fof(t42_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => m1_eqrel_1(k7_eqrel_1(A,B),A) ) ),
    inference(mizar_proof,[status(thm)],[t28_eqrel_1,d5_eqrel_1,d4_tarski,d5_eqrel_1,t28_eqrel_1,d5_eqrel_1,t32_eqrel_1,d6_eqrel_1,t40_eqrel_1,d6_eqrel_1]),
    [file(eqrel_1,t42_eqrel_1),interesting(1.00)]).

fof(t31_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(B,k6_eqrel_1(A,C,D))
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_eqrel_1,t12_eqrel_1,l37_eqrel_1,l37_eqrel_1,t12_eqrel_1,t27_eqrel_1]),
    [file(eqrel_1,t31_eqrel_1),interesting(0.82)]).

fof(t32_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C,D] : ~ ( r2_hidden(C,A)
          & r2_hidden(D,A)
          & k6_eqrel_1(A,B,C) != k6_eqrel_1(A,B,D)
          & ~ r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_eqrel_1,t31_eqrel_1,t3_xboole_0,t27_eqrel_1,t12_eqrel_1,t13_eqrel_1]),
    [file(eqrel_1,t32_eqrel_1),interesting(0.81)]).

fof(t43_eqrel_1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ? [C] : 
          ( v3_relat_2(C)
          & v8_relat_2(C)
          & v1_partfun1(C,A,A)
          & m2_relset_1(C,A,A)
          & B = k7_eqrel_1(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d4_tarski,d6_eqrel_1,t3_xboole_0,s1_eqrel_1,d6_eqrel_1,d3_tarski,t27_eqrel_1,t27_eqrel_1,t3_xboole_0,d6_eqrel_1,t2_tarski,d5_eqrel_1,d5_eqrel_1,t28_eqrel_1,t27_eqrel_1,t27_eqrel_1,t3_xboole_0,d6_eqrel_1,t27_eqrel_1,t2_tarski,t44_setfam_1,d6_eqrel_1,t40_eqrel_1]),
    [file(eqrel_1,t43_eqrel_1),interesting(0.80)]).

fof(t34_eqrel_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k6_eqrel_1(A,k1_eqrel_1(A),B) = A ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,t27_eqrel_1,t2_tarski]),
    [file(eqrel_1,t34_eqrel_1),interesting(0.79)]).

fof(t35_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( ? [C] : k6_eqrel_1(A,B,C) = A
       => B = k1_eqrel_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,t27_eqrel_1,t12_eqrel_1,t13_eqrel_1,t109_zfmisc_1,d10_xboole_0]),
    [file(eqrel_1,t35_eqrel_1),interesting(0.73)]).

fof(t33_eqrel_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k6_eqrel_1(A,k6_partfun1(A),B) = k1_tarski(B) ) ),
    inference(mizar_proof,[status(thm)],[t27_eqrel_1,d10_relat_1,t28_eqrel_1,d1_tarski]),
    [file(eqrel_1,t33_eqrel_1),interesting(0.72)]).

fof(l37_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(k4_tarski(D,B),C)
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_eqrel_1,t13_eqrel_1,t27_eqrel_1,d3_tarski,t27_eqrel_1,t12_eqrel_1,t13_eqrel_1,t27_eqrel_1,d3_tarski,d10_xboole_0,t28_eqrel_1,t27_eqrel_1]),
    [file(eqrel_1,l37_eqrel_1),interesting(0.72)]).

fof(t28_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,k6_eqrel_1(A,B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_eqrel_1,t27_eqrel_1]),
    [file(eqrel_1,t28_eqrel_1),interesting(0.70)]).

fof(t38_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ~ ( k3_eqrel_1(A,B,C) = k1_eqrel_1(A)
              & B != k1_eqrel_1(A)
              & C != k1_eqrel_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t113_zfmisc_1,t15_xboole_1,t37_eqrel_1,t34_eqrel_1,t35_eqrel_1]),
    [file(eqrel_1,t38_eqrel_1),interesting(0.69)]).

fof(l10_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( m2_relset_1(D,C,C)
     => ( r2_hidden(k4_tarski(A,B),D)
       => ( r2_hidden(A,C)
          & r2_hidden(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_relat_1]),
    [file(eqrel_1,l10_eqrel_1),interesting(0.67)]).

fof(t4_eqrel_1,theorem,(
    ! [A] : 
      ( r1_relat_2(k6_partfun1(A),A)
      & r3_relat_2(k6_partfun1(A),A)
      & r8_relat_2(k6_partfun1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d10_relat_1,d1_relat_2,d10_relat_1,d3_relat_2,d10_relat_1,d8_relat_2]),
    [file(eqrel_1,t4_eqrel_1),interesting(0.67)]).

fof(t12_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(k4_tarski(B,C),D)
       => r2_hidden(k4_tarski(C,B),D) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_orders_1,l10_eqrel_1,d11_relat_2,d3_relat_2]),
    [file(eqrel_1,t12_eqrel_1),interesting(0.66)]).

fof(t27_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
      <=> r2_hidden(k4_tarski(B,C),D) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_relat_1,d1_tarski,t12_eqrel_1,t12_eqrel_1,d1_tarski,d13_relat_1]),
    [file(eqrel_1,t27_eqrel_1),interesting(0.66)]).

fof(t11_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ( r2_hidden(B,A)
       => r2_hidden(k4_tarski(B,B),C) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_orders_1,d9_relat_2,d1_relat_2]),
    [file(eqrel_1,t11_eqrel_1),interesting(0.65)]).

fof(t44_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(k4_tarski(D,B),C)
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l37_eqrel_1]),
    [file(eqrel_1,t44_eqrel_1),interesting(0.65)]).

fof(t13_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(k4_tarski(B,C),E)
          & r2_hidden(k4_tarski(C,D),E) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_orders_1,l10_eqrel_1,d16_relat_2,d8_relat_2]),
    [file(eqrel_1,t13_eqrel_1),interesting(0.64)]).

fof(t29_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : ~ ( r2_hidden(C,A)
          & ! [D] : ~ r2_hidden(C,k6_eqrel_1(A,B,D)) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_eqrel_1]),
    [file(eqrel_1,t29_eqrel_1),interesting(0.63)]).

fof(t37_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ! [D] : 
              ( ( v3_relat_2(D)
                & v8_relat_2(D)
                & v1_partfun1(D,A,A)
                & m2_relset_1(D,A,A) )
             => ( D = k3_eqrel_1(A,B,C)
               => ! [E] : ~ ( r2_hidden(E,A)
                    & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,E)
                    & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_tarski,t27_eqrel_1,d2_xboole_0,t27_eqrel_1,t2_tarski,t27_eqrel_1,d2_xboole_0,t27_eqrel_1,t27_eqrel_1,t27_eqrel_1,d2_xboole_0,t27_eqrel_1,t12_eqrel_1,t13_eqrel_1,t27_eqrel_1,d2_xboole_0,t12_eqrel_1,t13_eqrel_1,t12_eqrel_1,t27_eqrel_1,t12_eqrel_1,t12_eqrel_1,t13_eqrel_1,t12_eqrel_1,t27_eqrel_1,d2_xboole_0]),
    [file(eqrel_1,t37_eqrel_1),interesting(0.63)]).

fof(t7_eqrel_1,theorem,(
    ! [A] : 
      ( v3_relat_2(k1_eqrel_1(A))
      & v8_relat_2(k1_eqrel_1(A))
      & v1_partfun1(k1_eqrel_1(A),A,A)
      & m2_relset_1(k1_eqrel_1(A),A,A) ) ),
    inference(mizar_proof,[status(thm)],[t107_zfmisc_1,d3_relat_2,t106_zfmisc_1,d8_relat_2,t97_orders_1,d11_relat_2,d16_relat_2]),
    [file(eqrel_1,t7_eqrel_1),interesting(0.61)]).

fof(t40_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( A = k1_xboole_0
       => k7_eqrel_1(A,B) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_eqrel_1]),
    [file(eqrel_1,t40_eqrel_1),interesting(0.60)]).

fof(l2_eqrel_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
           => m2_subset_1(k6_xcmplx_0(B,A),k1_numbers,k5_numbers) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t61_nat_1]),
    [file(eqrel_1,l2_eqrel_1),interesting(0.59)]).

fof(t18_eqrel_1,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => k2_eqrel_1(A,k1_eqrel_1(A),B) = B ) ),
    inference(mizar_proof,[status(thm)],[t28_xboole_1]),
    [file(eqrel_1,t18_eqrel_1),interesting(0.58)]).

fof(t17_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A) ) ),
    inference(mizar_proof,[status(thm)],[d10_relat_1,t11_eqrel_1,d3_relat_1,t28_xboole_1]),
    [file(eqrel_1,t17_eqrel_1),interesting(0.57)]).

fof(t24_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,d10_xboole_0,t7_xboole_1,d3_eqrel_1,t1_xboole_1,t19_xboole_1]),
    [file(eqrel_1,t24_eqrel_1),interesting(0.56)]).

fof(t14_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ~ ( ? [C] : r2_hidden(C,A)
          & B = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t11_eqrel_1]),
    [file(eqrel_1,t14_eqrel_1),interesting(0.55)]).

fof(t20_eqrel_1,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ? [C] : 
          ( v3_relat_2(C)
          & v8_relat_2(C)
          & v1_partfun1(C,A,A)
          & m2_relset_1(C,A,A)
          & r1_tarski(B,C)
          & ! [D] : 
              ( ( v3_relat_2(D)
                & v8_relat_2(D)
                & v1_partfun1(D,A,A)
                & m2_relset_1(D,A,A) )
             => ( r1_tarski(B,D)
               => r1_tarski(C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_subset_1,t19_eqrel_1,t4_setfam_1,t6_setfam_1]),
    [file(eqrel_1,t20_eqrel_1),interesting(0.55)]).

fof(t30_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_2(E)
        & v3_relat_2(E)
        & v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(B,k6_eqrel_1(A,E,C))
          & r2_hidden(D,k6_eqrel_1(A,E,C)) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_eqrel_1,t12_eqrel_1,t13_eqrel_1]),
    [file(eqrel_1,t30_eqrel_1),interesting(0.55)]).

fof(t16_eqrel_1,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ( ( v3_relat_2(B)
          & v8_relat_2(B)
          & v1_partfun1(B,A,A)
          & m2_relset_1(B,A,A) )
      <=> ( v1_relat_2(B)
          & v3_relat_2(B)
          & v8_relat_2(B)
          & k3_relat_1(B) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_orders_1,d9_relat_2,t98_orders_1,d4_partfun1]),
    [file(eqrel_1,t16_eqrel_1),interesting(0.51)]).

fof(t25_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t22_xboole_1,t22_xboole_1,d3_eqrel_1]),
    [file(eqrel_1,t25_eqrel_1),interesting(0.51)]).

fof(s1_eqrel_1,theorem,
    ( ( ! [A] : 
          ( r2_hidden(A,f1_s1_eqrel_1)
         => p1_s1_eqrel_1(A,A) )
      & ! [A,B] : 
          ( p1_s1_eqrel_1(A,B)
         => p1_s1_eqrel_1(B,A) )
      & ! [A,B,C] : 
          ( ( p1_s1_eqrel_1(A,B)
            & p1_s1_eqrel_1(B,C) )
         => p1_s1_eqrel_1(A,C) ) )
   => ? [A] : 
        ( v3_relat_2(A)
        & v8_relat_2(A)
        & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1)
        & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1)
        & ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),A)
          <=> ( r2_hidden(B,f1_s1_eqrel_1)
              & r2_hidden(C,f1_s1_eqrel_1)
              & p1_s1_eqrel_1(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_relset_1,d1_relat_2,d3_relat_2,d8_relat_2,t98_orders_1,t98_orders_1,d4_partfun1,d11_relat_2,d16_relat_2]),
    [file(eqrel_1,s1_eqrel_1),interesting(0.48)]).

fof(t45_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,B,B)
        & m2_relset_1(C,B,B) )
     => ~ ( r2_hidden(A,k7_eqrel_1(B,C))
          & ! [D] : 
              ( m1_subset_1(D,B)
             => A != k6_eqrel_1(B,C,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_eqrel_1]),
    [file(eqrel_1,t45_eqrel_1),interesting(0.46)]).

fof(t19_eqrel_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A))))
     => ( ! [C] : 
            ( r2_hidden(C,B)
           => ( v3_relat_2(C)
              & v8_relat_2(C)
              & v1_partfun1(C,A,A)
              & m2_relset_1(C,A,A) ) )
       => ( B = k1_xboole_0
          | ( v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B))
            & v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B))
            & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A)
            & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_relset_1,d1_relat_2,t11_eqrel_1,d1_setfam_1,d3_relat_2,d1_setfam_1,t12_eqrel_1,d1_setfam_1,d8_relat_2,d1_setfam_1,t13_eqrel_1,d1_setfam_1,t98_orders_1,t98_orders_1,d4_partfun1,d11_relat_2,d16_relat_2]),
    [file(eqrel_1,t19_eqrel_1),interesting(0.44)]).

fof(t10_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t10_eqrel_1),
    [interesting(0.00)]).

fof(t97_orders_1,theorem,(
    ! [A,B] : 
      ( ( v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => k3_relat_1(B) = A ) ),
    file(orders_1,t97_orders_1),
    [interesting(0.00)]).

fof(d9_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_2(A)
      <=> r1_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d9_relat_2),
    [interesting(0.00)]).

fof(d1_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
        <=> ! [C] : 
              ( r2_hidden(C,B)
             => r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d1_relat_2),
    [interesting(0.00)]).

fof(t15_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t15_eqrel_1),
    [interesting(0.00)]).

fof(t98_orders_1,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ( r1_relat_2(B,A)
       => ( k4_relset_1(A,A,B) = A
          & k3_relat_1(B) = A ) ) ) ),
    file(orders_1,t98_orders_1),
    [interesting(0.00)]).

fof(d4_partfun1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( v1_partfun1(C,A,B)
      <=> k4_relset_1(A,B,C) = A ) ) ),
    file(partfun1,d4_partfun1),
    [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(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(t1_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t1_eqrel_1),
    [interesting(0.00)]).

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) ) ) ) ),
    file(subset_1,s3_subset_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(d1_setfam_1,definition,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    [interesting(0.00)]).

fof(d3_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r3_relat_2(A,B)
        <=> ! [C,D] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(k4_tarski(C,D),A) )
             => r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d3_relat_2),
    [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(d11_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_relat_2(A)
      <=> r3_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d11_relat_2),
    [interesting(0.00)]).

fof(d8_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    [interesting(0.00)]).

fof(d16_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    [interesting(0.00)]).

fof(t4_setfam_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(k1_setfam_1(B),A) ) ),
    file(setfam_1,t4_setfam_1),
    [interesting(0.00)]).

fof(t6_setfam_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    file(setfam_1,t6_setfam_1),
    [interesting(0.00)]).

fof(t21_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t21_eqrel_1),
    [interesting(0.00)]).

fof(t22_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => k5_eqrel_1(A,B,B) = B ) ),
    file(eqrel_1,t22_eqrel_1),
    [interesting(0.00)]).

fof(t23_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B) ) ) ),
    file(eqrel_1,t23_eqrel_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(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(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(d3_eqrel_1,definition,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ! [D] : 
              ( ( v3_relat_2(D)
                & v8_relat_2(D)
                & v1_partfun1(D,A,A)
                & m2_relset_1(D,A,A) )
             => ( D = k5_eqrel_1(A,B,C)
              <=> ( r1_tarski(k3_eqrel_1(A,B,C),D)
                  & ! [E] : 
                      ( ( v3_relat_2(E)
                        & v8_relat_2(E)
                        & v1_partfun1(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( r1_tarski(k3_eqrel_1(A,B,C),E)
                       => r1_tarski(D,E) ) ) ) ) ) ) ) ),
    file(eqrel_1,d3_eqrel_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(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(t22_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(A,k3_xboole_0(A,B)) = A ),
    file(xboole_1,t22_xboole_1),
    [interesting(0.00)]).

fof(t26_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t26_eqrel_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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t2_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t2_eqrel_1),
    [interesting(0.00)]).

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) ) ) ) ),
    file(relset_1,s1_relset_1),
    [interesting(0.00)]).

fof(t57_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,t57_finseq_1),
    [interesting(0.00)]).

fof(s1_finseq_1,theorem,
    ( ( ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B,C] : 
              ( ( r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))
                & p1_s1_finseq_1(A,B)
                & p1_s1_finseq_1(A,C) )
             => B = C ) )
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))
              & ! [B] : ~ p1_s1_finseq_1(A,B) ) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f1_s1_finseq_1))
             => p1_s1_finseq_1(B,k1_funct_1(A,B)) ) ) ) ),
    file(finseq_1,s1_finseq_1),
    [interesting(0.00)]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.00)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.00)]).

fof(t37_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r1_xreal_0(A,B)
               => r1_xreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(nat_1,t37_nat_1),
    [interesting(0.00)]).

fof(t38_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    [interesting(0.00)]).

fof(t61_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
           => m2_subset_1(k6_xcmplx_0(B,A),k1_numbers,k5_numbers) ) ) ) ),
    file(nat_1,t61_nat_1),
    [interesting(0.00)]).

fof(t11_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t11_xreal_1),
    [interesting(0.00)]).

fof(t26_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) ),
    file(xreal_1,t26_xreal_1),
    [interesting(0.00)]).

fof(t8_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t8_xreal_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(t35_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    file(finseq_1,t35_finseq_1),
    [interesting(0.00)]).

fof(d7_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( C = k7_finseq_1(A,B)
              <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => k1_funct_1(C,D) = k1_funct_1(A,D) ) )
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(B))
                       => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ),
    file(finseq_1,d7_finseq_1),
    [interesting(0.00)]).

fof(t9_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ),
    file(xreal_1,t9_xreal_1),
    [interesting(0.00)]).

fof(t36_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( r1_xreal_0(k1_nat_1(k3_finseq_1(A),1),C)
                  & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) )
               => k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) ) ) ) ) ),
    file(finseq_1,t36_finseq_1),
    [interesting(0.00)]).

fof(d5_real_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> ~ ( r1_xreal_0(B,A)
                & B != A ) ) ) ) ),
    file(real_1,d5_real_1),
    [interesting(0.00)]).

fof(t21_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(k2_xcmplx_0(A,B),C)
              <=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ),
    file(xreal_1,t21_xreal_1),
    [interesting(0.00)]).

fof(t61_finseq_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    file(finseq_1,t61_finseq_1),
    [interesting(0.00)]).

fof(t1_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_1),
    [interesting(0.00)]).

fof(t26_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,k2_xcmplx_0(B,1))
              & ~ r1_xreal_0(A,B)
              & A != k2_xcmplx_0(B,1) ) ) ) ),
    file(nat_1,t26_nat_1),
    [interesting(0.00)]).

fof(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(t36_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v3_relat_2(D)
        & v8_relat_2(D)
        & v1_partfun1(D,B,B)
        & m2_relset_1(D,B,B) )
     => ! [E] : 
          ( ( v3_relat_2(E)
            & v8_relat_2(E)
            & v1_partfun1(E,B,B)
            & m2_relset_1(E,B,B) )
         => ( r2_hidden(A,B)
           => ( r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E))
            <=> ? [F] : 
                  ( v1_relat_1(F)
                  & v1_funct_1(F)
                  & v1_finseq_1(F)
                  & r1_xreal_0(1,k3_finseq_1(F))
                  & A = k1_funct_1(F,1)
                  & C = k1_funct_1(F,k3_finseq_1(F))
                  & ! [G] : 
                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(1,G)
                       => ( r1_xreal_0(k3_finseq_1(F),G)
                          | r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,1))),k3_eqrel_1(B,D,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_relset_1,d1_relat_2,t57_finseq_1,t57_finseq_1,d3_relat_2,s1_finseq_1,d3_finseq_1,d3_finseq_1,t3_finseq_1,t3_finseq_1,d3_finseq_1,t3_finseq_1,t37_nat_1,t38_nat_1,t3_finseq_1,l2_eqrel_1,t11_xreal_1,t26_xreal_1,t38_nat_1,t26_xreal_1,t8_xreal_1,t12_eqrel_1,d2_xboole_0,t12_eqrel_1,d2_xboole_0,d2_xboole_0,d8_relat_2,t35_finseq_1,t37_nat_1,t3_finseq_1,d3_finseq_1,d7_finseq_1,t9_xreal_1,t36_finseq_1,d5_real_1,t3_finseq_1,d3_finseq_1,d7_finseq_1,t38_nat_1,t3_finseq_1,d3_finseq_1,d7_finseq_1,t3_finseq_1,d3_finseq_1,d7_finseq_1,t36_finseq_1,t11_eqrel_1,d2_xboole_0,t38_nat_1,t36_finseq_1,t38_nat_1,l2_eqrel_1,t35_finseq_1,t11_xreal_1,t21_xreal_1,t36_finseq_1,t38_nat_1,t98_orders_1,d4_partfun1,d11_relat_2,d16_relat_2,l10_eqrel_1,t61_finseq_1,t61_finseq_1,t61_finseq_1,t61_finseq_1,t38_nat_1,t1_xreal_1,d3_relat_1,d3_eqrel_1,t38_nat_1,t26_nat_1,d3_eqrel_1,t13_eqrel_1,t38_nat_1,t11_eqrel_1,d2_xboole_0,s1_nat_1]),
    [file(eqrel_1,t36_eqrel_1),interesting(0.00)]).

fof(t113_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    [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(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [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(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) ) ),
    file(zfmisc_1,t109_zfmisc_1),
    [interesting(0.00)]).

fof(t39_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t39_eqrel_1),
    [interesting(0.00)]).

fof(t3_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t3_eqrel_1),
    [interesting(0.00)]).

fof(t41_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t41_eqrel_1),
    [interesting(0.00)]).

fof(d5_eqrel_1,definition,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_eqrel_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( r2_hidden(E,A)
                      & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ),
    file(eqrel_1,d5_eqrel_1),
    [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(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(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(d6_eqrel_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    [interesting(0.00)]).

fof(t44_setfam_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,B)
                <=> r2_hidden(D,C) ) )
           => B = C ) ) ) ),
    file(setfam_1,t44_setfam_1),
    [interesting(0.00)]).

fof(t5_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t5_eqrel_1),
    [interesting(0.00)]).

fof(t6_eqrel_1,theorem,(
    ! [A] : 
      ( v3_relat_2(k6_partfun1(A))
      & v8_relat_2(k6_partfun1(A))
      & v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(eqrel_1,t6_eqrel_1),
    [interesting(0.00)]).

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)) ) ),
    file(zfmisc_1,t107_zfmisc_1),
    [interesting(0.00)]).

fof(t8_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t8_eqrel_1),
    [interesting(0.00)]).

fof(t9_eqrel_1,theorem,(
    $true ),
    file(eqrel_1,t9_eqrel_1),
    [interesting(0.00)]).