fof(l72_subset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(B))
     => ( r2_hidden(A,C)
       => m1_subset_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[l3_subset_1,d2_subset_1]),
    [file(subset_1,l72_subset_1),interesting(1.00)]).

fof(l3_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( r2_hidden(C,B)
         => r2_hidden(C,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d1_zfmisc_1,d3_tarski]),
    [file(subset_1,l3_subset_1),interesting(0.94)]).

fof(l71_subset_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) )
     => m1_subset_1(A,k1_zfmisc_1(B)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,l71_subset_1),interesting(0.94)]).

fof(t8_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( r2_hidden(D,B)
                <=> r2_hidden(D,C) ) )
           => B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_subset_1,d10_xboole_0]),
    [file(subset_1,t8_subset_1),interesting(0.81)]).

fof(t49_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( ! [C] : 
            ( m1_subset_1(C,A)
           => r2_hidden(C,B) )
       => A = B ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_subset_1,d10_xboole_0,d2_subset_1,d1_zfmisc_1]),
    [file(subset_1,t49_subset_1),interesting(0.79)]).

fof(t21_subset_1,theorem,(
    ! [A] : k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A)) ),
    inference(mizar_proof,[status(thm)],[t37_xboole_1]),
    [file(subset_1,t21_subset_1),interesting(0.77)]).

fof(t63_subset_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)) ) ),
    inference(mizar_proof,[status(thm)],[t37_zfmisc_1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t63_subset_1),interesting(0.76)]).

fof(t43_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_xboole_0(B,C)
          <=> r1_tarski(B,k3_subset_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,l3_subset_1,t3_xboole_0,d4_xboole_0,t3_xboole_0,d3_tarski,d4_xboole_0]),
    [file(subset_1,t43_subset_1),interesting(0.75)]).

fof(t26_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => r1_xboole_0(B,k3_subset_1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t79_xboole_1]),
    [file(subset_1,t26_subset_1),interesting(0.72)]).

fof(t7_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( r2_hidden(D,B)
                 => r2_hidden(D,C) ) )
           => r1_tarski(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,l3_subset_1,d2_subset_1]),
    [file(subset_1,t7_subset_1),interesting(0.71)]).

fof(t44_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_xboole_0(B,k3_subset_1(A,C))
          <=> r1_tarski(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_subset_1]),
    [file(subset_1,t44_subset_1),interesting(0.71)]).

fof(t39_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( r1_tarski(k3_subset_1(A,B),B)
      <=> B = k2_subset_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_xboole_1,t25_subset_1,t21_subset_1,t2_xboole_1]),
    [file(subset_1,t39_subset_1),interesting(0.66)]).

fof(t10_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ~ ( B != k1_xboole_0
          & ! [C] : 
              ( m1_subset_1(C,A)
             => ~ r2_hidden(C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,l3_subset_1,d2_subset_1]),
    [file(subset_1,t10_subset_1),interesting(0.64)]).

fof(t51_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( r2_hidden(D,B)
                <=> ~ r2_hidden(D,C) ) )
           => B = k3_subset_1(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_subset_1,d1_zfmisc_1,d3_tarski,d2_subset_1,l3_subset_1,d4_xboole_0,d10_xboole_0,d3_tarski,d2_subset_1,d1_zfmisc_1,d3_tarski,d2_subset_1,d4_xboole_0]),
    [file(subset_1,t51_subset_1),interesting(0.64)]).

fof(t54_subset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ~ ( r2_hidden(B,k3_subset_1(A,C))
          & r2_hidden(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_xboole_0]),
    [file(subset_1,t54_subset_1),interesting(0.63)]).

fof(t31_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(B,C)
          <=> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_xboole_1,t34_xboole_1]),
    [file(subset_1,t31_subset_1),interesting(0.62)]).

fof(t18_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ! [E] : 
                    ( m1_subset_1(E,A)
                   => ( r2_hidden(E,B)
                    <=> ~ ( r2_hidden(E,C)
                        <=> r2_hidden(E,D) ) ) )
               => B = k7_subset_1(A,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_xboole_0,d2_xboole_0,t7_subset_1,d10_xboole_0,d2_xboole_0,d4_xboole_0,t7_subset_1]),
    [file(subset_1,t18_subset_1),interesting(0.59)]).

fof(t52_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( ~ r2_hidden(D,B)
                <=> r2_hidden(D,C) ) )
           => B = k3_subset_1(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t51_subset_1]),
    [file(subset_1,t52_subset_1),interesting(0.58)]).

fof(t53_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ~ ( r2_hidden(D,B)
                  <=> r2_hidden(D,C) ) )
           => B = k3_subset_1(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t51_subset_1]),
    [file(subset_1,t53_subset_1),interesting(0.58)]).

fof(t15_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ! [E] : 
                    ( m1_subset_1(E,A)
                   => ( r2_hidden(E,B)
                    <=> ( r2_hidden(E,C)
                        | r2_hidden(E,D) ) ) )
               => B = k4_subset_1(A,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_xboole_0,t7_subset_1,d10_xboole_0,d2_xboole_0,t7_subset_1]),
    [file(subset_1,t15_subset_1),interesting(0.57)]).

fof(t16_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ! [E] : 
                    ( m1_subset_1(E,A)
                   => ( r2_hidden(E,B)
                    <=> ( r2_hidden(E,C)
                        & r2_hidden(E,D) ) ) )
               => B = k5_subset_1(A,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,t7_subset_1,d10_xboole_0,d3_xboole_0,t7_subset_1]),
    [file(subset_1,t16_subset_1),interesting(0.57)]).

fof(t17_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ! [E] : 
                    ( m1_subset_1(E,A)
                   => ( r2_hidden(E,B)
                    <=> ( r2_hidden(E,C)
                        & ~ r2_hidden(E,D) ) ) )
               => B = k6_subset_1(A,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_xboole_0,t7_subset_1,d10_xboole_0,d4_xboole_0,t7_subset_1]),
    [file(subset_1,t17_subset_1),interesting(0.57)]).

fof(t48_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,B)
               => r2_hidden(D,C) )
           => r1_tarski(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_subset_1]),
    [file(subset_1,t48_subset_1),interesting(0.57)]).

fof(t55_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ( A != k1_xboole_0
       => m1_subset_1(k1_tarski(B),k1_zfmisc_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d3_tarski,d1_tarski,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t55_subset_1),interesting(0.57)]).

fof(s3_subset_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1))
      & ! [B] : 
          ( m1_subset_1(B,f1_s3_subset_1)
         => ( r2_hidden(B,A)
          <=> p1_s3_subset_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,l71_subset_1,d2_subset_1]),
    [file(subset_1,s3_subset_1),interesting(0.56)]).

fof(t35_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(B,k3_subset_1(A,C))
           => r1_tarski(C,k3_subset_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_subset_1]),
    [file(subset_1,t35_subset_1),interesting(0.56)]).

fof(t36_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(k3_subset_1(A,B),C)
           => r1_tarski(k3_subset_1(A,C),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_subset_1]),
    [file(subset_1,t36_subset_1),interesting(0.56)]).

fof(t47_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ( r1_tarski(B,C)
                  & r1_xboole_0(D,C) )
               => r1_tarski(B,k3_subset_1(A,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t63_xboole_1,t43_subset_1]),
    [file(subset_1,t47_subset_1),interesting(0.55)]).

fof(t25_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d1_zfmisc_1,t45_xboole_1]),
    [file(subset_1,t25_subset_1),interesting(0.53)]).

fof(s1_subset_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1))
      & ! [B] : 
          ( r2_hidden(B,A)
        <=> ( r2_hidden(B,f1_s1_subset_1)
            & p1_s1_subset_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,d3_tarski,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,s1_subset_1),interesting(0.51)]).

fof(t56_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ( A != k1_xboole_0
           => m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d3_tarski,d2_tarski,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t56_subset_1),interesting(0.51)]).

fof(t28_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k4_subset_1(A,B,k2_subset_1(A)) = k2_subset_1(A) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d1_zfmisc_1,t12_xboole_1]),
    [file(subset_1,t28_subset_1),interesting(0.47)]).

fof(t41_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t31_subset_1]),
    [file(subset_1,t41_subset_1),interesting(0.46)]).

fof(t57_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ( A != k1_xboole_0
               => m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d3_tarski,d1_enumset1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t57_subset_1),interesting(0.46)]).

fof(t42_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,t31_subset_1]),
    [file(subset_1,t42_subset_1),interesting(0.44)]).

fof(t58_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => ( A != k1_xboole_0
                   => m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d3_tarski,d2_enumset1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t58_subset_1),interesting(0.41)]).

fof(t46_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ( r1_xboole_0(B,C)
              & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) )
           => B = k3_subset_1(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d3_tarski,d1_zfmisc_1,d3_tarski,t3_xboole_0,d4_xboole_0,d10_xboole_0,d3_tarski,d4_xboole_0,t3_xboole_0,d4_xboole_0]),
    [file(subset_1,t46_subset_1),interesting(0.39)]).

fof(t59_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => ! [F] : 
                      ( m1_subset_1(F,A)
                     => ( A != k1_xboole_0
                       => m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_enumset1,d2_subset_1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t59_subset_1),interesting(0.36)]).

fof(t38_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( r1_tarski(B,k3_subset_1(A,B))
      <=> B = k1_subset_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_xboole_1,d2_subset_1,d1_zfmisc_1]),
    [file(subset_1,t38_subset_1),interesting(0.35)]).

fof(t60_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => ! [F] : 
                      ( m1_subset_1(F,A)
                     => ! [G] : 
                          ( m1_subset_1(G,A)
                         => ( A != k1_xboole_0
                           => m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_enumset1,d2_subset_1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t60_subset_1),interesting(0.32)]).

fof(s4_subset_1,theorem,
    ( ( ! [A] : 
          ( m1_subset_1(A,f1_s4_subset_1)
         => ( r2_hidden(A,f2_s4_subset_1)
          <=> p1_s4_subset_1(A) ) )
      & ! [A] : 
          ( m1_subset_1(A,f1_s4_subset_1)
         => ( r2_hidden(A,f3_s4_subset_1)
          <=> p1_s4_subset_1(A) ) ) )
   => f2_s4_subset_1 = f3_s4_subset_1 ),
    inference(mizar_proof,[status(thm)],[d3_tarski,l72_subset_1,d10_xboole_0,d3_tarski,l72_subset_1]),
    [file(subset_1,s4_subset_1),interesting(0.30)]).

fof(t40_subset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ( ( r1_tarski(B,C)
          & r1_tarski(B,k3_subset_1(A,C)) )
       => B = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t26_subset_1,t67_xboole_1]),
    [file(subset_1,t40_subset_1),interesting(0.29)]).

fof(t32_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d1_zfmisc_1,t49_xboole_1,t28_xboole_1]),
    [file(subset_1,t32_subset_1),interesting(0.28)]).

fof(t61_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => ! [F] : 
                      ( m1_subset_1(F,A)
                     => ! [G] : 
                          ( m1_subset_1(G,A)
                         => ! [H] : 
                              ( m1_subset_1(H,A)
                             => ( A != k1_xboole_0
                               => m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_enumset1,d2_subset_1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t61_subset_1),interesting(0.28)]).

fof(t50_subset_1,theorem,(
    ! [A] : 
      ( A != k1_xboole_0
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ( ~ r2_hidden(C,B)
               => r2_hidden(C,k3_subset_1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d4_xboole_0]),
    [file(subset_1,t50_subset_1),interesting(0.27)]).

fof(t62_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => ! [F] : 
                      ( m1_subset_1(F,A)
                     => ! [G] : 
                          ( m1_subset_1(G,A)
                         => ! [H] : 
                              ( m1_subset_1(H,A)
                             => ! [I] : 
                                  ( m1_subset_1(I,A)
                                 => ( A != k1_xboole_0
                                   => m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_enumset1,d2_subset_1,d1_zfmisc_1,d2_subset_1]),
    [file(subset_1,t62_subset_1),interesting(0.24)]).

fof(s2_subset_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1))
         => ( ( ! [C] : 
                  ( m1_subset_1(C,f1_s2_subset_1)
                 => ( r2_hidden(C,A)
                  <=> p1_s2_subset_1(C) ) )
              & ! [C] : 
                  ( m1_subset_1(C,f1_s2_subset_1)
                 => ( r2_hidden(C,B)
                  <=> p1_s2_subset_1(C) ) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_subset_1]),
    [file(subset_1,s2_subset_1),interesting(0.23)]).

fof(t33_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k3_subset_1(A,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d1_zfmisc_1,t52_xboole_1,t28_xboole_1]),
    [file(subset_1,t33_subset_1),interesting(0.22)]).

fof(t29_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k3_subset_1(A,k4_subset_1(A,B,C)) = k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t53_xboole_1]),
    [file(subset_1,t29_subset_1),interesting(0.10)]).

fof(t30_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k3_subset_1(A,k5_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_xboole_1]),
    [file(subset_1,t30_subset_1),interesting(0.10)]).

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(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_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(d2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
       => ( m1_subset_1(B,A)
        <=> r2_hidden(B,A) ) )
      & ( v1_xboole_0(A)
       => ( m1_subset_1(B,A)
        <=> v1_xboole_0(B) ) ) ) ),
    file(subset_1,d2_subset_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(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(t11_subset_1,theorem,(
    $true ),
    file(subset_1,t11_subset_1),
    [interesting(0.00)]).

fof(t12_subset_1,theorem,(
    $true ),
    file(subset_1,t12_subset_1),
    [interesting(0.00)]).

fof(t13_subset_1,theorem,(
    $true ),
    file(subset_1,t13_subset_1),
    [interesting(0.00)]).

fof(t14_subset_1,theorem,(
    $true ),
    file(subset_1,t14_subset_1),
    [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(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(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(t19_subset_1,theorem,(
    $true ),
    file(subset_1,t19_subset_1),
    [interesting(0.00)]).

fof(t1_subset_1,theorem,(
    $true ),
    file(subset_1,t1_subset_1),
    [interesting(0.00)]).

fof(t20_subset_1,theorem,(
    $true ),
    file(subset_1,t20_subset_1),
    [interesting(0.00)]).

fof(t22_subset_1,theorem,(
    ! [A] : k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A)) ),
    file(subset_1,t22_subset_1),
    [interesting(0.00)]).

fof(t23_subset_1,theorem,(
    $true ),
    file(subset_1,t23_subset_1),
    [interesting(0.00)]).

fof(t24_subset_1,theorem,(
    $true ),
    file(subset_1,t24_subset_1),
    [interesting(0.00)]).

fof(t27_subset_1,theorem,(
    $true ),
    file(subset_1,t27_subset_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(t53_xboole_1,theorem,(
    ! [A,B,C] : k4_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) ),
    file(xboole_1,t53_xboole_1),
    [interesting(0.00)]).

fof(t2_subset_1,theorem,(
    $true ),
    file(subset_1,t2_subset_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(t49_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C) ),
    file(xboole_1,t49_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(t52_xboole_1,theorem,(
    ! [A,B,C] : k4_xboole_0(A,k4_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t52_xboole_1),
    [interesting(0.00)]).

fof(t102_xboole_1,theorem,(
    ! [A,B,C] : k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C)) ),
    file(xboole_1,t102_xboole_1),
    [interesting(0.00)]).

fof(t34_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_subset_1,d1_zfmisc_1,t102_xboole_1,t28_xboole_1,t53_xboole_1]),
    [file(subset_1,t34_subset_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(t37_subset_1,theorem,(
    $true ),
    file(subset_1,t37_subset_1),
    [interesting(0.00)]).

fof(t38_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,k4_xboole_0(B,A))
     => A = k1_xboole_0 ) ),
    file(xboole_1,t38_xboole_1),
    [interesting(0.00)]).

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

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

fof(t3_subset_1,theorem,(
    $true ),
    file(subset_1,t3_subset_1),
    [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(t67_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C)
        & r1_xboole_0(B,C) )
     => A = k1_xboole_0 ) ),
    file(xboole_1,t67_xboole_1),
    [interesting(0.00)]).

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

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

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.00)]).

fof(t45_subset_1,theorem,(
    $true ),
    file(subset_1,t45_subset_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(t4_subset_1,theorem,(
    ! [A] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(A)) ),
    file(subset_1,t4_subset_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(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(d1_enumset1,definition,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    [interesting(0.00)]).

fof(d2_enumset1,definition,(
    ! [A,B,C,D,E] : 
      ( E = k2_enumset1(A,B,C,D)
    <=> ! [F] : 
          ( r2_hidden(F,E)
        <=> ~ ( F != A
              & F != B
              & F != C
              & F != D ) ) ) ),
    file(enumset1,d2_enumset1),
    [interesting(0.00)]).

fof(d3_enumset1,definition,(
    ! [A,B,C,D,E,F] : 
      ( F = k3_enumset1(A,B,C,D,E)
    <=> ! [G] : 
          ( r2_hidden(G,F)
        <=> ~ ( G != A
              & G != B
              & G != C
              & G != D
              & G != E ) ) ) ),
    file(enumset1,d3_enumset1),
    [interesting(0.00)]).

fof(t5_subset_1,theorem,(
    $true ),
    file(subset_1,t5_subset_1),
    [interesting(0.00)]).

fof(d4_enumset1,definition,(
    ! [A,B,C,D,E,F,G] : 
      ( G = k4_enumset1(A,B,C,D,E,F)
    <=> ! [H] : 
          ( r2_hidden(H,G)
        <=> ~ ( H != A
              & H != B
              & H != C
              & H != D
              & H != E
              & H != F ) ) ) ),
    file(enumset1,d4_enumset1),
    [interesting(0.00)]).

fof(d5_enumset1,definition,(
    ! [A,B,C,D,E,F,G,H] : 
      ( H = k5_enumset1(A,B,C,D,E,F,G)
    <=> ! [I] : 
          ( r2_hidden(I,H)
        <=> ~ ( I != A
              & I != B
              & I != C
              & I != D
              & I != E
              & I != F
              & I != G ) ) ) ),
    file(enumset1,d5_enumset1),
    [interesting(0.00)]).

fof(d6_enumset1,definition,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( I = k6_enumset1(A,B,C,D,E,F,G,H)
    <=> ! [J] : 
          ( r2_hidden(J,I)
        <=> ~ ( J != A
              & J != B
              & J != C
              & J != D
              & J != E
              & J != F
              & J != G
              & J != H ) ) ) ),
    file(enumset1,d6_enumset1),
    [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(t6_subset_1,theorem,(
    $true ),
    file(subset_1,t6_subset_1),
    [interesting(0.00)]).

fof(t9_subset_1,theorem,(
    $true ),
    file(subset_1,t9_subset_1),
    [interesting(0.00)]).