fof(t52_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k10_margrel1(B,C)) = k10_margrel1(k10_margrel1(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_margrel1,t45_margrel1,t45_margrel1,t39_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t39_margrel1,t39_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t39_margrel1]),
    [file(margrel1,t52_margrel1),interesting(1.00)]).

fof(t46_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(A,k9_margrel1(A)) = k7_margrel1 ) ),
    inference(mizar_proof,[status(thm)],[t41_margrel1,t45_margrel1,t45_margrel1,t39_margrel1]),
    [file(margrel1,t46_margrel1),interesting(0.96)]).

fof(t50_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k8_margrel1,A) = A ) ),
    inference(mizar_proof,[status(thm)],[t45_margrel1,t45_margrel1,t39_margrel1]),
    [file(margrel1,t50_margrel1),interesting(0.87)]).

fof(t7_margrel1,theorem,(
    ! [A,B] : 
      ( v1_margrel1(B)
     => ( r1_tarski(A,B)
       => v1_margrel1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_margrel1,d1_margrel1,d1_margrel1]),
    [file(margrel1,t7_margrel1),interesting(0.84)]).

fof(t47_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k10_margrel1(A,k9_margrel1(A))) = k8_margrel1 ) ),
    inference(mizar_proof,[status(thm)],[t46_margrel1,t41_margrel1]),
    [file(margrel1,t47_margrel1),interesting(0.81)]).

fof(t20_margrel1,theorem,(
    ! [A] : m2_margrel1(k1_xboole_0,A) ),
    inference(mizar_proof,[status(thm)],[d6_margrel1]),
    [file(margrel1,t20_margrel1),interesting(0.79)]).

fof(t32_margrel1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k4_margrel1(A) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d8_margrel1,d3_tarski,d11_finseq_1,d10_margrel1]),
    [file(margrel1,t32_margrel1),interesting(0.78)]).

fof(t39_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A = k7_margrel1
        | A = k8_margrel1 ) ) ),
    inference(mizar_proof,[status(thm)],[d15_margrel1,d2_tarski]),
    [file(margrel1,t39_margrel1),interesting(0.78)]).

fof(t49_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k7_margrel1,A) = k7_margrel1 ) ),
    inference(mizar_proof,[status(thm)],[t45_margrel1]),
    [file(margrel1,t49_margrel1),interesting(0.77)]).

fof(t51_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( k10_margrel1(A,A) = k7_margrel1
       => A = k7_margrel1 ) ) ),
    inference(mizar_proof,[status(thm)],[t45_margrel1]),
    [file(margrel1,t51_margrel1),interesting(0.72)]).

fof(t8_margrel1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => v1_margrel1(k1_tarski(A)) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_margrel1,d1_tarski]),
    [file(margrel1,t8_margrel1),interesting(0.72)]).

fof(t27_margrel1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => m1_subset_1(k1_tarski(B),k3_margrel1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_finseq_1,t37_zfmisc_1,d1_tarski,d8_margrel1]),
    [file(margrel1,t27_margrel1),interesting(0.70)]).

fof(t43_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A != k8_margrel1
      <=> A = k7_margrel1 ) ) ),
    inference(mizar_proof,[status(thm)],[t39_margrel1]),
    [file(margrel1,t43_margrel1),interesting(0.66)]).

fof(t26_margrel1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( m1_subset_1(C,k3_margrel1(A))
         => ( r1_tarski(B,C)
           => m1_subset_1(B,k3_margrel1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_margrel1,t1_xboole_1,d8_margrel1,d8_margrel1]),
    [file(margrel1,t26_margrel1),interesting(0.64)]).

fof(t21_margrel1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => m1_margrel1(k1_xboole_0,A) ) ),
    inference(mizar_proof,[status(thm)],[d5_margrel1]),
    [file(margrel1,t21_margrel1),interesting(0.57)]).

fof(t28_margrel1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => m1_subset_1(k1_tarski(k10_finseq_1(B,C)),k3_margrel1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_finseq_1,d11_finseq_1,t37_zfmisc_1,d1_tarski,d8_margrel1]),
    [file(margrel1,t28_margrel1),interesting(0.56)]).

fof(t41_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( k9_margrel1(A) = k8_margrel1
         => A = k7_margrel1 )
        & ( A = k8_margrel1
         => k9_margrel1(A) = k7_margrel1 )
        & ( k9_margrel1(A) = k7_margrel1
         => A = k8_margrel1 ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_margrel1,d16_margrel1,d16_margrel1,d16_margrel1]),
    [file(margrel1,t41_margrel1),interesting(0.48)]).

fof(t9_margrel1,theorem,(
    ! [A] : 
      ( v1_margrel1(A)
     => ( ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) )
           => ~ r2_hidden(B,A) )
       => A = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_margrel1]),
    [file(margrel1,t9_margrel1),interesting(0.46)]).

fof(t45_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( ( k10_margrel1(A,B) = k8_margrel1
             => ( A = k8_margrel1
                & B = k8_margrel1 ) )
            & ( ( A = k8_margrel1
                & B = k8_margrel1 )
             => k10_margrel1(A,B) = k8_margrel1 )
            & ~ ( k10_margrel1(A,B) = k7_margrel1
                & A != k7_margrel1
                & B != k7_margrel1 )
            & ( ( A = k7_margrel1
                | B = k7_margrel1 )
             => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_margrel1,d17_margrel1,d17_margrel1,t39_margrel1,d17_margrel1]),
    [file(margrel1,t45_margrel1),interesting(0.39)]).

fof(t53_margrel1,theorem,(
    ! [A] : 
      ( ( ~ r2_hidden(k7_margrel1,A)
       => k14_margrel1(A) = k8_margrel1 )
      & ~ ( k14_margrel1(A) = k8_margrel1
          & r2_hidden(k7_margrel1,A) )
      & ( r2_hidden(k7_margrel1,A)
       => k14_margrel1(A) = k7_margrel1 )
      & ( k14_margrel1(A) = k7_margrel1
       => r2_hidden(k7_margrel1,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_margrel1]),
    [file(margrel1,t53_margrel1),interesting(0.31)]).

fof(s3_margrel1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k3_margrel1(f1_s3_margrel1))
      & ! [B] : 
          ( m2_finseq_1(B,f1_s3_margrel1)
         => ( k3_finseq_1(B) = f2_s3_margrel1
           => ( r2_hidden(B,A)
            <=> p1_s3_margrel1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,d3_tarski,d8_margrel1,d11_finseq_1]),
    [file(margrel1,s3_margrel1),interesting(0.13)]).

fof(s2_margrel1,theorem,
    ( ! [A] : 
        ( m2_finseq_1(A,f1_s2_margrel1)
       => ! [B] : 
            ( m2_finseq_1(B,f1_s2_margrel1)
           => ( ( p1_s2_margrel1(A)
                & p1_s2_margrel1(B) )
             => k3_finseq_1(A) = k3_finseq_1(B) ) ) )
   => ? [A] : 
        ( m1_subset_1(A,k3_margrel1(f1_s2_margrel1))
        & ! [B] : 
            ( m2_finseq_1(B,f1_s2_margrel1)
           => ( r2_hidden(B,A)
            <=> p1_s2_margrel1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,d3_tarski,d8_margrel1,d11_finseq_1]),
    [file(margrel1,s2_margrel1),interesting(0.08)]).

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(d1_margrel1,definition,(
    ! [A] : 
      ( v1_margrel1(A)
    <=> ( ! [B] : 
            ( r2_hidden(B,A)
           => ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) ) )
        & ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) )
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ( ( r2_hidden(B,A)
                    & r2_hidden(C,A) )
                 => k3_finseq_1(B) = k3_finseq_1(C) ) ) ) ) ) ),
    file(margrel1,d1_margrel1),
    [interesting(0.00)]).

fof(s1_margrel1,theorem,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) )
           => ( ( p1_s1_margrel1(A)
                & p1_s1_margrel1(B) )
             => k3_finseq_1(A) = k3_finseq_1(B) ) ) )
   => ? [A] : 
        ( v1_margrel1(A)
        & ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) )
           => ( r2_hidden(B,A)
            <=> ( r2_hidden(B,f1_s1_margrel1)
                & p1_s1_margrel1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,d1_margrel1]),
    [file(margrel1,s1_margrel1),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(d8_margrel1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( B = k3_margrel1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( r1_tarski(C,k13_finseq_1(A))
                & ! [D] : 
                    ( m2_finseq_1(D,A)
                   => ! [E] : 
                        ( m2_finseq_1(E,A)
                       => ( ( r2_hidden(D,C)
                            & r2_hidden(E,C) )
                         => k3_finseq_1(D) = k3_finseq_1(E) ) ) ) ) ) ) ) ),
    file(margrel1,d8_margrel1),
    [interesting(0.00)]).

fof(d11_finseq_1,definition,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    [interesting(0.00)]).

fof(t10_margrel1,theorem,(
    $true ),
    file(margrel1,t10_margrel1),
    [interesting(0.00)]).

fof(t11_margrel1,theorem,(
    $true ),
    file(margrel1,t11_margrel1),
    [interesting(0.00)]).

fof(t12_margrel1,theorem,(
    $true ),
    file(margrel1,t12_margrel1),
    [interesting(0.00)]).

fof(t13_margrel1,theorem,(
    $true ),
    file(margrel1,t13_margrel1),
    [interesting(0.00)]).

fof(t14_margrel1,theorem,(
    $true ),
    file(margrel1,t14_margrel1),
    [interesting(0.00)]).

fof(t15_margrel1,theorem,(
    $true ),
    file(margrel1,t15_margrel1),
    [interesting(0.00)]).

fof(t16_margrel1,theorem,(
    $true ),
    file(margrel1,t16_margrel1),
    [interesting(0.00)]).

fof(t17_margrel1,theorem,(
    $true ),
    file(margrel1,t17_margrel1),
    [interesting(0.00)]).

fof(t18_margrel1,theorem,(
    $true ),
    file(margrel1,t18_margrel1),
    [interesting(0.00)]).

fof(t19_margrel1,theorem,(
    $true ),
    file(margrel1,t19_margrel1),
    [interesting(0.00)]).

fof(t1_margrel1,theorem,(
    $true ),
    file(margrel1,t1_margrel1),
    [interesting(0.00)]).

fof(d6_margrel1,definition,(
    ! [A,B] : 
      ( v1_margrel1(B)
     => ( m2_margrel1(B,A)
      <=> ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finseq_1(C) )
           => ( r2_hidden(C,B)
             => r1_tarski(k2_relat_1(C),A) ) ) ) ) ),
    file(margrel1,d6_margrel1),
    [interesting(0.00)]).

fof(d5_margrel1,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v1_margrel1(B)
         => ( m1_margrel1(B,A)
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ( r2_hidden(C,B)
                 => k3_finseq_1(C) = A ) ) ) ) ) ),
    file(margrel1,d5_margrel1),
    [interesting(0.00)]).

fof(t22_margrel1,theorem,(
    $true ),
    file(margrel1,t22_margrel1),
    [interesting(0.00)]).

fof(t23_margrel1,theorem,(
    $true ),
    file(margrel1,t23_margrel1),
    [interesting(0.00)]).

fof(t24_margrel1,theorem,(
    $true ),
    file(margrel1,t24_margrel1),
    [interesting(0.00)]).

fof(t25_margrel1,theorem,(
    $true ),
    file(margrel1,t25_margrel1),
    [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_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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(d9_finseq_1,definition,(
    ! [A,B] : k10_finseq_1(A,B) = k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) ),
    file(finseq_1,d9_finseq_1),
    [interesting(0.00)]).

fof(t29_margrel1,theorem,(
    $true ),
    file(margrel1,t29_margrel1),
    [interesting(0.00)]).

fof(t2_margrel1,theorem,(
    $true ),
    file(margrel1,t2_margrel1),
    [interesting(0.00)]).

fof(t30_margrel1,theorem,(
    $true ),
    file(margrel1,t30_margrel1),
    [interesting(0.00)]).

fof(t31_margrel1,theorem,(
    $true ),
    file(margrel1,t31_margrel1),
    [interesting(0.00)]).

fof(d10_margrel1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k3_margrel1(A))
         => ( B = k4_margrel1(A)
          <=> ! [C] : 
                ( m2_finseq_1(C,A)
               => ~ r2_hidden(C,B) ) ) ) ) ),
    file(margrel1,d10_margrel1),
    [interesting(0.00)]).

fof(t33_margrel1,theorem,(
    $true ),
    file(margrel1,t33_margrel1),
    [interesting(0.00)]).

fof(t34_margrel1,theorem,(
    $true ),
    file(margrel1,t34_margrel1),
    [interesting(0.00)]).

fof(t35_margrel1,theorem,(
    $true ),
    file(margrel1,t35_margrel1),
    [interesting(0.00)]).

fof(t36_margrel1,theorem,
    ( k7_margrel1 = 0
    & k8_margrel1 = 1 ),
    file(margrel1,t36_margrel1),
    [interesting(0.00)]).

fof(t37_margrel1,theorem,(
    k6_margrel1 = k2_tarski(k7_margrel1,k8_margrel1) ),
    file(margrel1,t37_margrel1),
    [interesting(0.00)]).

fof(t38_margrel1,theorem,(
    k7_margrel1 != k8_margrel1 ),
    file(margrel1,t38_margrel1),
    [interesting(0.00)]).

fof(t3_margrel1,theorem,(
    $true ),
    file(margrel1,t3_margrel1),
    [interesting(0.00)]).

fof(t40_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_margrel1),
    [interesting(0.00)]).

fof(t42_margrel1,theorem,(
    $true ),
    file(margrel1,t42_margrel1),
    [interesting(0.00)]).

fof(d15_margrel1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
    <=> r2_hidden(A,k6_margrel1) ) ),
    file(margrel1,d15_margrel1),
    [interesting(0.00)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.00)]).

fof(t44_margrel1,theorem,(
    $true ),
    file(margrel1,t44_margrel1),
    [interesting(0.00)]).

fof(d16_margrel1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( A != k7_margrel1
         => k9_margrel1(A) = k7_margrel1 ) ) ) ),
    file(margrel1,d16_margrel1),
    [interesting(0.00)]).

fof(d17_margrel1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( ( ( A = k8_margrel1
                & B = k8_margrel1 )
             => k10_margrel1(A,B) = k8_margrel1 )
            & ( ~ ( A = k8_margrel1
                  & B = k8_margrel1 )
             => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ),
    file(margrel1,d17_margrel1),
    [interesting(0.00)]).

fof(t48_margrel1,theorem,(
    $true ),
    file(margrel1,t48_margrel1),
    [interesting(0.00)]).

fof(t4_margrel1,theorem,(
    $true ),
    file(margrel1,t4_margrel1),
    [interesting(0.00)]).

fof(d18_margrel1,definition,(
    ! [A] : 
      ( ( ~ r2_hidden(k7_margrel1,A)
       => k13_margrel1(A) = k8_margrel1 )
      & ( r2_hidden(k7_margrel1,A)
       => k13_margrel1(A) = k7_margrel1 ) ) ),
    file(margrel1,d18_margrel1),
    [interesting(0.00)]).

fof(t5_margrel1,theorem,(
    $true ),
    file(margrel1,t5_margrel1),
    [interesting(0.00)]).

fof(t6_margrel1,theorem,(
    $true ),
    file(margrel1,t6_margrel1),
    [interesting(0.00)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).