fof(t15_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,A,C)
     => ( r1_tarski(A,B)
       => m2_relset_1(D,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,t1_xboole_1,t13_relset_1]),
    [file(relset_1,t15_relset_1),interesting(1.00)]).

fof(t16_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,C,A)
     => ( r1_tarski(A,B)
       => m2_relset_1(D,C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,t1_xboole_1,t14_relset_1]),
    [file(relset_1,t16_relset_1),interesting(1.00)]).

fof(t29_relset_1,theorem,(
    ! [A] : m2_relset_1(k6_relat_1(A),A,A) ),
    inference(mizar_proof,[status(thm)],[t28_relset_1,d1_relset_1]),
    [file(relset_1,t29_relset_1),interesting(0.86)]).

fof(t13_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,A,C)
     => ( r1_tarski(k1_relat_1(D),B)
       => m2_relset_1(D,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_relat_1,t12_relset_1,t119_zfmisc_1,t1_xboole_1,d1_relset_1]),
    [file(relset_1,t13_relset_1),interesting(0.82)]).

fof(t14_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,C,A)
     => ( r1_tarski(k2_relat_1(D),B)
       => m2_relset_1(D,C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_relat_1,t12_relset_1,t119_zfmisc_1,t1_xboole_1,d1_relset_1]),
    [file(relset_1,t14_relset_1),interesting(0.82)]).

fof(t28_relset_1,theorem,(
    ! [A] : r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A)) ),
    inference(mizar_proof,[status(thm)],[d1_relset_1,d10_relat_1,t106_zfmisc_1,d3_relat_1]),
    [file(relset_1,t28_relset_1),interesting(0.70)]).

fof(t33_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,A,C)
     => m2_relset_1(k8_relset_1(A,C,D,B),B,C) ) ),
    inference(mizar_proof,[status(thm)],[d11_relat_1,t106_zfmisc_1,t106_zfmisc_1,t6_relat_1,d3_relat_1,d1_relset_1]),
    [file(relset_1,t33_relset_1),interesting(0.70)]).

fof(t35_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,C,A)
     => m2_relset_1(k9_relset_1(C,A,B,D),C,B) ) ),
    inference(mizar_proof,[status(thm)],[d12_relat_1,t106_zfmisc_1,t106_zfmisc_1,t6_relat_1,d3_relat_1,d1_relset_1]),
    [file(relset_1,t35_relset_1),interesting(0.70)]).

fof(t17_relset_1,theorem,(
    ! [A,B,C,D,E] : 
      ( m2_relset_1(E,A,C)
     => ( ( r1_tarski(A,B)
          & r1_tarski(C,D) )
       => m2_relset_1(E,B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[t119_zfmisc_1,t1_xboole_1,d1_relset_1]),
    [file(relset_1,t17_relset_1),interesting(0.66)]).

fof(t25_relset_1,theorem,(
    ! [A,B] : m2_relset_1(k1_xboole_0,A,B) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d1_relset_1]),
    [file(relset_1,t25_relset_1),interesting(0.65)]).

fof(t26_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( m2_relset_1(C,k1_xboole_0,B)
       => C = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,t3_xboole_1,t64_relat_1]),
    [file(relset_1,t26_relset_1),interesting(0.64)]).

fof(t27_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( m2_relset_1(C,B,k1_xboole_0)
       => C = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,t3_xboole_1,t64_relat_1]),
    [file(relset_1,t27_relset_1),interesting(0.64)]).

fof(t4_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,B,C)
     => ( r1_tarski(A,D)
       => m2_relset_1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_xboole_1,d1_relset_1]),
    [file(relset_1,t4_relset_1),interesting(0.63)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_relat_1,t106_zfmisc_1,d3_tarski,d5_relat_1,t106_zfmisc_1]),
    [file(relset_1,t12_relset_1),interesting(0.58)]).

fof(t34_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,B,A)
     => ( r1_tarski(B,C)
       => k8_relset_1(B,A,D,C) = D ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,d11_relat_1,d11_relat_1,d2_relat_1]),
    [file(relset_1,t34_relset_1),interesting(0.56)]).

fof(t36_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,A,B)
     => ( r1_tarski(B,C)
       => k9_relset_1(A,B,C,D) = D ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,d12_relat_1,d12_relat_1,d2_relat_1]),
    [file(relset_1,t36_relset_1),interesting(0.56)]).

fof(t38_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C)
        & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_relat_1,t20_relat_1,d5_relat_1,t106_zfmisc_1,d13_relat_1,t2_tarski,d14_relat_1,t20_relat_1,d4_relat_1,t106_zfmisc_1,d14_relat_1,t2_tarski]),
    [file(relset_1,t38_relset_1),interesting(0.52)]).

fof(t30_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,A,B)
     => ( r1_tarski(k6_relat_1(C),D)
       => ( r1_tarski(C,k4_relset_1(A,B,D))
          & r1_tarski(C,k5_relset_1(A,B,D)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d10_relat_1,t20_relat_1,d3_tarski,d10_relat_1,t20_relat_1]),
    [file(relset_1,t30_relset_1),interesting(0.46)]).

fof(t19_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t13_xboole_1,d6_relat_1]),
    [file(relset_1,t19_relset_1),interesting(0.45)]).

fof(t39_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) = k5_relset_1(B,A,C)
        & k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_relset_1,t146_relat_1,t169_relat_1]),
    [file(relset_1,t39_relset_1),interesting(0.43)]).

fof(t10_relset_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => m2_relset_1(B,k1_relat_1(B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_relat_1,t118_zfmisc_1,t1_xboole_1,d1_relset_1]),
    [file(relset_1,t10_relset_1),interesting(0.41)]).

fof(t9_relset_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => m2_relset_1(B,A,k2_relat_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_relat_1,t118_zfmisc_1,t1_xboole_1,d1_relset_1]),
    [file(relset_1,t9_relset_1),interesting(0.41)]).

fof(t8_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r2_hidden(C,A)
        & r2_hidden(D,B) )
     => m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,t37_zfmisc_1,d1_relset_1]),
    [file(relset_1,t8_relset_1),interesting(0.40)]).

fof(t46_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k6_relat_1(A) != k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d10_relat_1]),
    [file(relset_1,t46_relset_1),interesting(0.39)]).

fof(t6_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,A,B)
     => ~ ( r2_hidden(C,D)
          & ! [E,F] : ~ ( C = k4_tarski(E,F)
              & r2_hidden(E,A)
              & r2_hidden(F,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_relat_1,t106_zfmisc_1]),
    [file(relset_1,t6_relset_1),interesting(0.35)]).

fof(t31_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( r1_tarski(k6_relat_1(B),C)
       => ( B = k4_relset_1(B,A,C)
          & r1_tarski(B,k5_relset_1(B,A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_relset_1,d10_xboole_0,t30_relset_1]),
    [file(relset_1,t31_relset_1),interesting(0.33)]).

fof(t32_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k6_relat_1(B),C)
       => ( r1_tarski(B,k4_relset_1(A,B,C))
          & B = k5_relset_1(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_relset_1,t30_relset_1,d10_xboole_0]),
    [file(relset_1,t32_relset_1),interesting(0.33)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_relat_1,t119_zfmisc_1,t1_xboole_1,d1_relset_1]),
    [file(relset_1,t11_relset_1),interesting(0.32)]).

fof(t24_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k4_relset_1(B,A,k6_relset_1(A,B,C)) = k5_relset_1(A,B,C)
        & k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_relat_1,d7_relat_1,t20_relat_1,d5_relat_1,d7_relat_1,t20_relat_1,t2_tarski,d5_relat_1,d7_relat_1,t20_relat_1,d4_relat_1,d7_relat_1,t20_relat_1,t2_tarski]),
    [file(relset_1,t24_relset_1),interesting(0.32)]).

fof(t45_relset_1,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ( k5_relat_1(B,k6_relat_1(A)) = B
        & k5_relat_1(k6_relat_1(A),B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t77_relat_1,t79_relat_1]),
    [file(relset_1,t45_relset_1),interesting(0.32)]).

fof(t22_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( ! [D] : ~ ( r2_hidden(D,B)
            & ! [E] : ~ r2_hidden(k4_tarski(D,E),C) )
      <=> k4_relset_1(B,A,C) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t20_relat_1,t2_tarski,d4_relat_1]),
    [file(relset_1,t22_relset_1),interesting(0.29)]).

fof(t23_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ! [D] : ~ ( r2_hidden(D,B)
            & ! [E] : ~ r2_hidden(k4_tarski(E,D),C) )
      <=> k5_relset_1(A,B,C) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t20_relat_1,t2_tarski,d5_relat_1]),
    [file(relset_1,t23_relset_1),interesting(0.29)]).

fof(s1_relset_1,theorem,(
    ? [A] : 
      ( m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1)
      & ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
        <=> ( r2_hidden(B,f1_s1_relset_1)
            & r2_hidden(C,f2_s1_relset_1)
            & p1_s1_relset_1(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_relat_1,d3_tarski,d1_relat_1,t106_zfmisc_1,d1_relset_1]),
    [file(relset_1,s1_relset_1),interesting(0.26)]).

fof(t47_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_relset_1(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ( r2_hidden(D,k4_relset_1(A,B,C))
                  <=> ? [E] : 
                        ( m1_subset_1(E,B)
                        & r2_hidden(k4_tarski(D,E),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_relat_1,t106_zfmisc_1,t20_relat_1]),
    [file(relset_1,t47_relset_1),interesting(0.17)]).

fof(t48_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_relset_1(C,B,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ( r2_hidden(D,k5_relset_1(B,A,C))
                  <=> ? [E] : 
                        ( m1_subset_1(E,B)
                        & r2_hidden(k4_tarski(E,D),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_relat_1,t106_zfmisc_1,t20_relat_1]),
    [file(relset_1,t48_relset_1),interesting(0.17)]).

fof(s2_relset_1,theorem,(
    ? [A] : 
      ( m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1)
      & ! [B] : 
          ( m1_subset_1(B,f1_s2_relset_1)
         => ! [C] : 
              ( m1_subset_1(C,f2_s2_relset_1)
             => ( r2_hidden(k4_tarski(B,C),A)
              <=> p1_s2_relset_1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_relset_1]),
    [file(relset_1,s2_relset_1),interesting(0.11)]).

fof(t49_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_relset_1(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ~ ( r2_hidden(D,k4_relset_1(A,B,C))
                      & ! [E] : 
                          ( m1_subset_1(E,B)
                         => ~ r2_hidden(E,k5_relset_1(A,B,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_relat_1]),
    [file(relset_1,t49_relset_1),interesting(0.10)]).

fof(t50_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_relset_1(C,B,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ~ ( r2_hidden(D,k5_relset_1(B,A,C))
                      & ! [E] : 
                          ( m1_subset_1(E,B)
                         => ~ r2_hidden(E,k4_relset_1(B,A,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_relat_1]),
    [file(relset_1,t50_relset_1),interesting(0.10)]).

fof(t52_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_relset_1(D,C,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ( r2_hidden(E,k10_relset_1(C,A,D,B))
                      <=> ? [F] : 
                            ( m1_subset_1(F,C)
                            & r2_hidden(k4_tarski(F,E),D)
                            & r2_hidden(F,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_relat_1,t106_zfmisc_1,d13_relat_1]),
    [file(relset_1,t52_relset_1),interesting(0.08)]).

fof(t53_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_relset_1(D,A,C)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ( r2_hidden(E,k11_relset_1(A,C,D,B))
                      <=> ? [F] : 
                            ( m1_subset_1(F,C)
                            & r2_hidden(k4_tarski(E,F),D)
                            & r2_hidden(F,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_relat_1,t106_zfmisc_1,d14_relat_1]),
    [file(relset_1,t53_relset_1),interesting(0.08)]).

fof(s1_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
        <=> ( r2_hidden(B,f1_s1_relat_1)
            & r2_hidden(C,f2_s1_relat_1)
            & p1_s1_relat_1(B,C) ) ) ) ),
    file(relat_1,s1_relat_1),
    [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(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_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(d1_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
    <=> r1_tarski(C,k2_zfmisc_1(A,B)) ) ),
    file(relset_1,d1_relset_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(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(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(t119_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    [interesting(0.00)]).

fof(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.00)]).

fof(d5_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_1,d5_relat_1),
    [interesting(0.00)]).

fof(t18_relset_1,theorem,(
    $true ),
    file(relset_1,t18_relset_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(d6_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    [interesting(0.00)]).

fof(t1_relset_1,theorem,(
    $true ),
    file(relset_1,t1_relset_1),
    [interesting(0.00)]).

fof(t20_relset_1,theorem,(
    $true ),
    file(relset_1,t20_relset_1),
    [interesting(0.00)]).

fof(t21_relset_1,theorem,(
    $true ),
    file(relset_1,t21_relset_1),
    [interesting(0.00)]).

fof(t20_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k2_relat_1(C)) ) ) ) ),
    file(relat_1,t20_relat_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(d7_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ),
    file(relat_1,d7_relat_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(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.00)]).

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(0.00)]).

fof(d10_relat_1,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k6_relat_1(A)
      <=> ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),B)
          <=> ( r2_hidden(C,A)
              & C = D ) ) ) ) ),
    file(relat_1,d10_relat_1),
    [interesting(0.00)]).

fof(d3_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    [interesting(0.00)]).

fof(t2_relset_1,theorem,(
    $true ),
    file(relset_1,t2_relset_1),
    [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(d11_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( v1_relat_1(C)
         => ( C = k7_relat_1(A,B)
          <=> ! [D,E] : 
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(D,B)
                  & r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) ),
    file(relat_1,d11_relat_1),
    [interesting(0.00)]).

fof(t6_relat_1,theorem,(
    ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ),
    file(relat_1,t6_relat_1),
    [interesting(0.00)]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.00)]).

fof(d12_relat_1,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( C = k8_relat_1(A,B)
          <=> ! [D,E] : 
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(E,A)
                  & r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ),
    file(relat_1,d12_relat_1),
    [interesting(0.00)]).

fof(t37_relset_1,theorem,(
    $true ),
    file(relset_1,t37_relset_1),
    [interesting(0.00)]).

fof(d13_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(k4_tarski(E,D),A)
                  & r2_hidden(E,B) ) ) ) ) ),
    file(relat_1,d13_relat_1),
    [interesting(0.00)]).

fof(d14_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(k4_tarski(D,E),A)
                  & r2_hidden(E,B) ) ) ) ) ),
    file(relat_1,d14_relat_1),
    [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(t169_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) ),
    file(relat_1,t169_relat_1),
    [interesting(0.00)]).

fof(t3_relset_1,theorem,(
    $true ),
    file(relset_1,t3_relset_1),
    [interesting(0.00)]).

fof(t40_relset_1,theorem,(
    $true ),
    file(relset_1,t40_relset_1),
    [interesting(0.00)]).

fof(t41_relset_1,theorem,(
    $true ),
    file(relset_1,t41_relset_1),
    [interesting(0.00)]).

fof(t42_relset_1,theorem,(
    $true ),
    file(relset_1,t42_relset_1),
    [interesting(0.00)]).

fof(t43_relset_1,theorem,(
    $true ),
    file(relset_1,t43_relset_1),
    [interesting(0.00)]).

fof(t44_relset_1,theorem,(
    $true ),
    file(relset_1,t44_relset_1),
    [interesting(0.00)]).

fof(t77_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k5_relat_1(k6_relat_1(A),B) = B ) ) ),
    file(relat_1,t77_relat_1),
    [interesting(0.00)]).

fof(t79_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) ),
    file(relat_1,t79_relat_1),
    [interesting(0.00)]).

fof(t18_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ~ ( r2_hidden(A,k1_relat_1(B))
          & ! [C] : ~ r2_hidden(C,k2_relat_1(B)) ) ) ),
    file(relat_1,t18_relat_1),
    [interesting(0.00)]).

fof(t19_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ~ ( r2_hidden(A,k2_relat_1(B))
          & ! [C] : ~ r2_hidden(C,k1_relat_1(B)) ) ) ),
    file(relat_1,t19_relat_1),
    [interesting(0.00)]).

fof(d8_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( C = k5_relat_1(A,B)
              <=> ! [D,E] : 
                    ( r2_hidden(k4_tarski(D,E),C)
                  <=> ? [F] : 
                        ( r2_hidden(k4_tarski(D,F),A)
                        & r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ),
    file(relat_1,d8_relat_1),
    [interesting(0.00)]).

fof(t51_relset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_relset_1(D,A,B)
                 => ! [E] : 
                      ( m2_relset_1(E,B,C)
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ! [G] : 
                              ( m1_subset_1(G,C)
                             => ( r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))
                              <=> ? [H] : 
                                    ( m1_subset_1(H,B)
                                    & r2_hidden(k4_tarski(F,H),D)
                                    & r2_hidden(k4_tarski(H,G),E) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_relat_1,t106_zfmisc_1,d8_relat_1]),
    [file(relset_1,t51_relset_1),interesting(0.00)]).

fof(t5_relset_1,theorem,(
    $true ),
    file(relset_1,t5_relset_1),
    [interesting(0.00)]).

fof(t7_relset_1,theorem,(
    $true ),
    file(relset_1,t7_relset_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)]).