fof(t24_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> v1_finset_1(k1_zfmisc_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,t2_xboole_1,t1_zfmisc_1,t37_zfmisc_1,t12_xboole_1,s2_funct_1,t17_finset_1,d5_funct_1,t13_xboole_1,d1_tarski,d2_xboole_0,d4_xboole_0,d4_xboole_0,d3_tarski,d1_tarski,d2_xboole_0,d4_xboole_0,t43_xboole_1,t39_xboole_1,t46_zfmisc_1,d5_funct_1,t2_tarski,t146_relat_1,t7_xboole_1,t79_zfmisc_1,t39_xboole_1,t12_xboole_1,l3_finset_1,t37_zfmisc_1,t8_xboole_1,s2_finset_1,s1_xboole_0,d4_tarski,t37_zfmisc_1,d1_tarski,d4_tarski,t2_tarski,d3_tarski,t13_finset_1,l22_finset_1]),
    [file(finset_1,t24_finset_1),interesting(1.00)]).

fof(t20_finset_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B)
        & v1_finset_1(C) )
     => v1_finset_1(k3_zfmisc_1(A,B,C)) ) ),
    inference(mizar_proof,[status(thm)],[t19_finset_1,t19_finset_1,d3_zfmisc_1]),
    [file(finset_1,t20_finset_1),interesting(0.92)]).

fof(t21_finset_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B)
        & v1_finset_1(C)
        & v1_finset_1(D) )
     => v1_finset_1(k4_zfmisc_1(A,B,C,D)) ) ),
    inference(mizar_proof,[status(thm)],[t20_finset_1,t19_finset_1,d4_zfmisc_1]),
    [file(finset_1,t21_finset_1),interesting(0.92)]).

fof(t29_finset_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_finset_1(k1_relat_1(A))
      <=> v1_finset_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_finset_1,t19_finset_1,t21_relat_1,t13_finset_1,t100_funct_3,t17_finset_1]),
    [file(finset_1,t29_finset_1),interesting(0.91)]).

fof(t25_finset_1,theorem,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & ! [B] : 
            ( r2_hidden(B,A)
           => v1_finset_1(B) ) )
    <=> v1_finset_1(k3_tarski(A)) ) ),
    inference(mizar_proof,[status(thm)],[l22_finset_1,t24_finset_1,t100_zfmisc_1,t13_finset_1,t92_zfmisc_1,t13_finset_1]),
    [file(finset_1,t25_finset_1),interesting(0.90)]).

fof(t19_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d5_funct_1,d1_tarski,t129_zfmisc_1,d2_zfmisc_1,d1_tarski,d5_funct_1,t2_tarski,t146_relat_1,t17_finset_1,s1_xboole_0,d4_tarski,d2_zfmisc_1,t129_zfmisc_1,t37_zfmisc_1,t118_zfmisc_1,d4_tarski,t2_tarski,s3_funct_1,d5_funct_1,t37_zfmisc_1,t118_zfmisc_1,d5_funct_1,t2_tarski,t146_relat_1,t17_finset_1,l22_finset_1]),
    [file(finset_1,t19_finset_1),interesting(0.89)]).

fof(l22_finset_1,theorem,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & ! [B] : 
            ( r2_hidden(B,A)
           => v1_finset_1(B) ) )
     => v1_finset_1(k3_tarski(A)) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,t2_xboole_1,t2_zfmisc_1,t96_zfmisc_1,t31_zfmisc_1,l3_finset_1,t37_zfmisc_1,t8_xboole_1,s2_finset_1]),
    [file(finset_1,l22_finset_1),interesting(0.81)]).

fof(l3_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d1_finset_1,d1_finset_1,t23_ordinal1,s1_finset_1,d1_finset_1,d21_ordinal2,d3_tarski,d5_funct_1,t23_ordinal1,d5_funct_1,d2_xboole_0,t26_ordinal1,d6_ordinal3,t25_ordinal3,d5_funct_1,d2_xboole_0,d10_xboole_0,d3_tarski,d5_funct_1,t23_ordinal1,t27_ordinal3,d5_funct_1,d5_funct_1,t23_ordinal1,t27_ordinal3,t7_ordinal1,t20_ordinal3,t65_ordinal3,d5_funct_1,d2_xboole_0,d21_ordinal2]),
    [file(finset_1,l3_finset_1),interesting(0.75)]).

fof(l2_finset_1,theorem,(
    ! [A] : v1_finset_1(k1_tarski(A)) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t13_funcop_1,d1_finset_1,d1_tarski,d1_tarski,d1_tarski,d1_tarski,d5_funct_1,t41_ordinal1,t19_ordinal2,d4_ordinal2,t18_ordinal3]),
    [file(finset_1,l2_finset_1),interesting(0.74)]).

fof(t15_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,t13_finset_1]),
    [file(finset_1,t15_finset_1),interesting(0.71)]).

fof(t16_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t36_xboole_1,t13_finset_1]),
    [file(finset_1,t16_finset_1),interesting(0.71)]).

fof(t28_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k5_xboole_0(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t16_finset_1,l3_finset_1]),
    [file(finset_1,t28_finset_1),interesting(0.68)]).

fof(t14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[l3_finset_1]),
    [file(finset_1,t14_finset_1),interesting(0.67)]).

fof(t17_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_finset_1(A)
       => v1_finset_1(k9_relat_1(B,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_finset_1,d1_finset_1,d1_finset_1,t160_relat_1,t145_relat_1,t17_xboole_1,t46_relat_1]),
    [file(finset_1,t17_finset_1),interesting(0.66)]).

fof(t26_finset_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_finset_1(k1_relat_1(A))
       => v1_finset_1(k2_relat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_finset_1,t146_relat_1]),
    [file(finset_1,t26_finset_1),interesting(0.63)]).

fof(t22_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(k2_zfmisc_1(B,A))
     => ( A = k1_xboole_0
        | v1_finset_1(B) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d5_funct_1,t10_mcart_1,t106_zfmisc_1,t7_mcart_1,d5_funct_1,t2_tarski,t146_relat_1,t17_finset_1]),
    [file(finset_1,t22_finset_1),interesting(0.61)]).

fof(t23_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(k2_zfmisc_1(A,B))
     => ( A = k1_xboole_0
        | v1_finset_1(B) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d5_funct_1,t10_mcart_1,t106_zfmisc_1,t7_mcart_1,d5_funct_1,t2_tarski,t146_relat_1,t17_finset_1]),
    [file(finset_1,t23_finset_1),interesting(0.61)]).

fof(t30_finset_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & A != k1_xboole_0
      & v6_ordinal1(A)
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C] : 
              ( r2_hidden(C,A)
             => r1_tarski(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d2_xboole_0,d2_xboole_0,d9_ordinal1,d1_tarski,d9_xboole_0,d1_tarski,t1_xboole_1,d2_xboole_0,d2_xboole_0,d1_tarski,s2_finset_1]),
    [file(finset_1,t30_finset_1),interesting(0.55)]).

fof(t31_finset_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & A != k1_xboole_0
      & v6_ordinal1(A)
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C] : 
              ( r2_hidden(C,A)
             => r1_tarski(C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d2_xboole_0,d2_xboole_0,d9_ordinal1,d1_tarski,d9_xboole_0,d1_tarski,t1_xboole_1,d2_xboole_0,d2_xboole_0,d1_tarski,s2_finset_1]),
    [file(finset_1,t31_finset_1),interesting(0.55)]).

fof(t18_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ~ ( B != k1_xboole_0
              & ! [C] : ~ ( r2_hidden(C,B)
                  & ! [D] : 
                      ( ( r2_hidden(D,B)
                        & r1_tarski(C,D) )
                     => D = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_finset_1,s1_xboole_0,d3_tarski,d3_tarski,t147_funct_1,t167_relat_1,t1_zfmisc_1,t39_zfmisc_1,d1_tarski,d2_ordinal1,s1_xboole_0,d3_tarski,d1_ordinal1,d3_tarski,t33_xboole_1,t40_xboole_1,t10_ordinal1,t65_zfmisc_1,d1_tarski,d4_xboole_0,t37_zfmisc_1,t45_xboole_1,t33_xboole_1,d4_xboole_0,t40_xboole_1,t65_zfmisc_1,t33_xboole_1,t40_xboole_1,t65_zfmisc_1,d1_tarski,d2_xboole_0,t46_zfmisc_1,t39_xboole_1,t65_zfmisc_1,t33_xboole_1,t40_xboole_1,t65_zfmisc_1,t33_xboole_1,t65_zfmisc_1,t39_xboole_1,t46_zfmisc_1,d3_tarski,d2_xboole_0,d1_tarski,t65_zfmisc_1,t24_ordinal1,d5_ordinal2,s1_ordinal2,t23_ordinal1,t178_relat_1,t146_funct_1,t1_xboole_1,t147_funct_1,t167_relat_1]),
    [file(finset_1,t18_finset_1),interesting(0.50)]).

fof(t27_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( r1_tarski(A,k2_relat_1(B))
          & v1_finset_1(k10_relat_1(B,A)) )
       => v1_finset_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t147_funct_1,t17_finset_1]),
    [file(finset_1,t27_finset_1),interesting(0.42)]).

fof(s2_finset_1,theorem,
    ( ( v1_finset_1(f1_s2_finset_1)
      & p1_s2_finset_1(k1_xboole_0)
      & ! [A,B] : 
          ( ( r2_hidden(A,f1_s2_finset_1)
            & r1_tarski(B,f1_s2_finset_1)
            & p1_s2_finset_1(B) )
         => p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))) ) )
   => p1_s2_finset_1(f1_s2_finset_1) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,d3_tarski,t2_xboole_1,t18_finset_1,d10_xboole_0,t37_xboole_1,d4_xboole_0,t37_zfmisc_1,t8_xboole_1,d4_xboole_0,t37_zfmisc_1,t7_xboole_1]),
    [file(finset_1,s2_finset_1),interesting(0.38)]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(d1_finset_1,definition,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & k2_relat_1(B) = A
          & r2_hidden(k1_relat_1(B),k5_ordinal2) ) ) ),
    file(finset_1,d1_finset_1),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

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(0.00)]).

fof(t41_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k1_ordinal1(B),A) ) ) ) ) ),
    file(ordinal1,t41_ordinal1),
    [interesting(0.00)]).

fof(t19_ordinal2,theorem,
    ( r2_hidden(k1_xboole_0,k5_ordinal2)
    & v4_ordinal1(k5_ordinal2)
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( ( r2_hidden(k1_xboole_0,A)
            & v4_ordinal1(A) )
         => r1_ordinal1(k5_ordinal2,A) ) ) ),
    file(ordinal2,t19_ordinal2),
    [interesting(0.00)]).

fof(d4_ordinal2,definition,(
    k4_ordinal2 = k1_ordinal1(k1_xboole_0) ),
    file(ordinal2,d4_ordinal2),
    [interesting(0.00)]).

fof(t18_ordinal3,theorem,(
    k4_ordinal2 = k1_tarski(k1_xboole_0) ),
    file(ordinal3,t18_ordinal3),
    [interesting(0.00)]).

fof(t10_finset_1,theorem,(
    $true ),
    file(finset_1,t10_finset_1),
    [interesting(0.00)]).

fof(t11_finset_1,theorem,(
    $true ),
    file(finset_1,t11_finset_1),
    [interesting(0.00)]).

fof(t12_finset_1,theorem,(
    $true ),
    file(finset_1,t12_finset_1),
    [interesting(0.00)]).

fof(t23_ordinal1,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    [interesting(0.00)]).

fof(s1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_partfun1
      & ! [B] : 
          ( r2_hidden(B,f1_s1_partfun1)
         => ( ( p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f2_s1_partfun1(B) )
            & ( ~ p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f3_s1_partfun1(B) ) ) ) ) ),
    file(partfun1,s1_partfun1),
    [interesting(0.00)]).

fof(s1_finset_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_finset_1
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(B,f1_s1_finset_1)
           => ( ( p1_s1_finset_1(B)
               => k1_funct_1(A,B) = f2_s1_finset_1(B) )
              & ( ~ p1_s1_finset_1(B)
               => k1_funct_1(A,B) = f3_s1_finset_1(B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_partfun1]),
    [file(finset_1,s1_finset_1),interesting(0.00)]).

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

fof(t26_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
            | r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t26_ordinal1),
    [interesting(0.00)]).

fof(d6_ordinal3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_ordinal1(B,A)
                 => ( C = k5_ordinal3(A,B)
                  <=> A = k14_ordinal2(B,C) ) )
                & ( ~ r1_ordinal1(B,A)
                 => ( C = k5_ordinal3(A,B)
                  <=> C = k1_xboole_0 ) ) ) ) ) ) ),
    file(ordinal3,d6_ordinal3),
    [interesting(0.00)]).

fof(t25_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(k14_ordinal2(A,B),k14_ordinal2(A,C))
               => r2_hidden(B,C) ) ) ) ) ),
    file(ordinal3,t25_ordinal3),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t27_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,k14_ordinal2(A,B))
            & r1_ordinal1(B,k14_ordinal2(A,B)) ) ) ) ),
    file(ordinal3,t27_ordinal3),
    [interesting(0.00)]).

fof(t7_ordinal1,theorem,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & r1_tarski(B,A) ) ),
    file(ordinal1,t7_ordinal1),
    [interesting(0.00)]).

fof(t20_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ( r2_hidden(C,D)
                   => ( ( ~ r1_ordinal1(A,B)
                        & ~ r2_hidden(A,B) )
                      | r2_hidden(k14_ordinal2(A,C),k14_ordinal2(B,D)) ) ) ) ) ) ) ),
    file(ordinal3,t20_ordinal3),
    [interesting(0.00)]).

fof(t65_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k5_ordinal3(k14_ordinal2(A,B),A) = B ) ) ),
    file(ordinal3,t65_ordinal3),
    [interesting(0.00)]).

fof(t1_finset_1,theorem,(
    $true ),
    file(finset_1,t1_finset_1),
    [interesting(0.00)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(t129_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D)))
    <=> ( r2_hidden(A,C)
        & B = D ) ) ),
    file(zfmisc_1,t129_zfmisc_1),
    [interesting(0.00)]).

fof(d2_zfmisc_1,definition,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t146_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    [interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t13_finset_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    [interesting(0.00)]).

fof(t160_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)) ) ) ),
    file(relat_1,t160_relat_1),
    [interesting(0.00)]).

fof(t145_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) ) ),
    file(relat_1,t145_relat_1),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

fof(s1_xboole_0,theorem,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,f1_s1_xboole_0)
        & p1_s1_xboole_0(B) ) ) ),
    file(xboole_0,s1_xboole_0),
    [interesting(0.00)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.00)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.00)]).

fof(t118_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
        & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) ),
    file(zfmisc_1,t118_zfmisc_1),
    [interesting(0.00)]).

fof(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

fof(t2_zfmisc_1,theorem,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    file(zfmisc_1,t2_zfmisc_1),
    [interesting(0.00)]).

fof(t96_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B)) ),
    file(zfmisc_1,t96_zfmisc_1),
    [interesting(0.00)]).

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    file(zfmisc_1,t31_zfmisc_1),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

fof(t147_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(A,k2_relat_1(B))
       => k9_relat_1(B,k10_relat_1(B,A)) = A ) ) ),
    file(funct_1,t147_funct_1),
    [interesting(0.00)]).

fof(t167_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k10_relat_1(B,A),k1_relat_1(B)) ) ),
    file(relat_1,t167_relat_1),
    [interesting(0.00)]).

fof(t1_zfmisc_1,theorem,(
    k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    file(zfmisc_1,t1_zfmisc_1),
    [interesting(0.00)]).

fof(t39_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,t39_zfmisc_1),
    [interesting(0.00)]).

fof(d2_ordinal1,definition,(
    ! [A] : 
      ( v1_ordinal1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => r1_tarski(B,A) ) ) ),
    file(ordinal1,d2_ordinal1),
    [interesting(0.00)]).

fof(d1_ordinal1,definition,(
    ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) ),
    file(ordinal1,d1_ordinal1),
    [interesting(0.00)]).

fof(t33_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ),
    file(xboole_1,t33_xboole_1),
    [interesting(0.00)]).

fof(t40_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) ),
    file(xboole_1,t40_xboole_1),
    [interesting(0.00)]).

fof(t10_ordinal1,theorem,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    [interesting(0.00)]).

fof(t65_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,k1_tarski(B)) = A
    <=> ~ r2_hidden(B,A) ) ),
    file(zfmisc_1,t65_zfmisc_1),
    [interesting(0.00)]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.00)]).

fof(t45_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) ),
    file(xboole_1,t45_xboole_1),
    [interesting(0.00)]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.00)]).

fof(t39_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    [interesting(0.00)]).

fof(t24_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( ~ r2_hidden(A,B)
              & A != B
              & ~ r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t24_ordinal1),
    [interesting(0.00)]).

fof(d5_ordinal2,definition,(
    ! [A] : 
      ( A = k5_ordinal2
    <=> ( r2_hidden(k1_xboole_0,A)
        & v4_ordinal1(A)
        & v3_ordinal1(A)
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( ( r2_hidden(k1_xboole_0,B)
                & v4_ordinal1(B) )
             => r1_tarski(A,B) ) ) ) ) ),
    file(ordinal2,d5_ordinal2),
    [interesting(0.00)]).

fof(s1_ordinal2,theorem,
    ( ( p1_s1_ordinal2(k1_xboole_0)
      & ! [A] : 
          ( v3_ordinal1(A)
         => ( p1_s1_ordinal2(A)
           => p1_s1_ordinal2(k1_ordinal1(A)) ) )
      & ! [A] : 
          ( v3_ordinal1(A)
         => ( ( v4_ordinal1(A)
              & ! [B] : 
                  ( v3_ordinal1(B)
                 => ( r2_hidden(B,A)
                   => p1_s1_ordinal2(B) ) ) )
           => ( A = k1_xboole_0
              | p1_s1_ordinal2(A) ) ) ) )
   => ! [A] : 
        ( v3_ordinal1(A)
       => p1_s1_ordinal2(A) ) ),
    file(ordinal2,s1_ordinal2),
    [interesting(0.00)]).

fof(t178_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) ) ) ),
    file(relat_1,t178_relat_1),
    [interesting(0.00)]).

fof(t146_funct_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A))) ) ) ),
    file(funct_1,t146_funct_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(t37_xboole_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    [interesting(0.00)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(d3_zfmisc_1,definition,(
    ! [A,B,C] : k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C) ),
    file(zfmisc_1,d3_zfmisc_1),
    [interesting(0.00)]).

fof(d4_zfmisc_1,definition,(
    ! [A,B,C,D] : k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) ),
    file(zfmisc_1,d4_zfmisc_1),
    [interesting(0.00)]).

fof(t10_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => ( r2_hidden(k1_mcart_1(A),B)
        & r2_hidden(k2_mcart_1(A),C) ) ) ),
    file(mcart_1,t10_mcart_1),
    [interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

fof(s2_funct_1,theorem,
    ( ( ! [A,B,C] : 
          ( ( r2_hidden(A,f1_s2_funct_1)
            & p1_s2_funct_1(A,B)
            & p1_s2_funct_1(A,C) )
         => B = C )
      & ! [A] : ~ ( r2_hidden(A,f1_s2_funct_1)
          & ! [B] : ~ p1_s2_funct_1(A,B) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s2_funct_1
        & ! [B] : 
            ( r2_hidden(B,f1_s2_funct_1)
           => p1_s2_funct_1(B,k1_funct_1(A,B)) ) ) ),
    file(funct_1,s2_funct_1),
    [interesting(0.00)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.00)]).

fof(t43_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_xboole_0(B,C))
     => r1_tarski(k4_xboole_0(A,B),C) ) ),
    file(xboole_1,t43_xboole_1),
    [interesting(0.00)]).

fof(t79_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ) ),
    file(zfmisc_1,t79_zfmisc_1),
    [interesting(0.00)]).

fof(t100_zfmisc_1,theorem,(
    ! [A] : r1_tarski(A,k1_zfmisc_1(k3_tarski(A))) ),
    file(zfmisc_1,t100_zfmisc_1),
    [interesting(0.00)]).

fof(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    [interesting(0.00)]).

fof(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.00)]).

fof(t21_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) ) ),
    file(relat_1,t21_relat_1),
    [interesting(0.00)]).

fof(t100_funct_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A) = k1_relat_1(A) ) ),
    file(funct_3,t100_funct_3),
    [interesting(0.00)]).

fof(t2_finset_1,theorem,(
    $true ),
    file(finset_1,t2_finset_1),
    [interesting(0.00)]).

fof(d9_ordinal1,definition,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    [interesting(0.00)]).

fof(d9_xboole_0,definition,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        | r1_tarski(B,A) ) ) ),
    file(xboole_0,d9_xboole_0),
    [interesting(0.00)]).

fof(t3_finset_1,theorem,(
    $true ),
    file(finset_1,t3_finset_1),
    [interesting(0.00)]).

fof(t4_finset_1,theorem,(
    $true ),
    file(finset_1,t4_finset_1),
    [interesting(0.00)]).

fof(t5_finset_1,theorem,(
    $true ),
    file(finset_1,t5_finset_1),
    [interesting(0.00)]).

fof(t6_finset_1,theorem,(
    $true ),
    file(finset_1,t6_finset_1),
    [interesting(0.00)]).

fof(t7_finset_1,theorem,(
    $true ),
    file(finset_1,t7_finset_1),
    [interesting(0.00)]).

fof(t8_finset_1,theorem,(
    $true ),
    file(finset_1,t8_finset_1),
    [interesting(0.00)]).

fof(t9_finset_1,theorem,(
    $true ),
    file(finset_1,t9_finset_1),
    [interesting(0.00)]).