% Mizar ND problem: t2_pboole,pboole,42,48 
fof(dh_c1_3__pboole,definition,
    ( ( ( v1_relat_1(c1_3__pboole)
        & v1_funct_1(c1_3__pboole) )
     => ( v3_relat_1(c1_3__pboole)
      <=> ( c1_3__pboole = k1_xboole_0
          | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( v3_relat_1(A)
        <=> ( A = k1_xboole_0
            | k2_relat_1(A) = k1_tarski(k1_xboole_0) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__pboole),file(pboole,c1_3__pboole)]),
    [interesting(0.8),axiom,file(pboole,c1_3__pboole)]).

fof(e1_3_1__pboole,assumption,(
    v3_relat_1(c1_3__pboole) ),
    introduced(assumption,[file(pboole,e1_3_1__pboole)]),
    [interesting(0.65),axiom,file(pboole,e1_3_1__pboole)]).

fof(e2_3_1__pboole,assumption,(
    c1_3__pboole != k1_xboole_0 ),
    introduced(assumption,[file(pboole,e2_3_1__pboole)]),
    [interesting(0.65),axiom,file(pboole,e2_3_1__pboole)]).

fof(cc1_finseq_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc2_funct_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_pboole,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    [interesting(0.9),axiom,file(pboole,rc1_pboole)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc3_finseq_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(rc6_finseq_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_c1_3__pboole,assumption,
    ( v1_relat_1(c1_3__pboole)
    & v1_funct_1(c1_3__pboole) ),
    introduced(assumption,[file(pboole,c1_3__pboole)]),
    [interesting(0.8),axiom,file(pboole,c1_3__pboole)]).

fof(fc2_finseq_1,theorem,
    ( 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),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(dh_c1_3_1_1_1__pboole,definition,
    ( ( r2_hidden(c1_3_1_1_1__pboole,k2_relat_1(c1_3__pboole))
     => r2_hidden(c1_3_1_1_1__pboole,k1_tarski(k1_xboole_0)) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c1_3__pboole))
       => r2_hidden(A,k1_tarski(k1_xboole_0)) ) ),
    introduced(definition,[new_symbol(c1_3_1_1_1__pboole),file(pboole,c1_3_1_1_1__pboole)]),
    [interesting(0.35),axiom,file(pboole,c1_3_1_1_1__pboole)]).

fof(e1_3_1_1_1__pboole,assumption,(
    r2_hidden(c1_3_1_1_1__pboole,k2_relat_1(c1_3__pboole)) ),
    introduced(assumption,[file(pboole,e1_3_1_1_1__pboole)]),
    [interesting(0.35),axiom,file(pboole,e1_3_1_1_1__pboole)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(dt_c1_3_1_1_1__pboole,assumption,(
    $true ),
    introduced(assumption,[file(pboole,c1_3_1_1_1__pboole)]),
    [interesting(0.35),axiom,file(pboole,c1_3_1_1_1__pboole)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_3_1_1_1__pboole,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_3__pboole))
      & k1_funct_1(c1_3__pboole,A) = c1_3_1_1_1__pboole ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,e1_3_1_1_1__pboole])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_pboole,rc3_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc2_finseq_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,rc1_funct_1,t1_subset,t7_boole,e1_3_1_1_1__pboole,d5_funct_1]),
    [interesting(0.35),file(pboole,e2_3_1_1_1__pboole),[file(pboole,e2_3_1_1_1__pboole)]]).

fof(d14_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v3_relat_1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => v1_xboole_0(k1_funct_1(A,B)) ) ) ) ),
    file(funct_1,d14_funct_1),
    [interesting(0.9),axiom,file(funct_1,d14_funct_1)]).

fof(e3_3_1_1_1__pboole,plain,(
    c1_3_1_1_1__pboole = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,e1_3_1_1_1__pboole,e1_3_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,cc1_funct_1,cc2_funct_1,fc2_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc4_funct_1,t1_subset,t6_boole,t7_boole,t8_boole,e2_3_1_1_1__pboole,e1_3_1__pboole,d14_funct_1]),
    [interesting(0.35),file(pboole,e3_3_1_1_1__pboole),[file(pboole,e3_3_1_1_1__pboole)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e4_3_1_1_1__pboole,plain,(
    r2_hidden(c1_3_1_1_1__pboole,k1_tarski(k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,e1_3_1_1_1__pboole,e1_3_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_c1_3_1_1_1__pboole,fc2_finseq_1,fc2_subset_1,t1_subset,t6_boole,t7_boole,e3_3_1_1_1__pboole,d1_tarski]),
    [interesting(0.35),file(pboole,e4_3_1_1_1__pboole),[file(pboole,e4_3_1_1_1__pboole)]]).

fof(i3_3_1_1_1__pboole,theorem,(
    $true ),
    introduced(tautology,[file(pboole,i3_3_1_1_1__pboole)]),
    [interesting(0.35),trivial,file(pboole,i3_3_1_1_1__pboole)]).

fof(i2_3_1_1_1__pboole,plain,(
    r2_hidden(c1_3_1_1_1__pboole,k1_tarski(k1_xboole_0)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,e1_3_1_1_1__pboole,e1_3_1__pboole])],[e4_3_1_1_1__pboole,i3_3_1_1_1__pboole]),
    [interesting(0.35),file(pboole,i2_3_1_1_1__pboole),[file(pboole,i2_3_1_1_1__pboole)]]).

fof(i1_3_1_1_1__pboole,plain,
    ( r2_hidden(c1_3_1_1_1__pboole,k2_relat_1(c1_3__pboole))
   => r2_hidden(c1_3_1_1_1__pboole,k1_tarski(k1_xboole_0)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_1_1_1__pboole,e1_3_1__pboole]),discharge_asm(discharge,[e1_3_1_1_1__pboole])],[e1_3_1_1_1__pboole,i2_3_1_1_1__pboole]),
    [interesting(0.35),file(pboole,i1_3_1_1_1__pboole),[file(pboole,i1_3_1_1_1__pboole)]]).

fof(i1_3_1_1_1_tmp__pboole,plain,
    ( r2_hidden(c1_3_1_1_1__pboole,k2_relat_1(c1_3__pboole))
   => r2_hidden(c1_3_1_1_1__pboole,k1_tarski(k1_xboole_0)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole,e1_3_1__pboole]),discharge_asm(discharge,[dt_c1_3_1_1_1__pboole])],[dt_c1_3_1_1_1__pboole,i1_3_1_1_1__pboole]),
    [interesting(0.5),e1_3_1_1__pboole]).

fof(e1_3_1_1__pboole,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c1_3__pboole))
     => r2_hidden(A,k1_tarski(k1_xboole_0)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__pboole,e1_3_1__pboole])],[i1_3_1_1_1_tmp__pboole,dh_c1_3_1_1_1__pboole]),
    [interesting(0.5),file(pboole,e1_3_1_1__pboole),[file(pboole,e1_3_1_1__pboole)]]).

fof(dt_c1_3_1_1__pboole,assumption,(
    $true ),
    introduced(assumption,[file(pboole,c1_3_1_1__pboole)]),
    [interesting(0.5),axiom,file(pboole,c1_3_1_1__pboole)]).

fof(dh_c1_3_1_1__pboole,definition,
    ( ~ ( r2_hidden(c1_3_1_1__pboole,k1_tarski(k1_xboole_0))
        & ~ r2_hidden(c1_3_1_1__pboole,k2_relat_1(c1_3__pboole)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_tarski(k1_xboole_0))
          & ~ r2_hidden(A,k2_relat_1(c1_3__pboole)) ) ),
    introduced(definition,[new_symbol(c1_3_1_1__pboole),file(pboole,c1_3_1_1__pboole)]),
    [interesting(0.5),axiom,file(pboole,c1_3_1_1__pboole)]).

fof(e5_3_1_1__pboole,assumption,(
    r2_hidden(c1_3_1_1__pboole,k1_tarski(k1_xboole_0)) ),
    introduced(assumption,[file(pboole,e5_3_1_1__pboole)]),
    [interesting(0.5),axiom,file(pboole,e5_3_1_1__pboole)]).

fof(dh_c2_3_1_1__pboole,definition,
    ( ? [A] : m1_subset_1(A,k1_relat_1(c1_3__pboole))
   => m1_subset_1(c2_3_1_1__pboole,k1_relat_1(c1_3__pboole)) ),
    introduced(definition,[new_symbol(c2_3_1_1__pboole),file(pboole,c2_3_1_1__pboole)]),
    [interesting(0.5),axiom,file(pboole,c2_3_1_1__pboole)]).

fof(e3_3_1_1__pboole,plain,(
    ? [A] : m1_subset_1(A,k1_relat_1(c1_3__pboole)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole])],[rc1_funct_1,existence_m1_subset_1,dt_k1_relat_1,dt_m1_subset_1,dt_c1_3__pboole]),
    [interesting(0.5),file(pboole,e3_3_1_1__pboole),[file(pboole,e3_3_1_1__pboole)]]).

fof(dt_c2_3_1_1__pboole,plain,(
    m1_subset_1(c2_3_1_1__pboole,k1_relat_1(c1_3__pboole)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__pboole])],[dh_c2_3_1_1__pboole,e3_3_1_1__pboole]),
    [interesting(0.5),file(pboole,c2_3_1_1__pboole),[file(pboole,c2_3_1_1__pboole)]]).

fof(e6_3_1_1__pboole,plain,(
    c1_3_1_1__pboole = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1_1__pboole,e5_3_1_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_c1_3_1_1__pboole,fc2_finseq_1,fc2_subset_1,t1_subset,t6_boole,t7_boole,e5_3_1_1__pboole,d1_tarski]),
    [interesting(0.5),file(pboole,e6_3_1_1__pboole),[file(pboole,e6_3_1_1__pboole)]]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.9),axiom,file(relat_1,t64_relat_1)]).

fof(e2_3_1_1__pboole,plain,(
    k1_relat_1(c1_3__pboole) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,e2_3_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_finseq_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,fc2_finseq_1,t6_boole,e2_3_1__pboole,t64_relat_1]),
    [interesting(0.5),file(pboole,e2_3_1_1__pboole),[file(pboole,e2_3_1_1__pboole)]]).

fof(e4_3_1_1__pboole,plain,(
    v1_xboole_0(k1_funct_1(c1_3__pboole,c2_3_1_1__pboole)) ),
    inference(mizar_by,[status(thm),assumptions([e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_c1_3__pboole,dt_c2_3_1_1__pboole,cc1_funct_1,cc2_funct_1,fc2_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc4_funct_1,t1_subset,t6_boole,t7_boole,t8_boole,e1_3_1__pboole,e2_3_1_1__pboole,d14_funct_1]),
    [interesting(0.5),file(pboole,e4_3_1_1__pboole),[file(pboole,e4_3_1_1__pboole)]]).

fof(e7_3_1_1__pboole,plain,(
    r2_hidden(c1_3_1_1__pboole,k2_relat_1(c1_3__pboole)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1_1__pboole,e5_3_1_1__pboole,e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,dt_c1_3_1_1__pboole,dt_c2_3_1_1__pboole,cc1_funct_1,cc2_funct_1,fc2_finseq_1,rc1_funct_1,rc2_funct_1,t1_subset,t6_boole,t7_boole,t8_boole,e6_3_1_1__pboole,e2_3_1_1__pboole,e4_3_1_1__pboole,d5_funct_1]),
    [interesting(0.5),file(pboole,e7_3_1_1__pboole),[file(pboole,e7_3_1_1__pboole)]]).

fof(i4_3_1_1__pboole,theorem,(
    $true ),
    introduced(tautology,[file(pboole,i4_3_1_1__pboole)]),
    [interesting(0.5),trivial,file(pboole,i4_3_1_1__pboole)]).

fof(i3_3_1_1__pboole,plain,(
    r2_hidden(c1_3_1_1__pboole,k2_relat_1(c1_3__pboole)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_1_1__pboole,e5_3_1_1__pboole,e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole])],[e7_3_1_1__pboole,i4_3_1_1__pboole]),
    [interesting(0.5),file(pboole,i3_3_1_1__pboole),[file(pboole,i3_3_1_1__pboole)]]).

fof(i2_3_1_1__pboole,plain,(
    ~ ( r2_hidden(c1_3_1_1__pboole,k1_tarski(k1_xboole_0))
      & ~ r2_hidden(c1_3_1_1__pboole,k2_relat_1(c1_3__pboole)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_1_1__pboole,e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole]),discharge_asm(discharge,[e5_3_1_1__pboole])],[e5_3_1_1__pboole,i3_3_1_1__pboole]),
    [interesting(0.5),file(pboole,i2_3_1_1__pboole),[file(pboole,i2_3_1_1__pboole)]]).

fof(i2_3_1_1_tmp__pboole,plain,(
    ~ ( r2_hidden(c1_3_1_1__pboole,k1_tarski(k1_xboole_0))
      & ~ r2_hidden(c1_3_1_1__pboole,k2_relat_1(c1_3__pboole)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole]),discharge_asm(discharge,[dt_c1_3_1_1__pboole])],[dt_c1_3_1_1__pboole,i2_3_1_1__pboole]),
    [interesting(0.5),i1_3_1_1__pboole]).

fof(i1_3_1_1__pboole,plain,(
    r1_tarski(k1_tarski(k1_xboole_0),k2_relat_1(c1_3__pboole)) ),
    inference(let,[status(thm),assumptions([e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole])],[i2_3_1_1_tmp__pboole,cc1_finseq_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,fc2_finseq_1,fc2_subset_1,d3_tarski,dh_c1_3_1_1__pboole]),
    [interesting(0.5),file(pboole,i1_3_1_1__pboole),[file(pboole,i1_3_1_1__pboole)]]).

fof(e3_3_1__pboole,plain,(
    k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole])],[cc1_finseq_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,fc2_finseq_1,fc2_subset_1,d3_tarski,d10_xboole_0,e1_3_1_1__pboole,i1_3_1_1__pboole]),
    [interesting(0.65),file(pboole,e3_3_1__pboole),[file(pboole,e3_3_1__pboole)]]).

fof(i2_3_1__pboole,theorem,(
    $true ),
    introduced(tautology,[file(pboole,i2_3_1__pboole)]),
    [interesting(0.65),trivial,file(pboole,i2_3_1__pboole)]).

fof(i1_3_1__pboole,plain,(
    k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([e1_3_1__pboole,dt_c1_3__pboole,e2_3_1__pboole])],[e3_3_1__pboole,i2_3_1__pboole]),
    [interesting(0.65),file(pboole,i1_3_1__pboole),[file(pboole,i1_3_1__pboole)]]).

fof(e1_3__pboole,plain,
    ( v3_relat_1(c1_3__pboole)
   => ( c1_3__pboole = k1_xboole_0
      | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole]),discharge_asm(discharge,[e1_3_1__pboole,e2_3_1__pboole])],[e1_3_1__pboole,e2_3_1__pboole,i1_3_1__pboole]),
    [interesting(0.8),file(pboole,e1_3__pboole),[file(pboole,e1_3__pboole)]]).

fof(e2_3__pboole,assumption,
    ( c1_3__pboole = k1_xboole_0
    | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ),
    introduced(assumption,[file(pboole,e2_3__pboole)]),
    [interesting(0.8),axiom,file(pboole,e2_3__pboole)]).

fof(e1_3_2_1__pboole,assumption,(
    c1_3__pboole = k1_xboole_0 ),
    introduced(assumption,[file(pboole,e1_3_2_1__pboole)]),
    [interesting(0.5),axiom,file(pboole,e1_3_2_1__pboole)]).

fof(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.9),axiom,file(relat_1,t60_relat_1)]).

fof(e2_3_2_1__pboole,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(c1_3__pboole))
     => v1_xboole_0(k1_funct_1(c1_3__pboole,A)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,e1_3_2_1__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,cc1_funct_1,fc2_finseq_1,t1_subset,t6_boole,t7_boole,t8_boole,e1_3_2_1__pboole,t60_relat_1]),
    [interesting(0.5),file(pboole,e2_3_2_1__pboole),[file(pboole,e2_3_2_1__pboole)]]).

fof(i2_3_2_1__pboole,theorem,(
    $true ),
    introduced(tautology,[file(pboole,i2_3_2_1__pboole)]),
    [interesting(0.5),trivial,file(pboole,i2_3_2_1__pboole)]).

fof(i1_3_2_1__pboole,plain,(
    v3_relat_1(c1_3__pboole) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__pboole,e1_3_2_1__pboole])],[rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_c1_3__pboole,cc1_funct_1,cc2_funct_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc4_funct_1,d14_funct_1,e2_3_2_1__pboole,i2_3_2_1__pboole]),
    [interesting(0.5),file(pboole,i1_3_2_1__pboole),[file(pboole,i1_3_2_1__pboole)]]).

fof(i1_3_2__pboole,plain,
    ( c1_3__pboole = k1_xboole_0
   => v3_relat_1(c1_3__pboole) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole]),discharge_asm(discharge,[e1_3_2_1__pboole])],[e1_3_2_1__pboole,i1_3_2_1__pboole]),
    [interesting(0.65),file(pboole,i1_3_2__pboole),[file(pboole,i1_3_2__pboole)]]).

fof(e1_3_2_2__pboole,assumption,(
    k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ),
    introduced(assumption,[file(pboole,e1_3_2_2__pboole)]),
    [interesting(0.5),axiom,file(pboole,e1_3_2_2__pboole)]).

fof(dt_c1_3_2_2__pboole,assumption,(
    $true ),
    introduced(assumption,[file(pboole,c1_3_2_2__pboole)]),
    [interesting(0.5),axiom,file(pboole,c1_3_2_2__pboole)]).

fof(dh_c1_3_2_2__pboole,definition,
    ( ~ ( r2_hidden(c1_3_2_2__pboole,k1_relat_1(c1_3__pboole))
        & ~ v1_xboole_0(k1_funct_1(c1_3__pboole,c1_3_2_2__pboole)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_relat_1(c1_3__pboole))
          & ~ v1_xboole_0(k1_funct_1(c1_3__pboole,A)) ) ),
    introduced(definition,[new_symbol(c1_3_2_2__pboole),file(pboole,c1_3_2_2__pboole)]),
    [interesting(0.5),axiom,file(pboole,c1_3_2_2__pboole)]).

fof(e2_3_2_2__pboole,assumption,(
    r2_hidden(c1_3_2_2__pboole,k1_relat_1(c1_3__pboole)) ),
    introduced(assumption,[file(pboole,e2_3_2_2__pboole)]),
    [interesting(0.5),axiom,file(pboole,e2_3_2_2__pboole)]).

fof(e3_3_2_2__pboole,plain,(
    r2_hidden(k1_funct_1(c1_3__pboole,c1_3_2_2__pboole),k2_relat_1(c1_3__pboole)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_2_2__pboole,e2_3_2_2__pboole])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_pboole,rc3_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc2_finseq_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_3__pboole,dt_c1_3_2_2__pboole,rc1_funct_1,t1_subset,t7_boole,e2_3_2_2__pboole,d5_funct_1]),
    [interesting(0.5),file(pboole,e3_3_2_2__pboole),[file(pboole,e3_3_2_2__pboole)]]).

fof(e4_3_2_2__pboole,plain,(
    v1_xboole_0(k1_funct_1(c1_3__pboole,c1_3_2_2__pboole)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_2_2__pboole,e2_3_2_2__pboole,e1_3_2_2__pboole])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc2_funct_1,fc11_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,dt_c1_3_2_2__pboole,cc1_funct_1,fc2_finseq_1,fc2_subset_1,t1_subset,t6_boole,t7_boole,t8_boole,e3_3_2_2__pboole,e1_3_2_2__pboole,d1_tarski]),
    [interesting(0.5),file(pboole,e4_3_2_2__pboole),[file(pboole,e4_3_2_2__pboole)]]).

fof(i4_3_2_2__pboole,theorem,(
    $true ),
    introduced(tautology,[file(pboole,i4_3_2_2__pboole)]),
    [interesting(0.5),trivial,file(pboole,i4_3_2_2__pboole)]).

fof(i3_3_2_2__pboole,plain,(
    v1_xboole_0(k1_funct_1(c1_3__pboole,c1_3_2_2__pboole)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_2_2__pboole,e2_3_2_2__pboole,e1_3_2_2__pboole])],[e4_3_2_2__pboole,i4_3_2_2__pboole]),
    [interesting(0.5),file(pboole,i3_3_2_2__pboole),[file(pboole,i3_3_2_2__pboole)]]).

fof(i2_3_2_2__pboole,plain,(
    ~ ( r2_hidden(c1_3_2_2__pboole,k1_relat_1(c1_3__pboole))
      & ~ v1_xboole_0(k1_funct_1(c1_3__pboole,c1_3_2_2__pboole)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole,dt_c1_3_2_2__pboole,e1_3_2_2__pboole]),discharge_asm(discharge,[e2_3_2_2__pboole])],[e2_3_2_2__pboole,i3_3_2_2__pboole]),
    [interesting(0.5),file(pboole,i2_3_2_2__pboole),[file(pboole,i2_3_2_2__pboole)]]).

fof(i2_3_2_2_tmp__pboole,plain,(
    ~ ( r2_hidden(c1_3_2_2__pboole,k1_relat_1(c1_3__pboole))
      & ~ v1_xboole_0(k1_funct_1(c1_3__pboole,c1_3_2_2__pboole)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole,e1_3_2_2__pboole]),discharge_asm(discharge,[dt_c1_3_2_2__pboole])],[dt_c1_3_2_2__pboole,i2_3_2_2__pboole]),
    [interesting(0.5),i1_3_2_2__pboole]).

fof(i1_3_2_2__pboole,plain,(
    v3_relat_1(c1_3__pboole) ),
    inference(let,[status(thm),assumptions([dt_c1_3__pboole,e1_3_2_2__pboole])],[i2_3_2_2_tmp__pboole,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_c1_3__pboole,cc1_funct_1,cc2_funct_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc4_funct_1,d14_funct_1,dh_c1_3_2_2__pboole]),
    [interesting(0.5),file(pboole,i1_3_2_2__pboole),[file(pboole,i1_3_2_2__pboole)]]).

fof(i2_3_2__pboole,plain,
    ( k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0)
   => v3_relat_1(c1_3__pboole) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole]),discharge_asm(discharge,[e1_3_2_2__pboole])],[e1_3_2_2__pboole,i1_3_2_2__pboole]),
    [interesting(0.65),file(pboole,i2_3_2__pboole),[file(pboole,i2_3_2__pboole)]]).

fof(e1_3_2__pboole,plain,
    ( c1_3__pboole = k1_xboole_0
    | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__pboole,e2_3__pboole])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_finseq_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__pboole,fc2_finseq_1,fc2_subset_1,t6_boole,e2_3__pboole]),
    [interesting(0.65),file(pboole,e1_3_2__pboole),[file(pboole,e1_3_2__pboole)]]).

fof(i3_3__pboole,plain,(
    v3_relat_1(c1_3__pboole) ),
    inference(percases,[status(thm),assumptions([dt_c1_3__pboole,e2_3__pboole])],[i1_3_2__pboole,i2_3_2__pboole,e1_3_2__pboole]),
    [interesting(0.8),file(pboole,i3_3__pboole),[file(pboole,i3_3__pboole)]]).

fof(i2_3__pboole,plain,
    ( ( c1_3__pboole = k1_xboole_0
      | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) )
   => v3_relat_1(c1_3__pboole) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__pboole]),discharge_asm(discharge,[e2_3__pboole])],[e2_3__pboole,i3_3__pboole]),
    [interesting(0.8),file(pboole,i2_3__pboole),[file(pboole,i2_3__pboole)]]).

fof(i1_3__pboole,plain,
    ( v3_relat_1(c1_3__pboole)
  <=> ( c1_3__pboole = k1_xboole_0
      | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__pboole])],[e1_3__pboole,i2_3__pboole]),
    [interesting(0.8),file(pboole,i1_3__pboole),[file(pboole,i1_3__pboole)]]).

fof(i1_3_tmp__pboole,plain,
    ( ( v1_relat_1(c1_3__pboole)
      & v1_funct_1(c1_3__pboole) )
   => ( v3_relat_1(c1_3__pboole)
    <=> ( c1_3__pboole = k1_xboole_0
        | k2_relat_1(c1_3__pboole) = k1_tarski(k1_xboole_0) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__pboole])],[dt_c1_3__pboole,i1_3__pboole]),
    [interesting(1),t2_pboole]).

fof(t2_pboole,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v3_relat_1(A)
      <=> ( A = k1_xboole_0
          | k2_relat_1(A) = k1_tarski(k1_xboole_0) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__pboole,dh_c1_3__pboole]),
    [interesting(1),file(pboole,t2_pboole),[file(pboole,t2_pboole)]]).