fof(t6_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_tarski,l4_zfmisc_1,l1_zfmisc_1]),
    [file(zfmisc_1,t6_zfmisc_1),interesting(1.00)]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    inference(mizar_proof,[status(thm)],[t69_enumset1,t8_zfmisc_1,t8_zfmisc_1,t9_zfmisc_1,t10_zfmisc_1,t6_zfmisc_1,t10_zfmisc_1,t10_zfmisc_1]),
    [file(zfmisc_1,t33_zfmisc_1),interesting(0.98)]).

fof(l28_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_xboole_0,d1_tarski,d7_xboole_0,d10_xboole_0,t2_xboole_1]),
    [file(zfmisc_1,l28_zfmisc_1),interesting(0.97)]).

fof(t127_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_xboole_0(A,B)
        | r1_xboole_0(C,D) )
     => r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    inference(mizar_proof,[status(thm)],[t4_xboole_0,t104_zfmisc_1,t4_xboole_0]),
    [file(zfmisc_1,t127_zfmisc_1),interesting(0.97)]).

fof(l55_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) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_zfmisc_1,t33_zfmisc_1,d2_zfmisc_1]),
    [file(zfmisc_1,l55_zfmisc_1),interesting(0.96)]).

fof(t115_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[l55_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t115_zfmisc_1),interesting(0.96)]).

fof(t55_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( r1_xboole_0(k2_tarski(A,B),C)
      & r2_hidden(A,C) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d2_tarski,d3_xboole_0,d1_xboole_0]),
    [file(zfmisc_1,t55_zfmisc_1),interesting(0.96)]).

fof(l25_zfmisc_1,theorem,(
    ! [A,B] : ~ ( r1_xboole_0(k1_tarski(A),B)
      & r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_tarski,d3_xboole_0,d1_xboole_0]),
    [file(zfmisc_1,l25_zfmisc_1),interesting(0.95)]).

fof(t12_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k1_tarski(A),k2_tarski(A,B)) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_tarski,d2_tarski]),
    [file(zfmisc_1,t12_zfmisc_1),interesting(0.93)]).

fof(t138_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
     => ( k2_zfmisc_1(A,B) = k1_xboole_0
        | ( r1_tarski(A,C)
          & r1_tarski(B,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t113_zfmisc_1,t28_xboole_1,t123_zfmisc_1,t134_zfmisc_1,t17_xboole_1]),
    [file(zfmisc_1,t138_zfmisc_1),interesting(0.91)]).

fof(t139_zfmisc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] : 
          ( ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
            | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) )
         => r1_tarski(B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,t113_zfmisc_1,t138_zfmisc_1]),
    [file(zfmisc_1,t139_zfmisc_1),interesting(0.91)]).

fof(t24_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[t6_zfmisc_1]),
    [file(zfmisc_1,t24_zfmisc_1),interesting(0.91)]).

fof(t107_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
     => r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)) ) ),
    inference(mizar_proof,[status(thm)],[l55_zfmisc_1]),
    [file(zfmisc_1,t107_zfmisc_1),interesting(0.90)]).

fof(t57_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( ~ r2_hidden(A,B)
      & ~ r2_hidden(C,B)
      & ~ r1_xboole_0(k2_tarski(A,C),B) ) ),
    inference(mizar_proof,[status(thm)],[t4_xboole_0,d3_xboole_0,d2_tarski]),
    [file(zfmisc_1,t57_zfmisc_1),interesting(0.90)]).

fof(t95_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_tarski(A),k3_tarski(B)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski,d3_tarski,d4_tarski]),
    [file(zfmisc_1,t95_zfmisc_1),interesting(0.90)]).

fof(l50_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski]),
    [file(zfmisc_1,l50_zfmisc_1),interesting(0.89)]).

fof(t17_zfmisc_1,theorem,(
    ! [A,B] : 
      ( A != B
     => r1_xboole_0(k1_tarski(A),k1_tarski(B)) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,l28_zfmisc_1]),
    [file(zfmisc_1,t17_zfmisc_1),interesting(0.89)]).

fof(t99_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_zfmisc_1(A)) = A ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d1_zfmisc_1,d3_tarski,l2_zfmisc_1,d1_zfmisc_1,d1_tarski,d4_tarski,t2_tarski]),
    [file(zfmisc_1,t99_zfmisc_1),interesting(0.89)]).

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)) ) ),
    inference(mizar_proof,[status(thm)],[t118_zfmisc_1,t1_xboole_1]),
    [file(zfmisc_1,t119_zfmisc_1),interesting(0.88)]).

fof(t134_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | ( A = C
          & B = D ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_xboole_0,t113_zfmisc_1,t113_zfmisc_1,l55_zfmisc_1,l55_zfmisc_1,d1_xboole_0,l55_zfmisc_1,l55_zfmisc_1,t2_tarski,l55_zfmisc_1,l55_zfmisc_1,d1_xboole_0,l55_zfmisc_1,l55_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t134_zfmisc_1),interesting(0.88)]).

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    inference(mizar_proof,[status(thm)],[d1_tarski,l50_zfmisc_1,d3_tarski,d4_tarski,d1_tarski,d10_xboole_0]),
    [file(zfmisc_1,t31_zfmisc_1),interesting(0.88)]).

fof(t56_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    inference(mizar_proof,[status(thm)],[l28_zfmisc_1]),
    [file(zfmisc_1,t56_zfmisc_1),interesting(0.88)]).

fof(l2_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d3_tarski,d3_tarski,d1_tarski]),
    [file(zfmisc_1,l2_zfmisc_1),interesting(0.87)]).

fof(t121_zfmisc_1,theorem,(
    ! [A,B,C,D] : k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) ),
    inference(mizar_proof,[status(thm)],[t120_zfmisc_1,t120_zfmisc_1,t120_zfmisc_1,t4_xboole_1]),
    [file(zfmisc_1,t121_zfmisc_1),interesting(0.87)]).

fof(t8_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d1_tarski]),
    [file(zfmisc_1,t8_zfmisc_1),interesting(0.86)]).

fof(t9_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => B = C ) ),
    inference(mizar_proof,[status(thm)],[t8_zfmisc_1]),
    [file(zfmisc_1,t9_zfmisc_1),interesting(0.86)]).

fof(t10_zfmisc_1,theorem,(
    ! [A,B,C,D] : ~ ( k2_tarski(A,B) = k2_tarski(C,D)
      & A != C
      & A != D ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d2_tarski]),
    [file(zfmisc_1,t10_zfmisc_1),interesting(0.86)]).

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) ) ) ),
    inference(mizar_proof,[status(thm)],[l55_zfmisc_1]),
    [file(zfmisc_1,t106_zfmisc_1),interesting(0.86)]).

fof(t123_zfmisc_1,theorem,(
    ! [A,B,C,D] : k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,t119_zfmisc_1,t19_xboole_1,d3_tarski,t104_zfmisc_1,d2_zfmisc_1,d10_xboole_0]),
    [file(zfmisc_1,t123_zfmisc_1),interesting(0.86)]).

fof(t65_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,k1_tarski(B)) = A
    <=> ~ r2_hidden(B,A) ) ),
    inference(mizar_proof,[status(thm)],[t83_xboole_1,l25_zfmisc_1,l28_zfmisc_1]),
    [file(zfmisc_1,t65_zfmisc_1),interesting(0.86)]).

fof(t54_zfmisc_1,theorem,(
    ! [A,B] : ~ ( r1_xboole_0(k1_tarski(A),B)
      & r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[l25_zfmisc_1]),
    [file(zfmisc_1,t54_zfmisc_1),interesting(0.85)]).

fof(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d3_tarski,d3_tarski,d2_tarski]),
    [file(zfmisc_1,t38_zfmisc_1),interesting(0.83)]).

fof(t100_zfmisc_1,theorem,(
    ! [A] : r1_tarski(A,k1_zfmisc_1(k3_tarski(A))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,l50_zfmisc_1,d1_zfmisc_1]),
    [file(zfmisc_1,t100_zfmisc_1),interesting(0.82)]).

fof(l52_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d2_tarski,d2_tarski,d4_tarski,d2_xboole_0]),
    [file(zfmisc_1,l52_zfmisc_1),interesting(0.82)]).

fof(t79_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_zfmisc_1,t1_xboole_1,d1_zfmisc_1]),
    [file(zfmisc_1,t79_zfmisc_1),interesting(0.82)]).

fof(l1_zfmisc_1,theorem,(
    ! [A] : k1_tarski(A) != k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_xboole_0]),
    [file(zfmisc_1,l1_zfmisc_1),interesting(0.81)]).

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)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_zfmisc_1,d3_tarski,d2_zfmisc_1,d3_tarski,d2_zfmisc_1,d3_tarski,d2_zfmisc_1]),
    [file(zfmisc_1,t118_zfmisc_1),interesting(0.80)]).

fof(t80_zfmisc_1,theorem,(
    ! [A] : r1_tarski(k1_tarski(A),k1_zfmisc_1(A)) ),
    inference(mizar_proof,[status(thm)],[d1_zfmisc_1,l2_zfmisc_1]),
    [file(zfmisc_1,t80_zfmisc_1),interesting(0.80)]).

fof(t98_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_xboole_0(C,B) )
     => r1_xboole_0(k3_tarski(A),B) ) ),
    inference(mizar_proof,[status(thm)],[t4_xboole_0,d3_xboole_0,d4_tarski,d3_xboole_0,t4_xboole_0]),
    [file(zfmisc_1,t98_zfmisc_1),interesting(0.79)]).

fof(l34_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_tarski(A)
    <=> ~ r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[t83_xboole_1,l25_zfmisc_1,l28_zfmisc_1]),
    [file(zfmisc_1,l34_zfmisc_1),interesting(0.78)]).

fof(t26_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),k1_tarski(C))
     => A = C ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d3_tarski,d1_tarski]),
    [file(zfmisc_1,t26_zfmisc_1),interesting(0.78)]).

fof(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    inference(mizar_proof,[status(thm)],[l50_zfmisc_1]),
    [file(zfmisc_1,t92_zfmisc_1),interesting(0.78)]).

fof(t97_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski,d3_xboole_0,d4_tarski,d3_xboole_0]),
    [file(zfmisc_1,t97_zfmisc_1),interesting(0.77)]).

fof(l21_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B)
     => r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d1_tarski]),
    [file(zfmisc_1,l21_zfmisc_1),interesting(0.77)]).

fof(t116_zfmisc_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k2_zfmisc_1(A,A))
     => A = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d2_xboole_0,t7_tarski,d3_tarski,t102_zfmisc_1,d2_tarski,l50_zfmisc_1,d3_tarski,d2_xboole_0,d2_xboole_0,d4_tarski,d3_tarski,d2_zfmisc_1,d2_tarski,d1_tarski,d2_tarski,d2_xboole_0]),
    [file(zfmisc_1,t116_zfmisc_1),interesting(0.76)]).

fof(t126_zfmisc_1,theorem,(
    ! [A,B,C,D] : k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) ),
    inference(mizar_proof,[status(thm)],[t123_zfmisc_1,t125_zfmisc_1,t17_xboole_1,t119_zfmisc_1,t54_xboole_1,t34_xboole_1,d3_tarski,d2_zfmisc_1,d4_xboole_0,l55_zfmisc_1,d4_xboole_0,d2_zfmisc_1,d4_xboole_0,l55_zfmisc_1,d4_xboole_0,d2_xboole_0,d10_xboole_0]),
    [file(zfmisc_1,t126_zfmisc_1),interesting(0.76)]).

fof(t128_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D))
    <=> ( A = C
        & r2_hidden(B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,l55_zfmisc_1,l55_zfmisc_1]),
    [file(zfmisc_1,t128_zfmisc_1),interesting(0.76)]).

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 ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,l55_zfmisc_1,l55_zfmisc_1]),
    [file(zfmisc_1,t129_zfmisc_1),interesting(0.76)]).

fof(t16_zfmisc_1,theorem,(
    ! [A,B] : ~ ( r1_xboole_0(k1_tarski(A),k1_tarski(B))
      & A = B ) ),
    inference(mizar_proof,[status(thm)],[l25_zfmisc_1,d1_tarski]),
    [file(zfmisc_1,t16_zfmisc_1),interesting(0.76)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[l2_zfmisc_1]),
    [file(zfmisc_1,t37_zfmisc_1),interesting(0.76)]).

fof(l23_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    inference(mizar_proof,[status(thm)],[l2_zfmisc_1,t12_xboole_1]),
    [file(zfmisc_1,l23_zfmisc_1),interesting(0.75)]).

fof(l4_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    inference(mizar_proof,[status(thm)],[l2_zfmisc_1,l3_zfmisc_1,d10_xboole_0,t37_xboole_1,t3_xboole_1,t2_xboole_1]),
    [file(zfmisc_1,l4_zfmisc_1),interesting(0.74)]).

fof(t102_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
      & ! [D,E] : k4_tarski(D,E) != A ) ),
    inference(mizar_proof,[status(thm)],[d2_zfmisc_1]),
    [file(zfmisc_1,t102_zfmisc_1),interesting(0.74)]).

fof(t125_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ),
    inference(mizar_proof,[status(thm)],[t36_xboole_1,l55_zfmisc_1,d4_xboole_0,l55_zfmisc_1,d4_xboole_0,d4_xboole_0,l55_zfmisc_1,d4_xboole_0,l55_zfmisc_1,t110_zfmisc_1,t36_xboole_1,t107_zfmisc_1,d4_xboole_0,d4_xboole_0,t110_zfmisc_1]),
    [file(zfmisc_1,t125_zfmisc_1),interesting(0.74)]).

fof(t28_zfmisc_1,theorem,(
    ! [A,B,C,D] : ~ ( r1_tarski(k2_tarski(A,B),k2_tarski(C,D))
      & A != C
      & A != D ) ),
    inference(mizar_proof,[status(thm)],[l46_zfmisc_1,d2_tarski,t8_zfmisc_1,t10_zfmisc_1,d1_xboole_0]),
    [file(zfmisc_1,t28_zfmisc_1),interesting(0.74)]).

fof(t72_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
    <=> ( ~ r2_hidden(A,C)
        & ~ r2_hidden(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t83_xboole_1,t55_zfmisc_1,t57_zfmisc_1]),
    [file(zfmisc_1,t72_zfmisc_1),interesting(0.74)]).

fof(t114_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | A = B ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_xboole_0,l55_zfmisc_1,l55_zfmisc_1,l55_zfmisc_1,l55_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t114_zfmisc_1),interesting(0.73)]).

fof(t120_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ),
    inference(mizar_proof,[status(thm)],[d2_xboole_0,t102_zfmisc_1,t102_zfmisc_1,l55_zfmisc_1,d2_xboole_0,l55_zfmisc_1,d2_xboole_0,d2_xboole_0,l55_zfmisc_1,d2_xboole_0,l55_zfmisc_1,t112_zfmisc_1,t102_zfmisc_1,t107_zfmisc_1,d2_xboole_0,d2_xboole_0,t112_zfmisc_1]),
    [file(zfmisc_1,t120_zfmisc_1),interesting(0.73)]).

fof(t96_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B)) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski,d2_xboole_0,d4_tarski,d2_xboole_0,t7_xboole_1,t95_zfmisc_1,t8_xboole_1,d10_xboole_0]),
    [file(zfmisc_1,t96_zfmisc_1),interesting(0.73)]).

fof(t113_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_xboole_0,d2_zfmisc_1,d1_xboole_0,d1_xboole_0,d2_zfmisc_1,d1_xboole_0,d2_zfmisc_1,d1_xboole_0]),
    [file(zfmisc_1,t113_zfmisc_1),interesting(0.72)]).

fof(t35_zfmisc_1,theorem,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    inference(mizar_proof,[status(thm)],[d2_zfmisc_1,d1_tarski,d1_tarski,d1_tarski,l55_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t35_zfmisc_1),interesting(0.72)]).

fof(l3_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r2_hidden(C,A)
        | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_tarski,d3_tarski,d4_xboole_0]),
    [file(zfmisc_1,l3_zfmisc_1),interesting(0.71)]).

fof(t64_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) ),
    inference(mizar_proof,[status(thm)],[d4_xboole_0,d1_tarski]),
    [file(zfmisc_1,t64_zfmisc_1),interesting(0.71)]).

fof(l30_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B)
     => r2_hidden(B,A) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d3_xboole_0]),
    [file(zfmisc_1,l30_zfmisc_1),interesting(0.71)]).

fof(t2_zfmisc_1,theorem,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d1_xboole_0,d1_xboole_0]),
    [file(zfmisc_1,t2_zfmisc_1),interesting(0.71)]).

fof(t83_zfmisc_1,theorem,(
    ! [A,B] : k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,t1_xboole_1,t19_xboole_1,d1_zfmisc_1,d3_xboole_0,t2_tarski]),
    [file(zfmisc_1,t83_zfmisc_1),interesting(0.71)]).

fof(t94_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(C,B) )
     => r1_tarski(k3_tarski(A),B) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski,d3_tarski]),
    [file(zfmisc_1,t94_zfmisc_1),interesting(0.71)]).

fof(t93_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) ),
    inference(mizar_proof,[status(thm)],[l52_zfmisc_1]),
    [file(zfmisc_1,t93_zfmisc_1),interesting(0.70)]).

fof(t137_zfmisc_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( r2_hidden(A,k2_zfmisc_1(B,C))
        & r2_hidden(A,k2_zfmisc_1(D,E)) )
     => r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,t123_zfmisc_1]),
    [file(zfmisc_1,t137_zfmisc_1),interesting(0.69)]).

fof(l32_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) ),
    inference(mizar_proof,[status(thm)],[l2_zfmisc_1,t28_xboole_1]),
    [file(zfmisc_1,l32_zfmisc_1),interesting(0.69)]).

fof(t124_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C) ) ),
    inference(mizar_proof,[status(thm)],[t123_zfmisc_1,t28_xboole_1]),
    [file(zfmisc_1,t124_zfmisc_1),interesting(0.68)]).

fof(t20_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
    <=> A != B ) ),
    inference(mizar_proof,[status(thm)],[l34_zfmisc_1,d1_tarski]),
    [file(zfmisc_1,t20_zfmisc_1),interesting(0.68)]).

fof(l45_zfmisc_1,theorem,(
    ! [A,B] : ~ ( A != k1_tarski(B)
      & A != k1_xboole_0
      & ! [C] : ~ ( r2_hidden(C,A)
          & C != B ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,t2_tarski,d1_tarski]),
    [file(zfmisc_1,l45_zfmisc_1),interesting(0.68)]).

fof(t81_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d1_zfmisc_1,t7_xboole_1,t1_xboole_1,d1_zfmisc_1]),
    [file(zfmisc_1,t81_zfmisc_1),interesting(0.67)]).

fof(t105_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B)))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_zfmisc_1,d3_tarski,l2_zfmisc_1,d2_xboole_0,t7_xboole_1,t38_zfmisc_1,d2_tarski,t1_xboole_1,d1_zfmisc_1,d1_zfmisc_1]),
    [file(zfmisc_1,t105_zfmisc_1),interesting(0.66)]).

fof(t47_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C)
     => r2_hidden(A,C) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d2_tarski]),
    [file(zfmisc_1,t47_zfmisc_1),interesting(0.66)]).

fof(t50_zfmisc_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d2_xboole_0,d1_xboole_0]),
    [file(zfmisc_1,t50_zfmisc_1),interesting(0.66)]).

fof(t49_zfmisc_1,theorem,(
    ! [A,B] : k2_xboole_0(k1_tarski(A),B) != k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d2_xboole_0,d1_xboole_0]),
    [file(zfmisc_1,t49_zfmisc_1),interesting(0.65)]).

fof(t67_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_tarski(A)
    <=> ~ r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[l34_zfmisc_1]),
    [file(zfmisc_1,t67_zfmisc_1),interesting(0.65)]).

fof(t45_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B)
     => r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[l21_zfmisc_1]),
    [file(zfmisc_1,t45_zfmisc_1),interesting(0.64)]).

fof(t13_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[l21_zfmisc_1,d1_tarski]),
    [file(zfmisc_1,t13_zfmisc_1),interesting(0.63)]).

fof(t39_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    inference(mizar_proof,[status(thm)],[l4_zfmisc_1]),
    [file(zfmisc_1,t39_zfmisc_1),interesting(0.63)]).

fof(t18_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[l30_zfmisc_1,d1_tarski]),
    [file(zfmisc_1,t18_zfmisc_1),interesting(0.62)]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    inference(mizar_proof,[status(thm)],[l23_zfmisc_1]),
    [file(zfmisc_1,t46_zfmisc_1),interesting(0.61)]).

fof(t135_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,k2_zfmisc_1(A,B))
        | r1_tarski(A,k2_zfmisc_1(B,A)) )
     => A = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d2_xboole_0,t7_tarski,d3_tarski,t102_zfmisc_1,d2_tarski,l50_zfmisc_1,d3_tarski,d2_xboole_0,d2_xboole_0,d4_tarski,d3_tarski,d2_zfmisc_1,d2_tarski,d1_tarski,d2_tarski,d2_xboole_0,s1_xboole_0,t15_xboole_1,d1_xboole_0,t7_tarski,d4_tarski,d2_xboole_0,d2_xboole_0,d2_xboole_0,d2_tarski,d3_tarski,d2_zfmisc_1]),
    [file(zfmisc_1,t135_zfmisc_1),interesting(0.60)]).

fof(t112_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ( ! [C] : ~ ( r2_hidden(C,A)
            & ! [D,E] : C != k4_tarski(D,E) )
        & ! [C] : ~ ( r2_hidden(C,B)
            & ! [D,E] : C != k4_tarski(D,E) )
        & ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),A)
          <=> r2_hidden(k4_tarski(C,D),B) ) )
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[t2_tarski]),
    [file(zfmisc_1,t112_zfmisc_1),interesting(0.59)]).

fof(t122_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,l55_zfmisc_1,d3_xboole_0,l55_zfmisc_1,d3_xboole_0,d3_xboole_0,l55_zfmisc_1,d3_xboole_0,l55_zfmisc_1,t110_zfmisc_1,t17_xboole_1,t107_zfmisc_1,d3_xboole_0,d3_xboole_0,t110_zfmisc_1]),
    [file(zfmisc_1,t122_zfmisc_1),interesting(0.59)]).

fof(t14_zfmisc_1,theorem,(
    ! [A,B] : k2_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,l23_zfmisc_1]),
    [file(zfmisc_1,t14_zfmisc_1),interesting(0.59)]).

fof(t19_zfmisc_1,theorem,(
    ! [A,B] : k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,l32_zfmisc_1]),
    [file(zfmisc_1,t19_zfmisc_1),interesting(0.59)]).

fof(t25_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( r1_tarski(k1_tarski(A),k2_tarski(B,C))
      & A != B
      & A != C ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d3_tarski,d2_tarski]),
    [file(zfmisc_1,t25_zfmisc_1),interesting(0.58)]).

fof(t32_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[l52_zfmisc_1,t41_enumset1]),
    [file(zfmisc_1,t32_zfmisc_1),interesting(0.58)]).

fof(t58_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(k1_tarski(A),B)
      | k3_xboole_0(k1_tarski(A),B) = k1_tarski(A) ) ),
    inference(mizar_proof,[status(thm)],[l28_zfmisc_1,l32_zfmisc_1]),
    [file(zfmisc_1,t58_zfmisc_1),interesting(0.58)]).

fof(t63_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
     => r2_hidden(A,C) ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d3_xboole_0]),
    [file(zfmisc_1,t63_zfmisc_1),interesting(0.58)]).

fof(t1_zfmisc_1,theorem,(
    k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_1,d1_zfmisc_1,d1_tarski,t2_tarski]),
    [file(zfmisc_1,t1_zfmisc_1),interesting(0.57)]).

fof(l36_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
    <=> r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[t37_xboole_1,l2_zfmisc_1]),
    [file(zfmisc_1,l36_zfmisc_1),interesting(0.56)]).

fof(t27_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),k1_tarski(C))
     => k2_tarski(A,B) = k1_tarski(C) ) ),
    inference(mizar_proof,[status(thm)],[t26_zfmisc_1,t69_enumset1]),
    [file(zfmisc_1,t27_zfmisc_1),interesting(0.56)]).

fof(t40_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r2_hidden(C,A)
        | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) ) ) ),
    inference(mizar_proof,[status(thm)],[l3_zfmisc_1]),
    [file(zfmisc_1,t40_zfmisc_1),interesting(0.56)]).

fof(t48_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k2_xboole_0(k2_tarski(A,C),B) = B ) ),
    inference(mizar_proof,[status(thm)],[t38_zfmisc_1,t12_xboole_1]),
    [file(zfmisc_1,t48_zfmisc_1),interesting(0.56)]).

fof(t51_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B)
     => r2_hidden(B,A) ) ),
    inference(mizar_proof,[status(thm)],[l30_zfmisc_1]),
    [file(zfmisc_1,t51_zfmisc_1),interesting(0.56)]).

fof(t23_zfmisc_1,theorem,(
    ! [A,B] : 
      ( A != B
     => k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,l39_zfmisc_1]),
    [file(zfmisc_1,t23_zfmisc_1),interesting(0.55)]).

fof(t30_zfmisc_1,theorem,(
    ! [A] : k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) ),
    inference(mizar_proof,[status(thm)],[l4_zfmisc_1,d1_zfmisc_1,d2_tarski,t2_tarski]),
    [file(zfmisc_1,t30_zfmisc_1),interesting(0.55)]).

fof(l39_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
    <=> ( ~ r2_hidden(A,C)
        & ( r2_hidden(B,C)
          | A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d4_xboole_0,d2_tarski,d4_xboole_0,d1_tarski,d2_tarski,d4_xboole_0,d1_tarski]),
    [file(zfmisc_1,l39_zfmisc_1),interesting(0.54)]).

fof(t52_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) ),
    inference(mizar_proof,[status(thm)],[l32_zfmisc_1]),
    [file(zfmisc_1,t52_zfmisc_1),interesting(0.54)]).

fof(t104_zfmisc_1,theorem,(
    ! [A,B,C,D,E] : ~ ( r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E)))
      & ! [F,G] : ~ ( A = k4_tarski(F,G)
          & r2_hidden(F,k3_xboole_0(B,D))
          & r2_hidden(G,k3_xboole_0(C,E)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,d2_zfmisc_1,d2_zfmisc_1,t33_zfmisc_1,d3_xboole_0]),
    [file(zfmisc_1,t104_zfmisc_1),interesting(0.53)]).

fof(t29_zfmisc_1,theorem,(
    ! [A,B] : 
      ( A != B
     => k5_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t1_xboole_0,d2_tarski]),
    [file(zfmisc_1,t29_zfmisc_1),interesting(0.53)]).

fof(t73_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_xboole_1,t38_zfmisc_1]),
    [file(zfmisc_1,t73_zfmisc_1),interesting(0.53)]).

fof(t130_zfmisc_1,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => ( k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0
        & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,t128_zfmisc_1,t129_zfmisc_1,d1_xboole_0]),
    [file(zfmisc_1,t130_zfmisc_1),interesting(0.52)]).

fof(t34_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D)))
    <=> ( A = C
        & B = D ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,l55_zfmisc_1]),
    [file(zfmisc_1,t34_zfmisc_1),interesting(0.52)]).

fof(t41_zfmisc_1,theorem,(
    ! [A,B] : ~ ( A != k1_tarski(B)
      & A != k1_xboole_0
      & ! [C] : ~ ( r2_hidden(C,A)
          & C != B ) ) ),
    inference(mizar_proof,[status(thm)],[l45_zfmisc_1]),
    [file(zfmisc_1,t41_zfmisc_1),interesting(0.52)]).

fof(t44_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( k1_tarski(A) = k2_xboole_0(B,C)
      & B != C
      & B != k1_xboole_0
      & C != k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[t43_zfmisc_1]),
    [file(zfmisc_1,t44_zfmisc_1),interesting(0.52)]).

fof(t66_zfmisc_1,theorem,(
    ! [A,B] : ~ ( k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0
      & A != k1_xboole_0
      & A != k1_tarski(B) ) ),
    inference(mizar_proof,[status(thm)],[t37_xboole_1,l4_zfmisc_1]),
    [file(zfmisc_1,t66_zfmisc_1),interesting(0.51)]).

fof(t103_zfmisc_1,theorem,(
    ! [A,B,C,D] : ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
      & r2_hidden(D,A)
      & ! [E,F] : ~ ( r2_hidden(E,B)
          & r2_hidden(F,C)
          & D = k4_tarski(E,F) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_zfmisc_1]),
    [file(zfmisc_1,t103_zfmisc_1),interesting(0.50)]).

fof(t117_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( A != k1_xboole_0
      & ( r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))
        | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) )
      & ~ r1_tarski(B,C) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d3_tarski,d2_zfmisc_1,d3_tarski,l55_zfmisc_1]),
    [file(zfmisc_1,t117_zfmisc_1),interesting(0.50)]).

fof(t53_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C) ) ),
    inference(mizar_proof,[status(thm)],[t38_zfmisc_1,t28_xboole_1]),
    [file(zfmisc_1,t53_zfmisc_1),interesting(0.50)]).

fof(t69_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
      | k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) ) ),
    inference(mizar_proof,[status(thm)],[l36_zfmisc_1,l34_zfmisc_1]),
    [file(zfmisc_1,t69_zfmisc_1),interesting(0.50)]).

fof(t21_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[l36_zfmisc_1,d1_tarski]),
    [file(zfmisc_1,t21_zfmisc_1),interesting(0.48)]).

fof(t82_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B))
     => r3_xboole_0(A,B) ) ),
    inference(mizar_proof,[status(thm)],[d1_zfmisc_1,d2_xboole_0,d1_zfmisc_1,t7_xboole_1,d10_xboole_0,d9_xboole_0]),
    [file(zfmisc_1,t82_zfmisc_1),interesting(0.48)]).

fof(t141_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B ) ),
    inference(mizar_proof,[status(thm)],[t40_xboole_1,t65_zfmisc_1]),
    [file(zfmisc_1,t141_zfmisc_1),interesting(0.47)]).

fof(t109_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & ! [E,F] : 
            ( r2_hidden(k4_tarski(E,F),A)
           => r2_hidden(k4_tarski(E,F),D) ) )
     => r1_tarski(A,D) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t103_zfmisc_1]),
    [file(zfmisc_1,t109_zfmisc_1),interesting(0.46)]).

fof(t110_zfmisc_1,theorem,(
    ! [A,B,C,D,E,F] : 
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r1_tarski(D,k2_zfmisc_1(E,F))
        & ! [G,H] : 
            ( r2_hidden(k4_tarski(G,H),A)
          <=> r2_hidden(k4_tarski(G,H),D) ) )
     => A = D ) ),
    inference(mizar_proof,[status(thm)],[t103_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t110_zfmisc_1),interesting(0.46)]).

fof(t140_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d1_tarski,t64_zfmisc_1,d10_xboole_0,d3_tarski,d4_xboole_0,d2_xboole_0]),
    [file(zfmisc_1,t140_zfmisc_1),interesting(0.45)]).

fof(l46_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_tarski(B,C))
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,l45_zfmisc_1,d3_tarski,d2_tarski,l45_zfmisc_1,d3_tarski,d2_tarski,d2_tarski,t2_tarski,t12_zfmisc_1,t2_xboole_1]),
    [file(zfmisc_1,l46_zfmisc_1),interesting(0.45)]).

fof(t22_zfmisc_1,theorem,(
    ! [A,B] : k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d2_tarski,l36_zfmisc_1]),
    [file(zfmisc_1,t22_zfmisc_1),interesting(0.43)]).

fof(t131_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => ( r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D))
        & r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_zfmisc_1,t127_zfmisc_1]),
    [file(zfmisc_1,t131_zfmisc_1),interesting(0.42)]).

fof(t108_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ! [E,F] : 
          ( r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B))
        <=> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)) )
     => k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) ) ),
    inference(mizar_proof,[status(thm)],[d2_zfmisc_1,d2_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t108_zfmisc_1),interesting(0.41)]).

fof(t59_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
      & r2_hidden(B,C)
      & A != B ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d3_xboole_0,d1_tarski]),
    [file(zfmisc_1,t59_zfmisc_1),interesting(0.41)]).

fof(t68_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
    <=> r2_hidden(A,B) ) ),
    inference(mizar_proof,[status(thm)],[l36_zfmisc_1]),
    [file(zfmisc_1,t68_zfmisc_1),interesting(0.39)]).

fof(t111_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ( ! [C] : ~ ( r2_hidden(C,A)
            & ! [D,E] : C != k4_tarski(D,E) )
        & ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),A)
           => r2_hidden(k4_tarski(C,D),B) ) )
     => r1_tarski(A,B) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski]),
    [file(zfmisc_1,t111_zfmisc_1),interesting(0.38)]).

fof(t136_zfmisc_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( r2_hidden(A,B)
      & ! [C,D] : 
          ( ( r2_hidden(C,B)
            & r1_tarski(D,C) )
         => r2_hidden(D,B) )
      & ! [C] : 
          ( r2_hidden(C,B)
         => r2_hidden(k1_zfmisc_1(C),B) )
      & ! [C] : ~ ( r1_tarski(C,B)
          & ~ r2_tarski(C,B)
          & ~ r2_hidden(C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_tarski,d1_zfmisc_1,d3_tarski]),
    [file(zfmisc_1,t136_zfmisc_1),interesting(0.38)]).

fof(t60_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,B)
     => ( ( r2_hidden(C,B)
          & A != C )
        | k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d3_xboole_0,d1_tarski]),
    [file(zfmisc_1,t60_zfmisc_1),interesting(0.36)]).

fof(t70_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
    <=> ( ~ r2_hidden(A,C)
        & ( r2_hidden(B,C)
          | A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[l39_zfmisc_1]),
    [file(zfmisc_1,t70_zfmisc_1),interesting(0.36)]).

fof(t86_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d1_zfmisc_1,d3_tarski,d3_tarski,d2_xboole_0,d1_zfmisc_1]),
    [file(zfmisc_1,t86_zfmisc_1),interesting(0.25)]).

fof(t42_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_tarski(B,C))
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[l46_zfmisc_1]),
    [file(zfmisc_1,t42_zfmisc_1),interesting(0.24)]).

fof(t132_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C))
      & k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) ) ),
    inference(mizar_proof,[status(thm)],[t41_enumset1,t120_zfmisc_1]),
    [file(zfmisc_1,t132_zfmisc_1),interesting(0.20)]).

fof(t36_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,C))
      & k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) ) ),
    inference(mizar_proof,[status(thm)],[d2_zfmisc_1,d1_tarski,d2_tarski,d2_tarski,d1_tarski,d2_tarski,l55_zfmisc_1,t2_tarski,d2_zfmisc_1,d1_tarski,d2_tarski,d2_tarski,d1_tarski,d2_tarski,l55_zfmisc_1,t2_tarski]),
    [file(zfmisc_1,t36_zfmisc_1),interesting(0.20)]).

fof(t75_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_xboole_1,l46_zfmisc_1]),
    [file(zfmisc_1,t75_zfmisc_1),interesting(0.17)]).

fof(t84_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_zfmisc_1,t36_xboole_1,t79_xboole_1,t1_xboole_1,t63_xboole_1,d7_xboole_0,t28_xboole_1,d1_zfmisc_1,d1_tarski,d4_xboole_0,d2_xboole_0]),
    [file(zfmisc_1,t84_zfmisc_1),interesting(0.12)]).

fof(t74_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0
      & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A)
      & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(B)
      & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B) ) ),
    inference(mizar_proof,[status(thm)],[l39_zfmisc_1,t73_zfmisc_1,t72_zfmisc_1]),
    [file(zfmisc_1,t74_zfmisc_1),interesting(0.07)]).

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(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(d1_zfmisc_1,definition,(
    ! [A,B] : 
      ( B = k1_zfmisc_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> r1_tarski(C,A) ) ) ),
    file(zfmisc_1,d1_zfmisc_1),
    [interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t4_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) )
      & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B))
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t4_xboole_0),
    [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(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(t101_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ! [C,D] : 
          ( ( r2_hidden(C,k2_xboole_0(A,B))
            & r2_hidden(D,k2_xboole_0(A,B)) )
         => ( C = D
            | r1_xboole_0(C,D) ) )
     => k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)) ) ),
    inference(mizar_proof,[status(thm)],[t97_zfmisc_1,d3_tarski,d3_xboole_0,d4_tarski,d4_tarski,d3_xboole_0,t4_xboole_0,d2_xboole_0,d3_xboole_0,d4_tarski,d10_xboole_0]),
    [file(zfmisc_1,t101_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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [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(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(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(t69_enumset1,theorem,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    [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(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(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(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [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)]).

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(t7_tarski,theorem,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & ! [C] : ~ ( r2_hidden(C,B)
          & ! [D] : ~ ( r2_hidden(D,B)
              & r2_hidden(D,C) ) ) ) ),
    file(tarski,t7_tarski),
    [interesting(0.00)]).

fof(t11_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t11_zfmisc_1),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_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(t19_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ) ),
    file(xboole_1,t19_xboole_1),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_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(t54_xboole_1,theorem,(
    ! [A,B,C] : k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) ),
    file(xboole_1,t54_xboole_1),
    [interesting(0.00)]).

fof(t34_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)) ) ),
    file(xboole_1,t34_xboole_1),
    [interesting(0.00)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(t41_enumset1,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    [interesting(0.00)]).

fof(t133_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t133_zfmisc_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(t15_xboole_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(A,B) = k1_xboole_0
     => A = k1_xboole_0 ) ),
    file(xboole_1,t15_xboole_1),
    [interesting(0.00)]).

fof(t9_tarski,theorem,(
    ! [A] : 
    ? [B] : 
      ( r2_hidden(A,B)
      & ! [C,D] : 
          ( ( r2_hidden(C,B)
            & r1_tarski(D,C) )
         => r2_hidden(D,B) )
      & ! [C] : ~ ( r2_hidden(C,B)
          & ! [D] : ~ ( r2_hidden(D,B)
              & ! [E] : 
                  ( r1_tarski(E,C)
                 => r2_hidden(E,D) ) ) )
      & ! [C] : ~ ( r1_tarski(C,B)
          & ~ r2_tarski(C,B)
          & ~ r2_hidden(C,B) ) ) ),
    file(tarski,t9_tarski),
    [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(t83_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_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(t15_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t15_zfmisc_1),
    [interesting(0.00)]).

fof(t1_xboole_0,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k5_xboole_0(B,C))
    <=> ~ ( r2_hidden(A,B)
        <=> r2_hidden(A,C) ) ) ),
    file(xboole_0,t1_xboole_0),
    [interesting(0.00)]).

fof(t3_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t3_zfmisc_1),
    [interesting(0.00)]).

fof(t43_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( k1_tarski(A) = k2_xboole_0(B,C)
      & ~ ( B = k1_tarski(A)
          & C = k1_tarski(A) )
      & ~ ( B = k1_xboole_0
          & C = k1_tarski(A) )
      & ~ ( B = k1_tarski(A)
          & C = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[l1_zfmisc_1,t7_xboole_1,l4_zfmisc_1]),
    [file(zfmisc_1,t43_zfmisc_1),interesting(0.00)]).

fof(t4_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t4_zfmisc_1),
    [interesting(0.00)]).

fof(t5_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t5_zfmisc_1),
    [interesting(0.00)]).

fof(t61_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t61_zfmisc_1),
    [interesting(0.00)]).

fof(t62_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t62_zfmisc_1),
    [interesting(0.00)]).

fof(t71_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t71_zfmisc_1),
    [interesting(0.00)]).

fof(t76_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t76_zfmisc_1),
    [interesting(0.00)]).

fof(t77_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t77_zfmisc_1),
    [interesting(0.00)]).

fof(t78_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t78_zfmisc_1),
    [interesting(0.00)]).

fof(t7_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t7_zfmisc_1),
    [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(t79_xboole_1,theorem,(
    ! [A,B] : r1_xboole_0(k4_xboole_0(A,B),B) ),
    file(xboole_1,t79_xboole_1),
    [interesting(0.00)]).

fof(t63_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_xboole_0(B,C) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t63_xboole_1),
    [interesting(0.00)]).

fof(t85_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t85_zfmisc_1),
    [interesting(0.00)]).

fof(t87_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t87_zfmisc_1),
    [interesting(0.00)]).

fof(t88_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t88_zfmisc_1),
    [interesting(0.00)]).

fof(t89_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t89_zfmisc_1),
    [interesting(0.00)]).

fof(t90_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t90_zfmisc_1),
    [interesting(0.00)]).

fof(t91_zfmisc_1,theorem,(
    $true ),
    file(zfmisc_1,t91_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)]).