  ( v1_finset_1(F)
                  & r1_tarski(F,k1_funct_1(C,E))
                  & v1_finset_1(G)
                  & r1_tarski(G,k1_funct_1(D,E))
                  & r1_tarski(k1_funct_1(B,E),k2_zfmisc_1(F,G)) ) )
       => ? [E] : 
            ( m1_pboole(E,A)
            & ! [F] : 
                ( r2_hidden(F,A)
               => ? [H] : 
                    ( v1_finset_1(k1_funct_1(E,F))
                    & r1_tarski(k1_funct_1(E,F),k1_funct_1(C,F))
                    & v1_finset_1(H)
                    & r1_tarski(H,k1_funct_1(D,F))
                    & r1_tarski(k1_funct_1(B,F),k2_zfmisc_1(k1_funct_1(E,F),H)) ) ) ) ) ) ),
    file(mssubfam,s3_pboole__e4_41__mssubfam),
    []).

fof(s3_pboole__e7_41__mssubfam,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_pboole(D,A)
        & m1_pboole(E,A) )
     => ( ! [F] : ~ ( r2_hidden(F,A)
            & ! [G] : ~ ( v1_finset_1(k1_funct_1(E,F))
                & r1_tarski(k1_funct_1(E,F),k1_funct_1(C,F))
                & v1_finset_1(G)
                & r1_tarski(G,k1_funct_1(D,F))
                & r1_tarski(k1_funct_1(B,F),k2_zfmisc_1(k1_funct_1(E,F),G)) ) )
       => ? [F] : 
            ( m1_pboole(F,A)
            & ! [G] : 
                ( r2_hidden(G,A)
               => ( v1_finset_1(k1_funct_1(E,G))
                  & r1_tarski(k1_funct_1(E,G),k1_funct_1(C,G))
                  & v1_finset_1(k1_funct_1(F,G))
                  & r1_tarski(k1_funct_1(F,G),k1_funct_1(D,G))
                  & r1_tarski(k1_funct_1(B,G),k2_zfmisc_1(k1_funct_1(E,G),k1_funct_1(F,G))) ) ) ) ) ) ),
    file(mssubfam,s3_pboole__e7_41__mssubfam),
    []).

fof(t13_cqc_the1,axiom,(
    ! [A,B,C] : ~ ( v1_finset_1(A)
      & r1_tarski(A,k2_zfmisc_1(B,C))
      & ! [D,E] : ~ ( v1_finset_1(D)
          & r1_tarski(D,B)
          & v1_finset_1(E)
          & r1_tarski(E,C)
          & r1_tarski(A,k2_zfmisc_1(D,E)) ) ) ),
    file(cqc_the1,t13_cqc_the1),
    []).

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_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),
    []).