fof(t10_numbers,theorem,(
    r2_xboole_0(k5_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t1_numbers,t9_numbers,t56_xboole_1]),
    [file(numbers,t10_numbers),interesting(1.00)]).

fof(t20_numbers,theorem,(
    r1_tarski(k5_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t10_numbers,d8_xboole_0]),
    [file(numbers,t20_numbers),interesting(1.00)]).

fof(t6_numbers,theorem,(
    r2_xboole_0(k4_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t1_numbers,t5_numbers,t56_xboole_1]),
    [file(numbers,t6_numbers),interesting(0.99)]).

fof(t16_numbers,theorem,(
    r1_tarski(k4_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t6_numbers,d8_xboole_0]),
    [file(numbers,t16_numbers),interesting(0.99)]).

fof(t30_numbers,theorem,(
    k5_numbers != k2_numbers ),
    inference(mizar_proof,[status(thm)],[t1_numbers,t9_numbers]),
    [file(numbers,t30_numbers),interesting(0.99)]).

fof(t26_numbers,theorem,(
    k4_numbers != k2_numbers ),
    inference(mizar_proof,[status(thm)],[t1_numbers,t5_numbers]),
    [file(numbers,t26_numbers),interesting(0.98)]).

fof(t9_numbers,theorem,(
    r2_xboole_0(k5_numbers,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t2_numbers,t8_numbers,t56_xboole_1]),
    [file(numbers,t9_numbers),interesting(0.97)]).

fof(t29_numbers,theorem,(
    k5_numbers != k1_numbers ),
    inference(mizar_proof,[status(thm)],[t2_numbers,t8_numbers]),
    [file(numbers,t29_numbers),interesting(0.96)]).

fof(t3_numbers,theorem,(
    r2_xboole_0(k3_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t1_numbers,t2_numbers,t56_xboole_1]),
    [file(numbers,t3_numbers),interesting(0.95)]).

fof(t13_numbers,theorem,(
    r1_tarski(k3_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t3_numbers,d8_xboole_0]),
    [file(numbers,t13_numbers),interesting(0.95)]).

fof(t23_numbers,theorem,(
    k3_numbers != k2_numbers ),
    inference(mizar_proof,[status(thm)],[t1_numbers,t2_numbers]),
    [file(numbers,t23_numbers),interesting(0.94)]).

fof(t5_numbers,theorem,(
    r2_xboole_0(k4_numbers,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t2_numbers,t4_numbers,t56_xboole_1]),
    [file(numbers,t5_numbers),interesting(0.93)]).

fof(t15_numbers,theorem,(
    r1_tarski(k4_numbers,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t5_numbers,d8_xboole_0]),
    [file(numbers,t15_numbers),interesting(0.92)]).

fof(t25_numbers,theorem,(
    k4_numbers != k1_numbers ),
    inference(mizar_proof,[status(thm)],[t2_numbers,t4_numbers]),
    [file(numbers,t25_numbers),interesting(0.92)]).

fof(t2_numbers,theorem,(
    r2_xboole_0(k3_numbers,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t34_arytm_3,s7_domain_1,t61_arytm_3,l21_numbers,d12_arytm_3,l1_numbers,t75_arytm_3,t90_arytm_3,t90_arytm_3,t74_arytm_3,t76_arytm_3,l1_numbers,t59_arytm_3,d1_ordinal1,t7_xboole_1,l14_numbers,t75_arytm_3,t71_arytm_3,l1_numbers,t59_arytm_3,t90_arytm_3,d5_tarski,t69_enumset1,t69_enumset1,d1_tarski,t65_arytm_3,l1_numbers,t56_ordinal2,t10_ordinal1,t22_ordinal3,t100_arytm_3,t71_arytm_3,t56_arytm_3,d12_arytm_3,t75_arytm_3,t101_arytm_3,t88_arytm_3,t59_arytm_3,t100_arytm_3,d12_arytm_3,t76_arytm_3,t77_arytm_3,t77_arytm_3,t83_arytm_3,t83_arytm_3,d12_arytm_3,t86_arytm_3,t61_arytm_3,t100_arytm_3,t58_arytm_3,t91_arytm_3,t90_arytm_3,t59_arytm_3,t74_arytm_3,t76_arytm_3,t88_arytm_3,t88_arytm_3,t77_arytm_3,t77_arytm_3,t77_arytm_3,t59_arytm_3,t76_arytm_3,t86_arytm_3,t54_arytm_3,t86_arytm_3,t57_arytm_3,t63_arytm_3,d12_arytm_3,t59_arytm_3,t59_arytm_3,l21_numbers,t63_arytm_3,t58_arytm_3,t58_arytm_3,t59_arytm_3,t57_arytm_3,d12_arytm_3,t63_arytm_3,d12_arytm_3,t63_arytm_3,t57_arytm_3,t57_arytm_3,t57_arytm_3,t69_arytm_3,d12_arytm_3,d12_arytm_3,t92_arytm_3,d12_arytm_3,t75_arytm_3,t76_arytm_3,t59_arytm_3,l1_numbers,t59_arytm_3,t91_arytm_3,t75_arytm_3,t54_arytm_3,t88_arytm_3,t59_arytm_3,t76_arytm_3,t77_arytm_3,t100_arytm_3,d12_arytm_3,t76_arytm_3,t77_arytm_3,t77_arytm_3,t83_arytm_3,t83_arytm_3,d12_arytm_3,t86_arytm_3,t61_arytm_3,t100_arytm_3,t58_arytm_3,t91_arytm_3,l21_numbers,d12_arytm_3,l1_numbers,t75_arytm_3,t90_arytm_3,t59_arytm_3,t74_arytm_3,t76_arytm_3,t88_arytm_3,t88_arytm_3,t77_arytm_3,t77_arytm_3,t77_arytm_3,t59_arytm_3,t76_arytm_3,t86_arytm_3,t54_arytm_3,t86_arytm_3,t57_arytm_3,t63_arytm_3,d12_arytm_3,t59_arytm_3,t59_arytm_3,l21_numbers,t63_arytm_3,t58_arytm_3,t58_arytm_3,t59_arytm_3,t57_arytm_3,d12_arytm_3,t63_arytm_3,d12_arytm_3,t63_arytm_3,t57_arytm_3,t57_arytm_3,t57_arytm_3,t69_arytm_3,d12_arytm_3,d12_arytm_3,t92_arytm_3,d12_arytm_3,t75_arytm_3,t76_arytm_3,t73_arytm_3,t41_arytm_3,t34_ordinal3,l1_numbers,t46_arytm_3,t51_arytm_3,l1_numbers,t56_ordinal2,l16_numbers,t58_ordinal3,t36_ordinal3,t58_ordinal3,l16_numbers,t40_arytm_3,l1_numbers,d1_arytm_3,d1_tarski,l13_numbers,d1_tarski,t75_arytm_3,t100_arytm_3,t70_arytm_3,t60_arytm_3,t56_arytm_3,t54_arytm_3,t86_arytm_3,t63_arytm_3,t63_arytm_3,t58_arytm_3,t59_arytm_3,t88_arytm_3,t83_arytm_3,t63_arytm_3,t63_arytm_3,t63_arytm_3,t57_arytm_3,t57_arytm_3,t83_arytm_3,d12_arytm_3,t71_arytm_3,t75_arytm_3,t83_arytm_3,t56_arytm_3,t58_arytm_3,t59_arytm_3,t90_arytm_3,t63_arytm_3,t57_arytm_3,l22_numbers,l22_numbers,t58_arytm_3,l22_numbers,t58_arytm_3,t58_arytm_3,t83_arytm_3,d12_arytm_3,t86_arytm_3,t70_arytm_3,t86_arytm_3,t59_arytm_3,t90_arytm_3,l21_numbers,t83_arytm_3,l1_numbers,t88_arytm_3,t88_arytm_3,t88_arytm_3,t77_arytm_3,t76_arytm_3,t54_arytm_3,t71_arytm_3,t75_arytm_3,t83_arytm_3,t56_arytm_3,l1_numbers,t88_arytm_3,t59_arytm_3,d1_arytm_2,d4_xboole_0,d2_xboole_0,d2_arytm_2,d4_xboole_0,d2_xboole_0,d4_xboole_0,d4_xboole_0,d4_xboole_0,d5_tarski,d2_tarski,t23_ordinal1,l15_numbers,t38_zfmisc_1,t7_ordinal1,l15_numbers,d2_tarski,l1_numbers,t54_arytm_3,t59_arytm_3,l13_numbers,t24_ordinal1,d6_arytm_3,d2_xboole_0,t102_zfmisc_1,d5_tarski,d2_tarski,d2_xboole_0,l12_numbers,d8_xboole_0]),
    [file(numbers,t2_numbers),interesting(0.90)]).

fof(t12_numbers,theorem,(
    r1_tarski(k3_numbers,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t2_numbers,d8_xboole_0]),
    [file(numbers,t12_numbers),interesting(0.88)]).

fof(t22_numbers,theorem,(
    k3_numbers != k1_numbers ),
    inference(mizar_proof,[status(thm)],[t2_numbers]),
    [file(numbers,t22_numbers),interesting(0.88)]).

fof(t8_numbers,theorem,(
    r2_xboole_0(k5_numbers,k3_numbers) ),
    inference(mizar_proof,[status(thm)],[t4_numbers,t7_numbers,t56_xboole_1]),
    [file(numbers,t8_numbers),interesting(0.66)]).

fof(t4_numbers,theorem,(
    r2_xboole_0(k4_numbers,k3_numbers) ),
    inference(mizar_proof,[status(thm)],[d1_arytm_3,l1_numbers,t41_ordinal3,l1_numbers,t39_arytm_3,t38_arytm_3,d1_tarski,t106_zfmisc_1,d2_xboole_0,l7_numbers,d4_xboole_0,l25_numbers,d8_xboole_0]),
    [file(numbers,t4_numbers),interesting(0.64)]).

fof(t1_numbers,theorem,(
    r2_xboole_0(k1_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,d8_xboole_0,t65_funct_4,t65_funct_4,t7_xboole_1,t3_arytm_2,t40_zfmisc_1,l1_numbers,t21_arytm_2,t38_zfmisc_1,t1_xboole_1,l1_numbers,d2_funct_2,l1_numbers,t21_arytm_2,l1_numbers,l10_numbers,l1_numbers,t66_funct_4,d4_xboole_0,d2_xboole_0]),
    [file(numbers,t1_numbers),interesting(0.63)]).

fof(t7_numbers,theorem,(
    r2_xboole_0(k5_numbers,k4_numbers) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t106_zfmisc_1,d2_xboole_0,t33_zfmisc_1,d1_tarski,d4_xboole_0,t38_arytm_3,l8_numbers,d8_xboole_0]),
    [file(numbers,t7_numbers),interesting(0.61)]).

fof(l25_numbers,theorem,(
    r1_tarski(k4_numbers,k3_numbers) ),
    inference(mizar_proof,[status(thm)],[t34_arytm_3,t118_zfmisc_1,t34_arytm_3,t13_xboole_1,t33_xboole_1]),
    [file(numbers,l25_numbers),interesting(0.60)]).

fof(t18_numbers,theorem,(
    r1_tarski(k5_numbers,k3_numbers) ),
    inference(mizar_proof,[status(thm)],[t8_numbers,d8_xboole_0]),
    [file(numbers,t18_numbers),interesting(0.59)]).

fof(l12_numbers,theorem,(
    r1_tarski(k3_numbers,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t1_arytm_2,t118_zfmisc_1,t1_arytm_2,t13_xboole_1,t33_xboole_1]),
    [file(numbers,l12_numbers),interesting(0.58)]).

fof(t28_numbers,theorem,(
    k5_numbers != k3_numbers ),
    inference(mizar_proof,[status(thm)],[t4_numbers,t7_numbers]),
    [file(numbers,t28_numbers),interesting(0.58)]).

fof(l7_numbers,theorem,(
    r1_tarski(k6_arytm_3,k3_numbers) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t68_arytm_3,t40_zfmisc_1]),
    [file(numbers,l7_numbers),interesting(0.57)]).

fof(t14_numbers,theorem,(
    r1_tarski(k4_numbers,k3_numbers) ),
    inference(mizar_proof,[status(thm)],[t4_numbers,d8_xboole_0]),
    [file(numbers,t14_numbers),interesting(0.57)]).

fof(l8_numbers,theorem,(
    r1_tarski(k5_numbers,k4_numbers) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t38_arytm_3,t40_zfmisc_1]),
    [file(numbers,l8_numbers),interesting(0.57)]).

fof(t24_numbers,theorem,(
    k4_numbers != k3_numbers ),
    inference(mizar_proof,[status(thm)],[t4_numbers]),
    [file(numbers,t24_numbers),interesting(0.57)]).

fof(t11_numbers,theorem,(
    r1_tarski(k1_numbers,k2_numbers) ),
    inference(mizar_proof,[status(thm)],[t1_numbers,d8_xboole_0]),
    [file(numbers,t11_numbers),interesting(0.56)]).

fof(t21_numbers,theorem,(
    k1_numbers != k2_numbers ),
    inference(mizar_proof,[status(thm)],[t1_numbers]),
    [file(numbers,t21_numbers),interesting(0.56)]).

fof(l1_numbers,theorem,(
    k13_arytm_3 = 1 ),
    inference(mizar_proof,[status(thm)],[d4_ordinal2]),
    [file(numbers,l1_numbers),interesting(0.54)]).

fof(t17_numbers,theorem,(
    r1_tarski(k5_numbers,k4_numbers) ),
    inference(mizar_proof,[status(thm)],[t7_numbers,d8_xboole_0]),
    [file(numbers,t17_numbers),interesting(0.54)]).

fof(t27_numbers,theorem,(
    k5_numbers != k4_numbers ),
    inference(mizar_proof,[status(thm)],[t7_numbers]),
    [file(numbers,t27_numbers),interesting(0.54)]).

fof(l9_numbers,theorem,(
    ! [A,B,C] : 
      ( k4_tarski(A,B) = k1_tarski(C)
     => ( C = k1_tarski(A)
        & A = B ) ) ),
    inference(mizar_proof,[status(thm)],[d5_tarski,d2_tarski,d1_tarski,d1_tarski,t9_zfmisc_1]),
    [file(numbers,l9_numbers),interesting(0.49)]).

fof(l18_numbers,theorem,(
    m1_subset_1(1,k6_arytm_3) ),
    inference(mizar_proof,[status(thm)],[l17_numbers,t34_arytm_3]),
    [file(numbers,l18_numbers),interesting(0.47)]).

fof(l3_numbers,theorem,(
    r1_tarski(k2_arytm_2,k1_numbers) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t3_arytm_2,t40_zfmisc_1]),
    [file(numbers,l3_numbers),interesting(0.46)]).

fof(l21_numbers,theorem,(
    k10_arytm_3(k13_arytm_3,k13_arytm_3) = c2 ),
    inference(mizar_proof,[status(thm)],[t45_ordinal2,d4_ordinal2,t44_ordinal2,l1_numbers,t64_arytm_3]),
    [file(numbers,l21_numbers),interesting(0.42)]).

fof(l20_numbers,theorem,
    ( v3_ordinal1(2)
    & m1_subset_1(2,k6_arytm_3) ),
    inference(mizar_proof,[status(thm)],[l19_numbers,t34_arytm_3]),
    [file(numbers,l20_numbers),interesting(0.25)]).

fof(l15_numbers,theorem,(
    2 = k2_tarski(0,1) ),
    inference(mizar_proof,[status(thm)],[d1_ordinal1,d1_ordinal1,t41_enumset1]),
    [file(numbers,l15_numbers),interesting(0.25)]).

fof(l13_numbers,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & m1_subset_1(A,k6_arytm_3) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & m1_subset_1(B,k6_arytm_3) )
         => ~ ( r2_hidden(A,B)
              & r3_arytm_3(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_arytm_3,t2_arytm_2,t19_arytm_2,d5_arytm_2,t73_arytm_3]),
    [file(numbers,l13_numbers),interesting(0.22)]).

fof(l14_numbers,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & m1_subset_1(A,k6_arytm_3) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & m1_subset_1(B,k6_arytm_3) )
         => ( r1_ordinal1(A,B)
           => r3_arytm_3(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_ordinal3,t1_arytm_3,t34_arytm_3,t64_arytm_3,d12_arytm_3]),
    [file(numbers,l14_numbers),interesting(0.18)]).

fof(l22_numbers,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => k10_arytm_3(A,A) = k11_arytm_3(c2,A) ) ),
    inference(mizar_proof,[status(thm)],[t59_arytm_3,t59_arytm_3,l21_numbers,t63_arytm_3]),
    [file(numbers,l22_numbers),interesting(0.16)]).

fof(l16_numbers,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => ~ ( k2_arytm_3(A,A) = k2_arytm_3(2,B)
              & ! [C] : 
                  ( ( v3_ordinal1(C)
                    & v4_ordinal2(C) )
                 => A != k2_arytm_3(2,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_ordinal1,t10_arytm_3,t78_ordinal3,t44_ordinal2,t78_ordinal3,l1_numbers,t54_ordinal3,t54_ordinal3,t56_ordinal2,t33_ordinal3,t54_ordinal3,t58_ordinal3,d2_arytm_3,d2_arytm_3,t16_arytm_3,l1_numbers,t14_arytm_3,t13_arytm_3,l15_numbers,d2_tarski]),
    [file(numbers,l16_numbers),interesting(0.07)]).

fof(l17_numbers,theorem,(
    r2_hidden(1,k5_ordinal2) ),
    file(numbers,l17_numbers),
    [interesting(0.00)]).

fof(t34_arytm_3,theorem,(
    r1_tarski(k5_ordinal2,k6_arytm_3) ),
    file(arytm_3,t34_arytm_3),
    [interesting(0.00)]).

fof(l19_numbers,theorem,(
    r2_hidden(2,k5_ordinal2) ),
    file(numbers,l19_numbers),
    [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(t3_arytm_2,theorem,(
    ! [A] : ~ r2_hidden(k4_tarski(k12_arytm_3,A),k2_arytm_2) ),
    file(arytm_2,t3_arytm_2),
    [interesting(0.00)]).

fof(t40_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r2_hidden(C,A)
        | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) ) ) ),
    file(zfmisc_1,t40_zfmisc_1),
    [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(t65_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B)
      & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ),
    file(funct_4,t65_funct_4),
    [interesting(0.00)]).

fof(d4_ordinal2,definition,(
    k4_ordinal2 = k1_ordinal1(k1_xboole_0) ),
    file(ordinal2,d4_ordinal2),
    [interesting(0.00)]).

fof(t21_arytm_2,theorem,
    ( r2_hidden(k12_arytm_3,k2_arytm_2)
    & r2_hidden(k13_arytm_3,k2_arytm_2) ),
    file(arytm_2,t21_arytm_2),
    [interesting(0.00)]).

fof(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t38_zfmisc_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(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(t71_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != C
     => k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) ) ),
    file(funct_4,t71_funct_4),
    [interesting(0.00)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_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(t69_enumset1,theorem,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    [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(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.00)]).

fof(t9_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => B = C ) ),
    file(zfmisc_1,t9_zfmisc_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(t23_ordinal1,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    [interesting(0.00)]).

fof(t10_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( A != k1_xboole_0
       => r2_hidden(k1_xboole_0,A) ) ) ),
    file(ordinal3,t10_ordinal3),
    [interesting(0.00)]).

fof(d6_arytm_3,definition,(
    k6_arytm_3 = k2_xboole_0(k4_xboole_0(a_0_0_arytm_3,a_0_1_arytm_3),k5_ordinal2) ),
    file(arytm_3,d6_arytm_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(t82_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k6_arytm_3))
     => ~ ( ? [B] : 
              ( m1_subset_1(B,k6_arytm_3)
              & r2_hidden(B,A)
              & B != k12_arytm_3 )
          & ! [B] : 
              ( m1_subset_1(B,k6_arytm_3)
             => ! [C] : 
                  ( m1_subset_1(C,k6_arytm_3)
                 => ( ( r2_hidden(B,A)
                      & r3_arytm_3(C,B) )
                   => r2_hidden(C,A) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k6_arytm_3)
             => ! [C] : 
                  ( m1_subset_1(C,k6_arytm_3)
                 => ! [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                     => ~ ( r2_hidden(B,A)
                          & r2_hidden(C,A)
                          & r2_hidden(D,A)
                          & B != C
                          & C != D
                          & D != B ) ) ) ) ) ) ),
    file(arytm_3,t82_arytm_3),
    [interesting(0.00)]).

fof(d1_arytm_2,definition,(
    k1_arytm_2 = k4_xboole_0(a_0_0_arytm_2,k1_tarski(k6_arytm_3)) ),
    file(arytm_2,d1_arytm_2),
    [interesting(0.00)]).

fof(d2_arytm_2,definition,(
    k2_arytm_2 = k4_xboole_0(k2_xboole_0(k6_arytm_3,k1_arytm_2),a_0_1_arytm_2) ),
    file(arytm_2,d2_arytm_2),
    [interesting(0.00)]).

fof(t103_zfmisc_1,theorem,(
    ! [A,B,C,D] : ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
      & r2_hidden(D,A)
      & ! [E,F] : ~ ( r2_hidden(E,B)
          & r2_hidden(F,C)
          & D = k4_tarski(E,F) ) ) ),
    file(zfmisc_1,t103_zfmisc_1),
    [interesting(0.00)]).

fof(l10_numbers,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ~ r2_hidden(k5_funct_4(k1_numbers,0,k13_arytm_3,A,B),k1_numbers) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_funct_4,d5_tarski,d2_tarski,d2_tarski,d5_tarski,d5_tarski,t69_enumset1,t69_enumset1,d2_tarski,d1_tarski,t33_zfmisc_1,t9_zfmisc_1,l9_numbers,d2_tarski,d2_tarski,d1_tarski,d2_tarski,d1_tarski,l9_numbers,d2_tarski,d2_tarski,d1_tarski,d2_tarski,d1_tarski,t9_zfmisc_1,d2_tarski,d4_xboole_0,t23_ordinal1,t10_ordinal3,d2_tarski,d6_arytm_3,d2_xboole_0,d2_tarski,t82_arytm_3,d2_tarski,d1_arytm_2,d4_xboole_0,d2_xboole_0,d2_arytm_2,d4_xboole_0,t103_zfmisc_1,d1_tarski,d5_tarski,t71_funct_4,d2_tarski,d2_tarski,d1_tarski,d2_tarski,d2_tarski,d2_tarski,d5_tarski,d2_xboole_0,d4_xboole_0]),
    [file(numbers,l10_numbers),interesting(0.00)]).

fof(t66_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C
        & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ),
    file(funct_4,t66_funct_4),
    [interesting(0.00)]).

fof(s7_domain_1,theorem,(
    m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(f1_s7_domain_1)) ),
    file(domain_1,s7_domain_1),
    [interesting(0.00)]).

fof(t61_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ~ ( A != k12_arytm_3
              & ! [C] : 
                  ( m1_subset_1(C,k6_arytm_3)
                 => B != k11_arytm_3(A,C) ) ) ) ) ),
    file(arytm_3,t61_arytm_3),
    [interesting(0.00)]).

fof(t45_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)) ) ) ),
    file(ordinal2,t45_ordinal2),
    [interesting(0.00)]).

fof(t44_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k14_ordinal2(A,k1_xboole_0) = A ) ),
    file(ordinal2,t44_ordinal2),
    [interesting(0.00)]).

fof(t64_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & m1_subset_1(A,k6_arytm_3) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & m1_subset_1(B,k6_arytm_3) )
         => k10_arytm_3(A,B) = k1_arytm_3(A,B) ) ) ),
    file(arytm_3,t64_arytm_3),
    [interesting(0.00)]).

fof(d12_arytm_3,definition,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ( r3_arytm_3(A,B)
          <=> ? [C] : 
                ( m1_subset_1(C,k6_arytm_3)
                & B = k10_arytm_3(A,C) ) ) ) ) ),
    file(arytm_3,d12_arytm_3),
    [interesting(0.00)]).

fof(t75_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ( ~ r3_arytm_3(B,A)
          <=> ( r3_arytm_3(A,B)
              & A != B ) ) ) ) ),
    file(arytm_3,t75_arytm_3),
    [interesting(0.00)]).

fof(t90_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r3_arytm_3(A,B)
               => r3_arytm_3(k11_arytm_3(A,C),k11_arytm_3(B,C)) ) ) ) ) ),
    file(arytm_3,t90_arytm_3),
    [interesting(0.00)]).

fof(t74_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( ( r3_arytm_3(A,B)
                  & r3_arytm_3(B,C) )
               => r3_arytm_3(A,C) ) ) ) ) ),
    file(arytm_3,t74_arytm_3),
    [interesting(0.00)]).

fof(t76_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ~ ( ( ( ~ r3_arytm_3(B,A)
                      & r3_arytm_3(B,C) )
                    | ( r3_arytm_3(A,B)
                      & ~ r3_arytm_3(C,B) ) )
                  & r3_arytm_3(C,A) ) ) ) ) ),
    file(arytm_3,t76_arytm_3),
    [interesting(0.00)]).

fof(t59_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => k11_arytm_3(A,k13_arytm_3) = A ) ),
    file(arytm_3,t59_arytm_3),
    [interesting(0.00)]).

fof(d1_ordinal1,definition,(
    ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) ),
    file(ordinal1,d1_ordinal1),
    [interesting(0.00)]).

fof(t30_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( r1_ordinal1(A,B)
              & ! [C] : 
                  ( v3_ordinal1(C)
                 => B != k14_ordinal2(A,C) ) ) ) ) ),
    file(ordinal3,t30_ordinal3),
    [interesting(0.00)]).

fof(t1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal2(k14_ordinal2(A,B))
           => ( r2_hidden(A,k5_ordinal2)
              & r2_hidden(B,k5_ordinal2) ) ) ) ) ),
    file(arytm_3,t1_arytm_3),
    [interesting(0.00)]).

fof(t71_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => r3_arytm_3(k12_arytm_3,A) ) ),
    file(arytm_3,t71_arytm_3),
    [interesting(0.00)]).

fof(t65_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & m1_subset_1(A,k6_arytm_3) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & m1_subset_1(B,k6_arytm_3) )
         => k11_arytm_3(A,B) = k2_arytm_3(A,B) ) ) ),
    file(arytm_3,t65_arytm_3),
    [interesting(0.00)]).

fof(t56_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( k15_ordinal2(k4_ordinal2,A) = A
        & k15_ordinal2(A,k4_ordinal2) = A ) ) ),
    file(ordinal2,t56_ordinal2),
    [interesting(0.00)]).

fof(t10_ordinal1,theorem,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    [interesting(0.00)]).

fof(t22_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ( r2_hidden(A,B)
                   => ( ( ~ ( r1_ordinal1(C,D)
                            & D != k1_xboole_0 )
                        & ~ r2_hidden(C,D) )
                      | r2_hidden(k15_ordinal2(A,C),k15_ordinal2(B,D)) ) ) ) ) ) ) ),
    file(ordinal3,t22_ordinal3),
    [interesting(0.00)]).

fof(t100_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ~ ! [C] : 
                ( m1_subset_1(C,k6_arytm_3)
               => ( k10_arytm_3(A,C) != B
                  & k10_arytm_3(B,C) != A ) ) ) ) ),
    file(arytm_3,t100_arytm_3),
    [interesting(0.00)]).

fof(t56_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => k10_arytm_3(A,k12_arytm_3) = A ) ),
    file(arytm_3,t56_arytm_3),
    [interesting(0.00)]).

fof(t101_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ~ ( ~ r3_arytm_3(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,k6_arytm_3)
                 => ~ ( ~ r3_arytm_3(C,A)
                      & ~ r3_arytm_3(B,C) ) ) ) ) ) ),
    file(arytm_3,t101_arytm_3),
    [interesting(0.00)]).

fof(t88_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r3_arytm_3(k11_arytm_3(B,A),k11_arytm_3(C,A))
               => ( A = k12_arytm_3
                  | r3_arytm_3(B,C) ) ) ) ) ) ),
    file(arytm_3,t88_arytm_3),
    [interesting(0.00)]).

fof(t77_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ~ ( ~ r3_arytm_3(B,A)
                  & ~ r3_arytm_3(C,B)
                  & r3_arytm_3(C,A) ) ) ) ) ),
    file(arytm_3,t77_arytm_3),
    [interesting(0.00)]).

fof(t83_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r3_arytm_3(k10_arytm_3(A,B),k10_arytm_3(C,B))
              <=> r3_arytm_3(A,C) ) ) ) ) ),
    file(arytm_3,t83_arytm_3),
    [interesting(0.00)]).

fof(t86_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ~ ( k11_arytm_3(A,B) = k12_arytm_3
              & A != k12_arytm_3
              & B != k12_arytm_3 ) ) ) ),
    file(arytm_3,t86_arytm_3),
    [interesting(0.00)]).

fof(t58_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => k11_arytm_3(k11_arytm_3(A,B),C) = k11_arytm_3(A,k11_arytm_3(B,C)) ) ) ) ),
    file(arytm_3,t58_arytm_3),
    [interesting(0.00)]).

fof(t91_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ! [D] : 
                  ( m1_subset_1(D,k6_arytm_3)
                 => ~ ( k11_arytm_3(A,B) = k11_arytm_3(C,D)
                      & ~ r3_arytm_3(A,C)
                      & ~ r3_arytm_3(B,D) ) ) ) ) ) ),
    file(arytm_3,t91_arytm_3),
    [interesting(0.00)]).

fof(t54_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => k11_arytm_3(A,k12_arytm_3) = k12_arytm_3 ) ),
    file(arytm_3,t54_arytm_3),
    [interesting(0.00)]).

fof(t57_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => k10_arytm_3(k10_arytm_3(A,B),C) = k10_arytm_3(A,k10_arytm_3(B,C)) ) ) ) ),
    file(arytm_3,t57_arytm_3),
    [interesting(0.00)]).

fof(t63_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => k11_arytm_3(A,k10_arytm_3(B,C)) = k10_arytm_3(k11_arytm_3(A,B),k11_arytm_3(A,C)) ) ) ) ),
    file(arytm_3,t63_arytm_3),
    [interesting(0.00)]).

fof(t69_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( k10_arytm_3(A,B) = k10_arytm_3(C,B)
               => A = C ) ) ) ) ),
    file(arytm_3,t69_arytm_3),
    [interesting(0.00)]).

fof(t92_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ( A = k12_arytm_3
          <=> k10_arytm_3(A,B) = B ) ) ) ),
    file(arytm_3,t92_arytm_3),
    [interesting(0.00)]).

fof(t73_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ( ( r3_arytm_3(A,B)
              & r3_arytm_3(B,A) )
           => A = B ) ) ) ),
    file(arytm_3,t73_arytm_3),
    [interesting(0.00)]).

fof(t41_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => k8_arytm_3(A) != k1_xboole_0 ) ),
    file(arytm_3,t41_arytm_3),
    [interesting(0.00)]).

fof(t34_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( k15_ordinal2(A,B) = k1_xboole_0
              & A != k1_xboole_0
              & B != k1_xboole_0 ) ) ) ),
    file(ordinal3,t34_ordinal3),
    [interesting(0.00)]).

fof(t46_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => ( k9_arytm_3(k1_xboole_0,A) = k1_xboole_0
            & k9_arytm_3(B,k4_ordinal2) = B ) ) ) ),
    file(arytm_3,t46_arytm_3),
    [interesting(0.00)]).

fof(t51_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => ! [C] : 
              ( ( v3_ordinal1(C)
                & v4_ordinal2(C) )
             => ! [D] : 
                  ( ( v3_ordinal1(D)
                    & v4_ordinal2(D) )
                 => ~ ( B != k1_xboole_0
                      & A != k1_xboole_0
                      & ~ ( k9_arytm_3(C,B) = k9_arytm_3(D,A)
                        <=> k2_arytm_3(C,A) = k2_arytm_3(B,D) ) ) ) ) ) ) ),
    file(arytm_3,t51_arytm_3),
    [interesting(0.00)]).

fof(t24_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( ~ r2_hidden(A,B)
              & A != B
              & ~ r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t24_ordinal1),
    [interesting(0.00)]).

fof(t10_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => ( r2_hidden(k1_xboole_0,A)
           => r2_hidden(k7_ordinal3(B,A),A) ) ) ) ),
    file(arytm_3,t10_arytm_3),
    [interesting(0.00)]).

fof(t78_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => A = k14_ordinal2(k15_ordinal2(k6_ordinal3(A,B),B),k7_ordinal3(A,B)) ) ) ),
    file(ordinal3,t78_ordinal3),
    [interesting(0.00)]).

fof(t54_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k15_ordinal2(k14_ordinal2(A,B),C) = k14_ordinal2(k15_ordinal2(A,C),k15_ordinal2(B,C)) ) ) ) ),
    file(ordinal3,t54_ordinal3),
    [interesting(0.00)]).

fof(t33_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k14_ordinal2(k14_ordinal2(A,B),C) = k14_ordinal2(A,k14_ordinal2(B,C)) ) ) ) ),
    file(ordinal3,t33_ordinal3),
    [interesting(0.00)]).

fof(t58_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k15_ordinal2(k15_ordinal2(A,B),C) = k15_ordinal2(A,k15_ordinal2(B,C)) ) ) ) ),
    file(ordinal3,t58_ordinal3),
    [interesting(0.00)]).

fof(d2_arytm_3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_arytm_3(A,B)
          <=> ? [C] : 
                ( v3_ordinal1(C)
                & B = k15_ordinal2(A,C) ) ) ) ) ),
    file(arytm_3,d2_arytm_3),
    [interesting(0.00)]).

fof(t16_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => ! [C] : 
              ( ( v3_ordinal1(C)
                & v4_ordinal2(C) )
             => ( ( r2_arytm_3(A,B)
                  & r2_arytm_3(A,k1_arytm_3(B,C)) )
               => r2_arytm_3(A,C) ) ) ) ) ),
    file(arytm_3,t16_arytm_3),
    [interesting(0.00)]).

fof(t14_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( r2_arytm_3(A,k1_xboole_0)
        & r2_arytm_3(k4_ordinal2,A) ) ) ),
    file(arytm_3,t14_arytm_3),
    [interesting(0.00)]).

fof(t13_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => ( ( r2_arytm_3(A,B)
              & r2_arytm_3(B,A) )
           => A = B ) ) ) ),
    file(arytm_3,t13_arytm_3),
    [interesting(0.00)]).

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

fof(t36_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( k15_ordinal2(A,B) = k15_ordinal2(C,B)
               => ( B = k1_xboole_0
                  | A = C ) ) ) ) ) ),
    file(ordinal3,t36_ordinal3),
    [interesting(0.00)]).

fof(t40_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => r1_arytm_3(k7_arytm_3(A),k8_arytm_3(A)) ) ),
    file(arytm_3,t40_arytm_3),
    [interesting(0.00)]).

fof(d1_arytm_3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_arytm_3(A,B)
          <=> ! [C] : 
                ( v3_ordinal1(C)
               => ! [D] : 
                    ( v3_ordinal1(D)
                   => ! [E] : 
                        ( v3_ordinal1(E)
                       => ( ( A = k15_ordinal2(C,D)
                            & B = k15_ordinal2(C,E) )
                         => C = k4_ordinal2 ) ) ) ) ) ) ) ),
    file(arytm_3,d1_arytm_3),
    [interesting(0.00)]).

fof(t37_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( r2_hidden(A,k6_arytm_3)
       => r2_hidden(A,k5_ordinal2) ) ) ),
    file(arytm_3,t37_arytm_3),
    [interesting(0.00)]).

fof(t2_arytm_2,theorem,(
    r1_tarski(k5_ordinal2,k2_arytm_2) ),
    file(arytm_2,t2_arytm_2),
    [interesting(0.00)]).

fof(t19_arytm_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ( r2_hidden(A,k5_ordinal2)
       => ! [B] : 
            ( m1_subset_1(B,k2_arytm_2)
           => ( r2_hidden(B,A)
            <=> ( r2_hidden(B,k5_ordinal2)
                & B != A
                & r1_arytm_2(B,A) ) ) ) ) ) ),
    file(arytm_2,t19_arytm_2),
    [interesting(0.00)]).

fof(d5_arytm_2,definition,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( ( r2_hidden(A,k6_arytm_3)
                & r2_hidden(B,k6_arytm_3) )
             => ( r1_arytm_2(A,B)
              <=> ? [C] : 
                    ( m1_subset_1(C,k6_arytm_3)
                    & ? [D] : 
                        ( m1_subset_1(D,k6_arytm_3)
                        & A = C
                        & B = D
                        & r3_arytm_3(C,D) ) ) ) )
            & ( r2_hidden(A,k6_arytm_3)
             => ( r2_hidden(B,k6_arytm_3)
                | ( r1_arytm_2(A,B)
                <=> r2_hidden(A,B) ) ) )
            & ( r2_hidden(B,k6_arytm_3)
             => ( r2_hidden(A,k6_arytm_3)
                | ( r1_arytm_2(A,B)
                <=> ~ r2_hidden(B,A) ) ) )
            & ~ ( ~ ( r2_hidden(A,k6_arytm_3)
                    & r2_hidden(B,k6_arytm_3) )
                & ~ ( r2_hidden(A,k6_arytm_3)
                    & ~ r2_hidden(B,k6_arytm_3) )
                & ~ ( ~ r2_hidden(A,k6_arytm_3)
                    & r2_hidden(B,k6_arytm_3) )
                & ~ ( r1_arytm_2(A,B)
                  <=> r1_tarski(A,B) ) ) ) ) ) ),
    file(arytm_2,d5_arytm_2),
    [interesting(0.00)]).

fof(t70_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ( k10_arytm_3(A,B) = k12_arytm_3
           => A = k12_arytm_3 ) ) ) ),
    file(arytm_3,t70_arytm_3),
    [interesting(0.00)]).

fof(t60_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ~ ( A != k12_arytm_3
          & ! [B] : 
              ( m1_subset_1(B,k6_arytm_3)
             => k11_arytm_3(A,B) != k13_arytm_3 ) ) ) ),
    file(arytm_3,t60_arytm_3),
    [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(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(t1_arytm_2,theorem,(
    r1_tarski(k6_arytm_3,k2_arytm_2) ),
    file(arytm_2,t1_arytm_2),
    [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(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(t33_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ),
    file(xboole_1,t33_xboole_1),
    [interesting(0.00)]).

fof(t56_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_xboole_0(A,B)
        & r2_xboole_0(B,C) )
     => r2_xboole_0(A,C) ) ),
    file(xboole_1,t56_xboole_1),
    [interesting(0.00)]).

fof(t41_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k15_ordinal2(A,B) = k4_ordinal2
           => ( A = k4_ordinal2
              & B = k4_ordinal2 ) ) ) ) ),
    file(ordinal3,t41_ordinal3),
    [interesting(0.00)]).

fof(t39_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ! [B] : 
          ( m1_subset_1(B,k5_ordinal2)
         => ( r2_hidden(k4_tarski(A,B),k6_arytm_3)
          <=> ( r1_arytm_3(A,B)
              & B != k1_xboole_0
              & B != k4_ordinal2 ) ) ) ) ),
    file(arytm_3,t39_arytm_3),
    [interesting(0.00)]).

fof(t38_arytm_3,theorem,(
    ! [A,B] : ~ r2_hidden(k4_tarski(A,B),k5_ordinal2) ),
    file(arytm_3,t38_arytm_3),
    [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(t68_arytm_3,theorem,(
    ! [A] : ~ r2_hidden(k4_tarski(k12_arytm_3,A),k6_arytm_3) ),
    file(arytm_3,t68_arytm_3),
    [interesting(0.00)]).

fof(t19_numbers,theorem,(
    r1_tarski(k5_numbers,k1_numbers) ),
    file(numbers,t19_numbers),
    [interesting(0.00)]).