fof(t20_card_3,theorem,(
    ! [A,B] : k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B)) ),
    inference(mizar_proof,[status(thm)],[t13_funcop_1,t19_funcop_1,d3_tarski,d2_funct_2,d5_funct_1,d5_card_3,d10_xboole_0,d3_tarski,d5_card_3,d3_tarski,d5_funct_1,d2_funct_2]),
    [file(card_3,t20_card_3),interesting(1.00)]).

fof(t50_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : k6_card_3(k2_funcop_1(k1_tarski(B),A)) = A ) ),
    inference(mizar_proof,[status(thm)],[t12_card_3,t16_card_3,t13_card_2,d5_card_1]),
    [file(card_3,t50_card_3),interesting(0.99)]).

fof(t36_card_3,theorem,(
    ! [A,B] : k3_card_3(k2_card_3(k2_funcop_1(A,B))) = k2_zfmisc_1(B,A) ),
    inference(mizar_proof,[status(thm)],[t13_funcop_1,t19_funcop_1,d3_tarski,d4_tarski,d5_funct_1,d3_card_3,d3_card_3,t37_zfmisc_1,t118_zfmisc_1,d10_xboole_0,d3_tarski,t102_zfmisc_1,t8_mcart_1,t10_mcart_1,d3_card_3,d1_tarski,d5_funct_1,t106_zfmisc_1,d4_tarski]),
    [file(card_3,t36_card_3),interesting(0.97)]).

fof(t31_card_3,theorem,(
    ! [A,B] : r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A)) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,s2_funct_1,d5_funct_1,d5_funct_1,d6_card_3,t28_card_1,d3_tarski,t27_card_1,t1_xboole_1]),
    [file(card_3,t31_card_3),interesting(0.97)]).

fof(t17_card_3,theorem,(
    ! [A,B] : k3_card_3(k2_funcop_1(k1_tarski(A),B)) = B ),
    inference(mizar_proof,[status(thm)],[t16_card_3]),
    [file(card_3,t17_card_3),interesting(0.91)]).

fof(t19_card_3,theorem,(
    k4_card_3(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_card_3,t64_relat_1,d1_tarski,d10_xboole_0,d3_tarski,d1_tarski,t18_card_3]),
    [file(card_3,t19_card_3),interesting(0.91)]).

fof(t62_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( ( ! [C] : 
                ( r2_hidden(C,B)
               => r2_hidden(k1_card_1(C),A) )
            & v6_ordinal1(B) )
         => r1_tarski(k1_card_1(k3_tarski(B)),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t61_card_3,d9_ordinal1,d9_xboole_0,t26_wellord2,d5_wellord1,s1_relat_1,d3_tarski,l67_card_3,d10_xboole_0,d3_tarski,d1_relat_2,t30_relat_1,d1_relat_2,d9_relat_2,d1_relat_2,d4_wellord1,d8_relat_2,d16_relat_2,d8_relat_2,d4_relat_2,d12_relat_2,d4_relat_2,d6_relat_2,d14_relat_2,d6_relat_2,d2_wellord1,s1_xboole_0,d3_tarski,d3_tarski,d4_tarski,d3_xboole_0,t17_xboole_1,t92_zfmisc_1,t1_xboole_1,t9_wellord1,d3_xboole_0,d7_xboole_0,d3_xboole_0,d3_xboole_0,d1_wellord1,d3_xboole_0,d3_xboole_0,d4_relat_2,d2_wellord2,t50_wellord1,d8_wellord1,d1_wellord2,d7_wellord1,d3_tarski,d1_wellord1,d4_wellord2,d2_ordinal1,t84_funct_1,t91_relat_1,d3_tarski,d5_funct_1,t23_ordinal1,t19_ordinal1,d2_ordinal1,t70_funct_1,d1_wellord2,d8_funct_1,d1_wellord1,d10_xboole_0,d3_tarski,d1_wellord1,d5_funct_1,t23_ordinal1,d1_wellord1,d1_wellord2,d8_xboole_0,t21_ordinal1,t73_funct_1,t21_card_1,d3_tarski,t23_ordinal1,d5_funct_1,d4_tarski,t27_card_1,t22_ordinal1,t60_card_3,d4_wellord2,t21_card_1,d5_card_1,t27_card_1]),
    [file(card_3,t62_card_3),interesting(0.91)]).

fof(t16_card_3,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => k3_card_3(k2_funcop_1(A,B)) = B ) ),
    inference(mizar_proof,[status(thm)],[t15_card_3,d10_xboole_0,t13_funcop_1,t19_funcop_1,d5_funct_1,t92_zfmisc_1]),
    [file(card_3,t16_card_3),interesting(0.90)]).

fof(t15_card_3,theorem,(
    ! [A,B] : r1_tarski(k3_card_3(k2_funcop_1(A,B)),B) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski,d5_funct_1,t19_funcop_1,t13_funcop_1]),
    [file(card_3,t15_card_3),interesting(0.88)]).

fof(t51_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : k7_card_3(k2_funcop_1(k1_tarski(B),A)) = A ) ),
    inference(mizar_proof,[status(thm)],[t20_card_3,t65_funct_5,d5_card_1]),
    [file(card_3,t51_card_3),interesting(0.87)]).

fof(t60_card_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(k1_card_1(A),B)
           => r2_hidden(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_1,t59_card_3]),
    [file(card_3,t60_card_3),interesting(0.85)]).

fof(t9_card_3,theorem,(
    k1_card_3(k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[t8_card_3]),
    [file(card_3,t9_card_3),interesting(0.85)]).

fof(t11_card_3,theorem,(
    k2_card_3(k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d3_card_3,t60_relat_1,t64_relat_1]),
    [file(card_3,t11_card_3),interesting(0.84)]).

fof(t27_card_3,theorem,(
    ! [A,B,C] : k5_card_3(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B)) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_card_3,d2_xboole_0,d6_card_3,d2_xboole_0,d10_xboole_0,d3_tarski,d2_xboole_0,d6_card_3,d2_xboole_0,d6_card_3,d6_card_3,d2_xboole_0,d6_card_3]),
    [file(card_3,t27_card_3),interesting(0.83)]).

fof(t29_card_3,theorem,(
    ! [A,B,C] : r1_tarski(k4_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k4_xboole_0(A,C))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_xboole_0,d6_card_3,d6_card_3,d4_xboole_0,d6_card_3]),
    [file(card_3,t29_card_3),interesting(0.82)]).

fof(t52_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k6_card_3(k2_funcop_1(A,B)) = k2_card_2(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_card_3,d2_card_2]),
    [file(card_3,t52_card_3),interesting(0.82)]).

fof(t8_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k1_card_3(A) = A ) ),
    inference(mizar_proof,[status(thm)],[d1_card_3,d5_card_1,d2_card_3]),
    [file(card_3,t8_card_3),interesting(0.82)]).

fof(t59_card_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(k1_card_1(A),k1_card_1(B))
           => r2_hidden(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_card_1,t26_ordinal1,t27_card_1]),
    [file(card_3,t59_card_3),interesting(0.82)]).

fof(l67_card_3,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ~ ( r2_hidden(A,k3_relat_1(B))
          & ! [C] : 
              ( ~ r2_hidden(k4_tarski(A,C),B)
              & ~ r2_hidden(k4_tarski(C,A),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_relat_1,d2_xboole_0,d4_relat_1,d5_relat_1]),
    [file(card_3,l67_card_3),interesting(0.79)]).

fof(t10_card_3,theorem,(
    ! [A,B] : k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B)) ),
    inference(mizar_proof,[status(thm)],[d2_card_3,t19_funcop_1,d2_card_3,t13_funcop_1,t9_funct_1]),
    [file(card_3,t10_card_3),interesting(0.77)]).

fof(t53_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k7_card_3(k2_funcop_1(A,B)) = k3_card_2(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_card_3,d3_card_2]),
    [file(card_3,t53_card_3),interesting(0.77)]).

fof(t34_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k2_card_3(A),k2_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_grfunc_1,d3_card_3,d3_card_3,t8_grfunc_1]),
    [file(card_3,t34_card_3),interesting(0.76)]).

fof(t57_card_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(k4_classes1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t33_classes1,l65_card_3,s1_nat_1]),
    [file(card_3,t57_card_3),interesting(0.76)]).

fof(t14_card_3,theorem,(
    k3_card_3(k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[t2_zfmisc_1]),
    [file(card_3,t14_card_3),interesting(0.75)]).

fof(t24_card_3,theorem,(
    ! [A] : k5_card_3(A,k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d6_card_3]),
    [file(card_3,t24_card_3),interesting(0.75)]).

fof(t12_card_3,theorem,(
    ! [A,B] : k2_card_3(k2_funcop_1(k1_tarski(A),B)) = k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A))) ),
    inference(mizar_proof,[status(thm)],[d3_card_3,t19_funcop_1,d3_card_3,t13_funcop_1,d1_tarski,t9_funct_1]),
    [file(card_3,t12_card_3),interesting(0.75)]).

fof(t30_card_3,theorem,(
    ! [A,B,C] : r1_tarski(k5_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k5_xboole_0(A,C))) ),
    inference(mizar_proof,[status(thm)],[t27_card_3,t29_card_3,t13_xboole_1]),
    [file(card_3,t30_card_3),interesting(0.73)]).

fof(t37_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,t65_relat_1,t28_wellord2,s3_funct_1,d5_funct_1,d5_card_3,d5_funct_1,d5_card_3]),
    [file(card_3,t37_card_3),interesting(0.73)]).

fof(t49_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => k7_card_3(k2_funcop_1(k1_xboole_0,A)) = 1 ) ),
    inference(mizar_proof,[status(thm)],[t19_card_3,t50_card_1,t20_card_2]),
    [file(card_3,t49_card_3),interesting(0.72)]).

fof(t58_card_3,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_1,t68_card_1,t86_card_1,t84_card_1]),
    [file(card_3,t58_card_3),interesting(0.71)]).

fof(t28_card_3,theorem,(
    ! [A,B,C] : r1_tarski(k5_card_3(C,k3_xboole_0(A,B)),k3_xboole_0(k5_card_3(C,A),k5_card_3(C,B))) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_card_3,d3_xboole_0,d6_card_3,d3_xboole_0]),
    [file(card_3,t28_card_3),interesting(0.70)]).

fof(t35_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k3_card_3(A),k3_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_grfunc_1,d3_tarski,d4_tarski,d5_funct_1,d5_funct_1,d4_tarski]),
    [file(card_3,t35_card_3),interesting(0.69)]).

fof(t32_card_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ~ ( r2_hidden(A,k3_card_3(k2_card_3(B)))
          & ! [C,D] : A != k4_tarski(C,D) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d5_funct_1,d3_card_3,d3_card_3,t102_zfmisc_1]),
    [file(card_3,t32_card_3),interesting(0.69)]).

fof(t54_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))) ) ),
    inference(mizar_proof,[status(thm)],[t65_relat_1,t2_zfmisc_1,t47_card_1,t2_xboole_1,s2_xboole_0,s1_xboole_0,s2_funct_1,t65_relat_1,d5_funct_1,d5_card_1,d4_wellord2,d2_funct_2,t28_wellord2,d4_tarski,d5_funct_1,d2_card_3,d3_card_3,d3_card_3,t10_mcart_1,d1_tarski,d5_funct_1,d2_funct_2,s2_funct_1,d3_tarski,d4_tarski,d5_funct_1,d5_funct_1,d2_funct_2,d5_funct_1,d2_card_3,d3_card_3,d1_tarski,d5_funct_1,t106_zfmisc_1,t7_mcart_1,d4_tarski,d5_funct_1,t28_card_1]),
    [file(card_3,t54_card_3),interesting(0.66)]).

fof(t61_card_3,theorem,(
    ! [A] : ~ ( v6_ordinal1(A)
      & ! [B] : ~ ( r1_tarski(B,A)
          & k3_tarski(B) = k3_tarski(A)
          & ! [C] : ~ ( r1_tarski(C,B)
              & C != k1_xboole_0
              & ! [D] : ~ ( r2_hidden(D,C)
                  & ! [E] : 
                      ( r2_hidden(E,C)
                     => r1_tarski(D,E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_wellord2,t25_wellord2,d2_wellord2,t50_wellord1,d8_wellord1,d1_wellord2,d7_wellord1,s1_xboole_0,t144_relat_1,t95_zfmisc_1,d10_xboole_0,d3_tarski,d4_tarski,d5_funct_1,t23_ordinal1,s1_ordinal1,t22_ordinal1,t7_ordinal1,t19_ordinal1,d5_funct_1,d2_ordinal1,d9_ordinal1,d9_xboole_0,d12_funct_1,d4_tarski,d3_tarski,d12_funct_1,t23_ordinal1,s1_ordinal1,d12_funct_1,t23_ordinal1,d8_xboole_0,t21_ordinal1]),
    [file(card_3,t61_card_3),interesting(0.66)]).

fof(t55_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)) ) ),
    inference(mizar_proof,[status(thm)],[t8_card_3,t54_card_3]),
    [file(card_3,t55_card_3),interesting(0.61)]).

fof(t48_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => k6_card_3(k2_funcop_1(k1_xboole_0,A)) = 0 ) ),
    inference(mizar_proof,[status(thm)],[d3_card_3,t65_relat_1,t2_zfmisc_1,t47_card_1]),
    [file(card_3,t48_card_3),interesting(0.60)]).

fof(l65_card_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( v1_finset_1(k4_classes1(A))
       => v1_finset_1(k4_classes1(k1_nat_1(A,1))) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_card_1,t34_classes1,t24_finset_1]),
    [file(card_3,l65_card_3),interesting(0.57)]).

fof(t25_card_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k5_card_3(A,k1_tarski(B)) = k1_tarski(k1_funct_1(B,A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_card_3,d1_tarski,d1_tarski,d10_xboole_0,d3_tarski,d1_tarski,d6_card_3]),
    [file(card_3,t25_card_3),interesting(0.56)]).

fof(t56_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r2_hidden(k6_card_3(A),k7_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d5_funct_1,d1_card_3,d4_xboole_0,t37_card_3,d5_card_3,t9_funct_1,s1_partfun1,s2_funct_1,d8_funct_1,t33_card_3,t32_card_3,t8_mcart_1,d4_xboole_0,d4_xboole_0,d3_tarski,d5_funct_1,d1_card_3,t33_card_3,t13_card_1,d4_xboole_0,d5_card_3,t26_card_1,t21_card_1,d4_wellord2,s3_funct_1,d5_funct_1,d1_card_3,t31_card_3,t3_card_2,t40_card_3,d5_card_1,t1_xboole_1,t22_ordinal1,t4_card_2,t37_card_3,d5_card_3,t36_xboole_1,t38_card_3,d3_tarski,d5_funct_1,d4_tarski,d5_funct_1,d12_funct_1,d3_card_3,d6_card_3,d4_xboole_0,t13_card_1]),
    [file(card_3,t56_card_3),interesting(0.55)]).

fof(t46_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k6_card_3(A),k6_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_card_3,t35_card_3,t27_card_1]),
    [file(card_3,t46_card_3),interesting(0.54)]).

fof(t44_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ( r2_hidden(k1_xboole_0,k2_relat_1(A))
      <=> k7_card_3(A) = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[t47_card_1,t37_card_3,t21_card_1,t46_card_1,t37_card_3]),
    [file(card_3,t44_card_3),interesting(0.53)]).

fof(t40_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k1_card_1(k1_funct_1(k2_card_3(A),B)) = k1_funct_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_card_3,d5_card_1,t13_card_2,d3_card_3,t21_card_1]),
    [file(card_3,t40_card_3),interesting(0.49)]).

fof(t18_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,d5_card_3]),
    [file(card_3,t18_card_3),interesting(0.48)]).

fof(t26_card_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => k5_card_3(A,k2_tarski(B,C)) = k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_card_3,d2_tarski,d2_tarski,d10_xboole_0,d3_tarski,d2_tarski,d6_card_3]),
    [file(card_3,t26_card_3),interesting(0.46)]).

fof(s3_card_3,theorem,
    ( ( f1_s3_card_3 != k1_xboole_0
      & ! [A,B] : 
          ( p1_s3_card_3(A,B)
          | p1_s3_card_3(B,A) )
      & ! [A,B,C] : 
          ( ( p1_s3_card_3(A,B)
            & p1_s3_card_3(B,C) )
         => p1_s3_card_3(A,C) ) )
   => ? [A] : 
        ( r2_hidden(A,f1_s3_card_3)
        & ! [B] : 
            ( r2_hidden(B,f1_s3_card_3)
           => p1_s3_card_3(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_card_2,t37_xboole_1,t37_zfmisc_1,d1_tarski,t37_zfmisc_1,t79_card_1,t63_card_2,t26_xcmplx_1,d4_xboole_0,d1_tarski,d4_xboole_0,s1_nat_1]),
    [file(card_3,s3_card_3),interesting(0.44)]).

fof(t38_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k4_card_3(A),k4_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_card_3,d5_card_3]),
    [file(card_3,t38_card_3),interesting(0.39)]).

fof(t22_card_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => ( k4_card_3(B) = k1_xboole_0
          | k5_card_3(A,k4_card_3(B)) = k1_funct_1(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_card_3,t18_card_3,d5_card_3,d3_tarski,s1_partfun1,t18_card_3,d6_card_3,d10_xboole_0]),
    [file(card_3,t22_card_3),interesting(0.38)]).

fof(t47_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( r1_tarski(A,B)
           => ( r2_hidden(0,k2_relat_1(B))
              | r1_tarski(k7_card_3(A),k7_card_3(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_grfunc_1,s1_funct_5,d3_tarski,d5_card_3,t37_card_3,d5_card_3,s1_partfun1,t8_grfunc_1,d5_card_3,t91_relat_1,t70_funct_1,t9_funct_1,d5_funct_1,t28_card_1]),
    [file(card_3,t47_card_3),interesting(0.34)]).

fof(t39_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k1_card_1(k1_funct_1(A,B)) = k1_funct_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_card_3,d5_card_1]),
    [file(card_3,t39_card_3),interesting(0.31)]).

fof(t13_card_3,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k1_relat_1(C)) )
       => ( A = B
          | r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d3_card_3,d3_xboole_0,t10_mcart_1,d1_tarski]),
    [file(card_3,t13_card_3),interesting(0.29)]).

fof(s4_card_3,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s4_card_3
      & ! [B] : 
          ( r2_hidden(B,f1_s4_card_3)
         => ! [C] : 
              ( r2_hidden(C,k1_funct_1(A,B))
            <=> ( r2_hidden(C,f2_s4_card_3(B))
                & p1_s4_card_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s2_xboole_0,s1_xboole_0,s2_funct_1]),
    [file(card_3,s4_card_3),interesting(0.23)]).

fof(s1_card_3,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_card_3(A)
      & k1_relat_1(A) = f1_s1_card_3
      & ! [B] : 
          ( r2_hidden(B,f1_s1_card_3)
         => k1_funct_1(A,B) = f2_s1_card_3(B) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d1_card_3]),
    [file(card_3,s1_card_3),interesting(0.21)]).

fof(t33_card_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(k2_card_3(B)))
      <=> ( r2_hidden(k2_mcart_1(A),k1_relat_1(B))
          & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A)))
          & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d5_funct_1,d3_card_3,d3_card_3,t10_mcart_1,t23_mcart_1,d1_tarski,d3_card_3,d1_tarski,d5_funct_1,t106_zfmisc_1,d4_tarski]),
    [file(card_3,t33_card_3),interesting(0.20)]).

fof(t45_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k7_card_3(A),k7_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_card_3,t27_card_1]),
    [file(card_3,t45_card_3),interesting(0.01)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(d1_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_card_3(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => v1_card_1(k1_funct_1(A,B)) ) ) ) ),
    file(card_3,d1_card_3),
    [interesting(0.00)]).

fof(t59_card_2,theorem,(
    ! [A] : 
      ( k1_card_1(A) = 0
     => A = k1_xboole_0 ) ),
    file(card_2,t59_card_2),
    [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(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t79_card_1,theorem,(
    ! [A] : k4_card_1(k1_tarski(A)) = 1 ),
    file(card_1,t79_card_1),
    [interesting(0.00)]).

fof(t63_card_2,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_tarski(B,A)
           => k4_card_1(k4_xboole_0(A,B)) = k5_real_1(k4_card_1(A),k4_card_1(B)) ) ) ) ),
    file(card_2,t63_card_2),
    [interesting(0.00)]).

fof(t26_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => A = k6_xcmplx_0(k2_xcmplx_0(A,B),B) ) ) ),
    file(xcmplx_1,t26_xcmplx_1),
    [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(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(s2_card_3,theorem,
    ( ( f1_s2_card_3 != k1_xboole_0
      & ! [A,B] : 
          ( ( p1_s2_card_3(A,B)
            & p1_s2_card_3(B,A) )
         => A = B )
      & ! [A,B,C] : 
          ( ( p1_s2_card_3(A,B)
            & p1_s2_card_3(B,C) )
         => p1_s2_card_3(A,C) ) )
   => ? [A] : 
        ( r2_hidden(A,f1_s2_card_3)
        & ! [B] : ~ ( r2_hidden(B,f1_s2_card_3)
            & B != A
            & p1_s2_card_3(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_card_2,t37_xboole_1,t37_zfmisc_1,d1_tarski,t37_zfmisc_1,t79_card_1,t63_card_2,t26_xcmplx_1,d1_tarski,d4_xboole_0,d1_tarski,d4_xboole_0,d1_tarski,d4_xboole_0,s1_nat_1]),
    [file(card_3,s2_card_3),interesting(0.00)]).

fof(s2_xboole_0,theorem,
    ( ( ! [A] : 
          ( r2_hidden(A,f1_s2_xboole_0)
        <=> p1_s2_xboole_0(A) )
      & ! [A] : 
          ( r2_hidden(A,f2_s2_xboole_0)
        <=> p1_s2_xboole_0(A) ) )
   => f1_s2_xboole_0 = f2_s2_xboole_0 ),
    file(xboole_0,s2_xboole_0),
    [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(s2_funct_1,theorem,
    ( ( ! [A,B,C] : 
          ( ( r2_hidden(A,f1_s2_funct_1)
            & p1_s2_funct_1(A,B)
            & p1_s2_funct_1(A,C) )
         => B = C )
      & ! [A] : ~ ( r2_hidden(A,f1_s2_funct_1)
          & ! [B] : ~ p1_s2_funct_1(A,B) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s2_funct_1
        & ! [B] : 
            ( r2_hidden(B,f1_s2_funct_1)
           => p1_s2_funct_1(B,k1_funct_1(A,B)) ) ) ),
    file(funct_1,s2_funct_1),
    [interesting(0.00)]).

fof(d2_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( B = k1_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(card_3,d2_card_3),
    [interesting(0.00)]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(d3_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) ) ) ) ) ) ),
    file(card_3,d3_card_3),
    [interesting(0.00)]).

fof(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.00)]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.00)]).

fof(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(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(t10_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => ( r2_hidden(k1_mcart_1(A),B)
        & r2_hidden(k2_mcart_1(A),C) ) ) ),
    file(mcart_1,t10_mcart_1),
    [interesting(0.00)]).

fof(t2_zfmisc_1,theorem,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    file(zfmisc_1,t2_zfmisc_1),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(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(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_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(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    [interesting(0.00)]).

fof(t1_card_3,theorem,(
    $true ),
    file(card_3,t1_card_3),
    [interesting(0.00)]).

fof(t21_card_3,theorem,(
    $true ),
    file(card_3,t21_card_3),
    [interesting(0.00)]).

fof(d6_card_3,definition,(
    ! [A,B,C] : 
      ( C = k5_card_3(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & r2_hidden(E,B)
              & D = k1_funct_1(E,A) ) ) ) ),
    file(card_3,d6_card_3),
    [interesting(0.00)]).

fof(d5_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    [interesting(0.00)]).

fof(s1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_partfun1
      & ! [B] : 
          ( r2_hidden(B,f1_s1_partfun1)
         => ( ( p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f2_s1_partfun1(B) )
            & ( ~ p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f3_s1_partfun1(B) ) ) ) ) ),
    file(partfun1,s1_partfun1),
    [interesting(0.00)]).

fof(t23_card_3,theorem,(
    $true ),
    file(card_3,t23_card_3),
    [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(t2_card_3,theorem,(
    $true ),
    file(card_3,t2_card_3),
    [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(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.00)]).

fof(d5_card_1,definition,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( B = k1_card_1(A)
      <=> r2_wellord2(A,B) ) ) ),
    file(card_1,d5_card_1),
    [interesting(0.00)]).

fof(t3_card_3,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v1_card_3(k1_xboole_0) ),
    file(card_3,t3_card_3),
    [interesting(0.00)]).

fof(t41_card_3,theorem,(
    $true ),
    file(card_3,t41_card_3),
    [interesting(0.00)]).

fof(t42_card_3,theorem,(
    $true ),
    file(card_3,t42_card_3),
    [interesting(0.00)]).

fof(t118_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
        & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) ),
    file(zfmisc_1,t118_zfmisc_1),
    [interesting(0.00)]).

fof(t27_card_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    [interesting(0.00)]).

fof(t43_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k6_card_3(A),k6_card_3(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_tarski,d5_funct_1,d3_card_3,d3_card_3,d5_funct_1,t118_zfmisc_1,d4_tarski,t27_card_1]),
    [file(card_3,t43_card_3),interesting(0.00)]).

fof(t47_card_1,theorem,(
    k1_card_1(k1_xboole_0) = k1_xboole_0 ),
    file(card_1,t47_card_1),
    [interesting(0.00)]).

fof(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.00)]).

fof(t28_wellord2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ ( ! [B] : ~ ( r2_hidden(B,A)
              & B = k1_xboole_0 )
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ~ ( k1_relat_1(B) = A
                  & ! [C] : 
                      ( r2_hidden(C,A)
                     => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) ) ),
    file(wellord2,t28_wellord2),
    [interesting(0.00)]).

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.00)]).

fof(t46_card_1,theorem,(
    ! [A] : 
      ( r2_wellord2(A,k1_xboole_0)
    <=> A = k1_xboole_0 ) ),
    file(card_1,t46_card_1),
    [interesting(0.00)]).

fof(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    [interesting(0.00)]).

fof(s1_funct_5,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_funct_5
      & ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(B,f1_s1_funct_5)
           => k1_funct_1(A,B) = f2_s1_funct_5(B) ) ) ) ),
    file(funct_5,s1_funct_5),
    [interesting(0.00)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.00)]).

fof(t70_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    [interesting(0.00)]).

fof(t28_card_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = B
          & r1_tarski(A,k2_relat_1(C)) ) ) ),
    file(card_1,t28_card_1),
    [interesting(0.00)]).

fof(t50_card_1,theorem,(
    ! [A] : k1_card_1(k1_tarski(A)) = k4_ordinal2 ),
    file(card_1,t50_card_1),
    [interesting(0.00)]).

fof(t20_card_2,theorem,(
    1 = k4_ordinal2 ),
    file(card_2,t20_card_2),
    [interesting(0.00)]).

fof(t4_card_3,theorem,(
    $true ),
    file(card_3,t4_card_3),
    [interesting(0.00)]).

fof(t13_card_2,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B)))
      & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))) ) ),
    file(card_2,t13_card_2),
    [interesting(0.00)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

fof(t65_funct_5,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,k1_funct_2(k1_tarski(B),A))
      & k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)) ) ),
    file(funct_5,t65_funct_5),
    [interesting(0.00)]).

fof(t102_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
      & ! [D,E] : k4_tarski(D,E) != A ) ),
    file(zfmisc_1,t102_zfmisc_1),
    [interesting(0.00)]).

fof(t8_mcart_1,theorem,(
    ! [A] : 
      ( ? [B,C] : A = k4_tarski(B,C)
     => k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A ) ),
    file(mcart_1,t8_mcart_1),
    [interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(d2_card_2,definition,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k2_card_2(A,B) = k1_card_1(k2_zfmisc_1(A,B)) ) ) ),
    file(card_2,d2_card_2),
    [interesting(0.00)]).

fof(d3_card_2,definition,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k3_card_2(A,B) = k1_card_1(k1_funct_2(B,A)) ) ) ),
    file(card_2,d3_card_2),
    [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(d4_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & k2_relat_1(C) = B ) ) ),
    file(wellord2,d4_wellord2),
    [interesting(0.00)]).

fof(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

fof(t23_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ),
    file(mcart_1,t23_mcart_1),
    [interesting(0.00)]).

fof(t13_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ( r1_tarski(A,B)
              & A != B ) ) ) ) ),
    file(card_1,t13_card_1),
    [interesting(0.00)]).

fof(t26_card_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(card_1,t26_card_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(t3_card_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k1_card_1(k9_relat_1(B,A)),k1_card_1(A)) ) ),
    file(card_2,t3_card_2),
    [interesting(0.00)]).

fof(t22_ordinal1,theorem,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_tarski(A,B)
                  & r2_hidden(B,C) )
               => r2_hidden(A,C) ) ) ) ) ),
    file(ordinal1,t22_ordinal1),
    [interesting(0.00)]).

fof(t4_card_2,theorem,(
    ! [A,B] : ~ ( r2_hidden(k1_card_1(A),k1_card_1(B))
      & k4_xboole_0(B,A) = k1_xboole_0 ) ),
    file(card_2,t4_card_2),
    [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(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(t33_classes1,theorem,(
    k4_classes1(k1_xboole_0) = k1_xboole_0 ),
    file(classes1,t33_classes1),
    [interesting(0.00)]).

fof(t52_card_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_ordinal1(A) = k1_nat_1(A,1) ) ),
    file(card_1,t52_card_1),
    [interesting(0.00)]).

fof(t34_classes1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k4_classes1(k1_ordinal1(A)) = k1_zfmisc_1(k4_classes1(A)) ) ),
    file(classes1,t34_classes1),
    [interesting(0.00)]).

fof(t24_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> v1_finset_1(k1_zfmisc_1(A)) ) ),
    file(finset_1,t24_finset_1),
    [interesting(0.00)]).

fof(t68_card_1,theorem,(
    ! [A,B] : 
      ( ( r2_wellord2(A,B)
        & v1_finset_1(A) )
     => v1_finset_1(B) ) ),
    file(card_1,t68_card_1),
    [interesting(0.00)]).

fof(t86_card_1,theorem,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & v1_card_1(A) )
     => ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k1_card_1(B) ) ) ),
    file(card_1,t86_card_1),
    [interesting(0.00)]).

fof(t84_card_1,theorem,(
    k1_card_1(k5_ordinal2) = k5_ordinal2 ),
    file(card_1,t84_card_1),
    [interesting(0.00)]).

fof(t5_card_3,theorem,(
    $true ),
    file(card_3,t5_card_3),
    [interesting(0.00)]).

fof(t26_wellord2,theorem,(
    ! [A] : 
    ? [B] : 
      ( v1_relat_1(B)
      & r2_wellord1(B,A) ) ),
    file(wellord2,t26_wellord2),
    [interesting(0.00)]).

fof(t25_wellord2,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r2_wellord1(B,A)
       => ( k3_relat_1(k2_wellord1(B,A)) = A
          & v2_wellord1(k2_wellord1(B,A)) ) ) ) ),
    file(wellord2,t25_wellord2),
    [interesting(0.00)]).

fof(d2_wellord2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ! [B] : 
            ( v3_ordinal1(B)
           => ( B = k2_wellord2(A)
            <=> r4_wellord1(A,k1_wellord2(B)) ) ) ) ) ),
    file(wellord2,d2_wellord2),
    [interesting(0.00)]).

fof(t50_wellord1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
           => r4_wellord1(B,A) ) ) ) ),
    file(wellord1,t50_wellord1),
    [interesting(0.00)]).

fof(d8_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r3_wellord1(A,B,C) ) ) ) ) ),
    file(wellord1,d8_wellord1),
    [interesting(0.00)]).

fof(d1_wellord2,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k1_wellord2(A)
      <=> ( k3_relat_1(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,A)
                & r2_hidden(D,A) )
             => ( r2_hidden(k4_tarski(C,D),B)
              <=> r1_tarski(C,D) ) ) ) ) ) ),
    file(wellord2,d1_wellord2),
    [interesting(0.00)]).

fof(d7_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
              <=> ( k1_relat_1(C) = k3_relat_1(A)
                  & k2_relat_1(C) = k3_relat_1(B)
                  & v2_funct_1(C)
                  & ! [D,E] : 
                      ( r2_hidden(k4_tarski(D,E),A)
                    <=> ( r2_hidden(D,k3_relat_1(A))
                        & r2_hidden(E,k3_relat_1(A))
                        & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) ) ) ) ) ) ) ) ),
    file(wellord1,d7_wellord1),
    [interesting(0.00)]).

fof(t144_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    [interesting(0.00)]).

fof(t95_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_tarski(A),k3_tarski(B)) ) ),
    file(zfmisc_1,t95_zfmisc_1),
    [interesting(0.00)]).

fof(t23_ordinal1,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    [interesting(0.00)]).

fof(s1_ordinal1,theorem,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & p1_s1_ordinal1(A) )
   => ? [A] : 
        ( v3_ordinal1(A)
        & p1_s1_ordinal1(A)
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( p1_s1_ordinal1(B)
             => r1_ordinal1(A,B) ) ) ) ),
    file(ordinal1,s1_ordinal1),
    [interesting(0.00)]).

fof(t7_ordinal1,theorem,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & r1_tarski(B,A) ) ),
    file(ordinal1,t7_ordinal1),
    [interesting(0.00)]).

fof(t19_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v1_ordinal1(C)
             => ( ( r2_hidden(C,A)
                  & r2_hidden(A,B) )
               => r2_hidden(C,B) ) ) ) ) ),
    file(ordinal1,t19_ordinal1),
    [interesting(0.00)]).

fof(d2_ordinal1,definition,(
    ! [A] : 
      ( v1_ordinal1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => r1_tarski(B,A) ) ) ),
    file(ordinal1,d2_ordinal1),
    [interesting(0.00)]).

fof(d9_ordinal1,definition,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    [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(d8_xboole_0,definition,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    [interesting(0.00)]).

fof(t21_ordinal1,theorem,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_xboole_0(A,B)
           => r2_hidden(A,B) ) ) ) ),
    file(ordinal1,t21_ordinal1),
    [interesting(0.00)]).

fof(d5_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_wellord1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B)
            & r1_wellord1(A,B) ) ) ) ),
    file(wellord1,d5_wellord1),
    [interesting(0.00)]).

fof(s1_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
        <=> ( r2_hidden(B,f1_s1_relat_1)
            & r2_hidden(C,f2_s1_relat_1)
            & p1_s1_relat_1(B,C) ) ) ) ),
    file(relat_1,s1_relat_1),
    [interesting(0.00)]).

fof(d6_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    [interesting(0.00)]).

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

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

fof(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(t30_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) ),
    file(relat_1,t30_relat_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(d4_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A)
          & v6_relat_2(A)
          & v1_wellord1(A) ) ) ) ),
    file(wellord1,d4_wellord1),
    [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(d4_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_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) )
             => C = D ) ) ) ),
    file(relat_2,d4_relat_2),
    [interesting(0.00)]).

fof(d12_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_relat_2(A)
      <=> r4_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d12_relat_2),
    [interesting(0.00)]).

fof(d6_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r6_relat_2(A,B)
        <=> ! [C,D] : ~ ( r2_hidden(C,B)
              & r2_hidden(D,B)
              & C != D
              & ~ r2_hidden(k4_tarski(C,D),A)
              & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d6_relat_2),
    [interesting(0.00)]).

fof(d14_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
      <=> r6_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d14_relat_2),
    [interesting(0.00)]).

fof(d2_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_wellord1(A)
      <=> ! [B] : ~ ( r1_tarski(B,k3_relat_1(A))
            & B != k1_xboole_0
            & ! [C] : ~ ( r2_hidden(C,B)
                & r1_xboole_0(k1_wellord1(A,C),B) ) ) ) ) ),
    file(wellord1,d2_wellord1),
    [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(t9_wellord1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r2_wellord1(B,A)
       => ! [C] : ~ ( r1_tarski(C,A)
            & C != k1_xboole_0
            & ! [D] : ~ ( r2_hidden(D,C)
                & ! [E] : 
                    ( r2_hidden(E,C)
                   => r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ),
    file(wellord1,t9_wellord1),
    [interesting(0.00)]).

fof(d1_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k1_wellord1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( D != B
                & r2_hidden(k4_tarski(D,B),A) ) ) ) ) ),
    file(wellord1,d1_wellord1),
    [interesting(0.00)]).

fof(t84_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v2_funct_1(B)
       => v2_funct_1(k7_relat_1(B,A)) ) ) ),
    file(funct_1,t84_funct_1),
    [interesting(0.00)]).

fof(t73_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(B,k1_relat_1(C))
          & r2_hidden(B,A) )
       => r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A))) ) ) ),
    file(funct_1,t73_funct_1),
    [interesting(0.00)]).

fof(t14_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ~ r1_tarski(B,A) ) ) ) ),
    file(card_1,t14_card_1),
    [interesting(0.00)]).

fof(t26_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
            | r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t26_ordinal1),
    [interesting(0.00)]).

fof(t6_card_3,theorem,(
    $true ),
    file(card_3,t6_card_3),
    [interesting(0.00)]).

fof(t7_card_3,theorem,(
    $true ),
    file(card_3,t7_card_3),
    [interesting(0.00)]).