% Mizar problem: t30_glib_002,glib_002,2373,40 
fof(t30_glib_002,conjecture,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ( ( v4_glib_002(A,A)
          & m2_glib_000(A,A) )
      <=> v1_glib_002(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,antisymmetry_r2_xboole_0,cc1_abian,cc1_finset_1,cc2_finset_1,cc3_polynom1,cc5_polynom1,cc8_glib_002,d7_glib_002,d8_xboole_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k25_glib_000,dt_k26_glib_000,dt_k6_glib_000,dt_k7_glib_000,dt_m1_glib_000,dt_m1_subset_1,dt_m2_glib_000,existence_m1_glib_000,existence_m1_subset_1,existence_m2_glib_000,fc14_polynom1,fc17_abian,fc1_glib_000,fc1_glib_002,fc20_polynom1,fc3_polynom1,irreflexivity_r2_xboole_0,irreflexivity_r7_glib_000,rc11_polynom1,rc1_finset_1,rc1_glib_000,rc2_polynom1,rc3_finset_1,rc4_finset_1,rc4_glib_002,rc7_polynom1,redefinition_k25_glib_000,redefinition_k26_glib_000,reflexivity_r1_tarski,t101_glib_000,t1_subset,t2_subset,t3_subset,t43_glib_000,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(glib_002,t30_glib_002)]).

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

fof(antisymmetry_r2_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(cc1_abian,axiom,(
    ! [A] : 
      ( v2_setfam_1(A)
     => v1_realset1(A) ) ),
    file(abian,cc1_abian),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_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(cc3_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_seqm_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) ) ) ),
    file(polynom1,cc3_polynom1),
    []).

fof(cc5_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_polynom1(A) ) ) ),
    file(polynom1,cc5_polynom1),
    []).

fof(cc8_glib_002,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ! [B] : 
          ( m2_glib_000(B,A)
         => ( v4_glib_002(B,A)
           => v1_glib_002(B) ) ) ) ),
    file(glib_002,cc8_glib_002),
    []).

fof(d7_glib_002,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ! [B] : 
          ( m2_glib_000(B,A)
         => ( v4_glib_002(B,A)
          <=> ( v1_glib_002(B)
              & ! [C] : 
                  ( ( v1_glib_002(C)
                    & m2_glib_000(C,A) )
                 => ~ r7_glib_000(B,C) ) ) ) ) ) ),
    file(glib_002,d7_glib_002),
    []).

fof(d8_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    []).

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_k25_glib_000,axiom,(
    ! [A,B] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A)
        & m2_glib_000(B,A) )
     => ( ~ v1_xboole_0(k25_glib_000(A,B))
        & m1_subset_1(k25_glib_000(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ) ),
    file(glib_000,k25_glib_000),
    []).

fof(dt_k26_glib_000,axiom,(
    ! [A,B] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A)
        & m2_glib_000(B,A) )
     => m1_subset_1(k26_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ),
    file(glib_000,k26_glib_000),
    []).

fof(dt_k6_glib_000,axiom,(
    $true ),
    file(glib_000,k6_glib_000),
    []).

fof(dt_k7_glib_000,axiom,(
    $true ),
    file(glib_000,k7_glib_000),
    []).

fof(dt_m1_glib_000,axiom,(
    ! [A] : 
      ( m1_glib_000(A)
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(glib_000,m1_glib_000),
    []).

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

fof(dt_m2_glib_000,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ! [B] : 
          ( m2_glib_000(B,A)
         => ( v1_glib_000(B)
            & m1_glib_000(B) ) ) ) ),
    file(glib_000,m2_glib_000),
    []).

fof(existence_m1_glib_000,axiom,(
    ? [A] : m1_glib_000(A) ),
    file(glib_000,m1_glib_000),
    []).

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

fof(existence_m2_glib_000,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ? [B] : m2_glib_000(B,A) ) ),
    file(glib_000,m2_glib_000),
    []).

fof(fc14_polynom1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0) ),
    file(polynom1,fc14_polynom1),
    []).

fof(fc17_abian,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_zfmisc_1(A))
        & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ),
    file(abian,fc17_abian),
    []).

fof(fc1_glib_000,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ~ v1_xboole_0(k6_glib_000(A)) ) ),
    file(glib_000,fc1_glib_000),
    []).

fof(fc1_glib_002,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => v1_finset_1(k1_zfmisc_1(A)) ) ),
    file(glib_002,fc1_glib_002),
    []).

fof(fc20_polynom1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0)
    & v1_polynom1(k1_xboole_0) ),
    file(polynom1,fc20_polynom1),
    []).

fof(fc3_polynom1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_matrlin(k1_xboole_0) ),
    file(polynom1,fc3_polynom1),
    []).

fof(irreflexivity_r2_xboole_0,axiom,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(irreflexivity_r7_glib_000,axiom,(
    ! [A,B] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A)
        & v1_glib_000(B)
        & m1_glib_000(B) )
     => ~ r7_glib_000(A,A) ) ),
    file(glib_000,r7_glib_000),
    []).

fof(rc11_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_seq_1(A)
      & v7_seqm_3(A)
      & v1_polynom1(A) ) ),
    file(polynom1,rc11_polynom1),
    []).

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

fof(rc1_glib_000,axiom,(
    ? [A] : 
      ( m1_glib_000(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_glib_000(A) ) ),
    file(glib_000,rc1_glib_000),
    []).

fof(rc2_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_funcop_1(A)
      & v1_matrlin(A) ) ),
    file(polynom1,rc2_polynom1),
    []).

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(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_glib_002,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ? [B] : 
          ( m2_glib_000(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_polynom1(B)
          & v1_glib_000(B)
          & v1_glib_002(B)
          & v4_glib_002(B,A) ) ) ),
    file(glib_002,rc4_glib_002),
    []).

fof(rc7_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A)
      & v7_seqm_3(A) ) ),
    file(polynom1,rc7_polynom1),
    []).

fof(redefinition_k25_glib_000,axiom,(
    ! [A,B] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A)
        & m2_glib_000(B,A) )
     => k25_glib_000(A,B) = k6_glib_000(B) ) ),
    file(glib_000,k25_glib_000),
    []).

fof(redefinition_k26_glib_000,axiom,(
    ! [A,B] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A)
        & m2_glib_000(B,A) )
     => k26_glib_000(A,B) = k7_glib_000(B) ) ),
    file(glib_000,k26_glib_000),
    []).

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

fof(t101_glib_000,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => ! [B] : 
          ( m2_glib_000(B,A)
         => ! [C] : 
              ( m2_glib_000(C,A)
             => ~ ( r7_glib_000(B,C)
                  & ~ r2_xboole_0(k25_glib_000(A,B),k25_glib_000(A,C))
                  & ~ r2_xboole_0(k26_glib_000(A,B),k26_glib_000(A,C)) ) ) ) ) ),
    file(glib_000,t101_glib_000),
    []).

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(t43_glib_000,axiom,(
    ! [A] : 
      ( ( v1_glib_000(A)
        & m1_glib_000(A) )
     => m2_glib_000(A,A) ) ),
    file(glib_000,t43_glib_000),
    []).

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),
    []).