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)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_ordinal2,t53_ordinal2,t54_ordinal3,t56_ordinal2,t54_ordinal3,t48_ordinal2,t26_ordinal1,t19_ordinal3,t52_ordinal2,t55_ordinal2,t56_ordinal2,t56_ordinal2,t22_ordinal3,s3_ordinal2,d5_ordinal3,d5_ordinal3,t48_ordinal3,t57_ordinal3,t52_ordinal3,s1_ordinal2]),
    [file(ordinal3,t58_ordinal3),interesting(1.00)]).

fof(t56_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ! [E] : 
                      ( v3_ordinal1(E)
                     => ( ( k14_ordinal2(k15_ordinal2(B,A),C) = k14_ordinal2(k15_ordinal2(D,A),E)
                          & r2_hidden(C,A)
                          & r2_hidden(E,A) )
                       => ( B = D
                          & C = E ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_ordinal3,t54_ordinal3,t33_ordinal3,t24_ordinal3,t27_ordinal3,t39_ordinal3,t7_ordinal1,t31_ordinal3,t54_ordinal3,t33_ordinal3,t24_ordinal3,t27_ordinal3,t39_ordinal3,t7_ordinal1,t24_ordinal1,t24_ordinal3]),
    [file(ordinal3,t56_ordinal3),interesting(0.90)]).

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)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_ordinal2,t44_ordinal2,t52_ordinal2,t45_ordinal2,t53_ordinal2,t33_ordinal3,t53_ordinal2,s3_ordinal2,s3_ordinal2,t32_ordinal3,t46_ordinal2,d2_ordinal3,d5_ordinal3,t23_ordinal1,d5_ordinal3,d2_ordinal3,t9_funct_1,t10_ordinal3,d5_funct_1,t27_ordinal2,t48_ordinal3,t35_ordinal2,t52_ordinal3,t51_ordinal3,d6_ordinal1,t53_ordinal3,t54_ordinal2,t44_ordinal2,t55_ordinal2,s1_ordinal2]),
    [file(ordinal3,t54_ordinal3),interesting(0.89)]).

fof(t76_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k5_ordinal3(k15_ordinal2(A,B),k15_ordinal2(C,B)) = k15_ordinal2(k5_ordinal3(A,C),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal3,t54_ordinal3,t65_ordinal3,d6_ordinal3,t38_ordinal3,t52_ordinal2,t55_ordinal2,d6_ordinal3,t69_ordinal3]),
    [file(ordinal3,t76_ordinal3),interesting(0.84)]).

fof(t65_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k5_ordinal3(k14_ordinal2(A,B),A) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t27_ordinal3,d6_ordinal3]),
    [file(ordinal3,t65_ordinal3),interesting(0.82)]).

fof(t77_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => r1_ordinal1(k15_ordinal2(k6_ordinal3(A,B),B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_ordinal3,t27_ordinal3,d7_ordinal3,t52_ordinal2,t2_xboole_1]),
    [file(ordinal3,t77_ordinal3),interesting(0.81)]).

fof(t48_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => v4_ordinal1(k15_ordinal2(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_ordinal2,t54_ordinal2,t35_ordinal2,d4_tarski,t23_ordinal1,t29_ordinal2,d5_funct_1,t23_ordinal1,t55_ordinal2,t10_ordinal3,t33_ordinal1,t44_ordinal2,t45_ordinal2,t50_ordinal2,t41_ordinal1,t53_ordinal2,d5_funct_1,t33_ordinal1,t27_ordinal2,t22_ordinal1,t34_ordinal1,d4_tarski,t41_ordinal1,t52_ordinal2]),
    [file(ordinal3,t48_ordinal3),interesting(0.80)]).

fof(t32_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => ( A = k1_xboole_0
              | v4_ordinal1(k14_ordinal2(B,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d8_xboole_0,t21_ordinal1,s3_ordinal2,t46_ordinal2,t35_ordinal2,t33_ordinal1,t44_ordinal2,t49_ordinal2,t51_ordinal2,t22_ordinal1,t26_ordinal1,t30_ordinal3,t26_ordinal1,t50_ordinal2,t41_ordinal1,t45_ordinal2,d5_funct_1,t27_ordinal2,t41_ordinal1]),
    [file(ordinal3,t32_ordinal3),interesting(0.79)]).

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) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_1,t47_ordinal2,t44_ordinal2,d8_xboole_0,t21_ordinal1,t34_ordinal1,t45_ordinal2,t2_xboole_1,t47_ordinal2,t51_ordinal2,s1_ordinal1,s3_ordinal2,t44_ordinal2,d10_xboole_0,t44_ordinal2,t42_ordinal1,t10_ordinal1,t7_ordinal1,t26_ordinal1,t33_ordinal1,t45_ordinal2,d10_xboole_0,t42_ordinal1,t46_ordinal2,t35_ordinal2,d5_funct_1,t23_ordinal1,t7_ordinal1,t26_ordinal1,t28_ordinal2,d10_xboole_0,s1_ordinal2]),
    [file(ordinal3,t30_ordinal3),interesting(0.78)]).

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)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_ordinal2,t44_ordinal2,t45_ordinal2,t45_ordinal2,t45_ordinal2,s3_ordinal2,t46_ordinal2,t35_ordinal2,s3_ordinal2,t29_ordinal3,t32_ordinal3,t46_ordinal2,t35_ordinal2,d3_tarski,d5_funct_1,t23_ordinal1,t49_ordinal2,d5_funct_1,t30_ordinal2,d10_xboole_0,d3_tarski,t23_ordinal1,t2_xboole_1,t44_ordinal2,t50_ordinal2,t27_ordinal3,t26_ordinal1,t1_xboole_1,t30_ordinal3,t26_ordinal1,t49_ordinal2,t30_ordinal3,t26_ordinal1,t50_ordinal2,t50_ordinal2,t49_ordinal2,s1_ordinal2]),
    [file(ordinal3,t33_ordinal3),interesting(0.77)]).

fof(t1_ordinal3,theorem,(
    ! [A] : r1_tarski(A,k1_ordinal1(A)) ),
    inference(mizar_proof,[status(thm)],[d1_ordinal1,t7_xboole_1]),
    [file(ordinal3,t1_ordinal3),interesting(0.76)]).

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)) ) ) ),
    inference(mizar_proof,[status(thm)],[t77_ordinal3,d6_ordinal3]),
    [file(ordinal3,t78_ordinal3),interesting(0.76)]).

fof(t67_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k5_ordinal3(A,A) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[t44_ordinal2,d6_ordinal3]),
    [file(ordinal3,t67_ordinal3),interesting(0.75)]).

fof(t8_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => k2_ordinal2(B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal2,t23_ordinal1,s2_xboole_0]),
    [file(ordinal3,t8_ordinal3),interesting(0.73)]).

fof(t27_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,k14_ordinal2(A,B))
            & r1_ordinal1(B,k14_ordinal2(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,t44_ordinal2,t47_ordinal2,t50_ordinal2,t51_ordinal2]),
    [file(ordinal3,t27_ordinal3),interesting(0.73)]).

fof(t31_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( r2_hidden(A,B)
              & ! [C] : 
                  ( v3_ordinal1(C)
                 => ~ ( B = k14_ordinal2(A,C)
                      & C != k1_xboole_0 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal1,t30_ordinal3,t44_ordinal2]),
    [file(ordinal3,t31_ordinal3),interesting(0.72)]).

fof(t53_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( A != k1_xboole_0
           => k3_tarski(k14_ordinal2(B,A)) = k14_ordinal2(B,k3_tarski(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_ordinal2,t2_ordinal2,t2_ordinal2,t42_ordinal1,t32_ordinal3,d6_ordinal1]),
    [file(ordinal3,t53_ordinal3),interesting(0.72)]).

fof(t71_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(A,B)
               => r1_ordinal1(k5_ordinal3(C,B),k5_ordinal3(C,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal3,d6_ordinal3,t1_xboole_1,d6_ordinal3,t33_ordinal3,t24_ordinal3,t27_ordinal3,d6_ordinal3,t2_xboole_1]),
    [file(ordinal3,t71_ordinal3),interesting(0.72)]).

fof(t26_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(k14_ordinal2(A,B),k14_ordinal2(A,C))
               => r1_ordinal1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_xboole_0,t21_ordinal1,t24_ordinal3,t25_ordinal3,d2_ordinal1]),
    [file(ordinal3,t26_ordinal3),interesting(0.72)]).

fof(t70_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k5_ordinal3(A,k14_ordinal2(B,C)) = k5_ordinal3(k5_ordinal3(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal3,t33_ordinal3,t65_ordinal3,t65_ordinal3,d6_ordinal3,d6_ordinal3,t50_ordinal2,d6_ordinal3,t69_ordinal3]),
    [file(ordinal3,t70_ordinal3),interesting(0.70)]).

fof(t11_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k6_ordinal2(A) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal2,t10_ordinal2,t10_ordinal3,t5_setfam_1,d1_setfam_1]),
    [file(ordinal3,t11_ordinal3),interesting(0.68)]).

fof(t9_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k2_ordinal2(k1_tarski(A)) = k1_tarski(A) ) ),
    inference(mizar_proof,[status(thm)],[d1_ordinal1,t7_xboole_1,t8_ordinal3]),
    [file(ordinal3,t9_ordinal3),interesting(0.68)]).

fof(t42_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ~ ( r2_hidden(A,k14_ordinal2(B,C))
                  & ~ r2_hidden(A,B)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ~ ( r2_hidden(D,C)
                          & A = k14_ordinal2(B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_ordinal1,t30_ordinal3,t26_ordinal1,t50_ordinal2,t7_ordinal1]),
    [file(ordinal3,t42_ordinal3),interesting(0.68)]).

fof(t24_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( k14_ordinal2(A,B) = k14_ordinal2(A,C)
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_ordinal1,t49_ordinal2]),
    [file(ordinal3,t24_ordinal3),interesting(0.68)]).

fof(t80_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(A,k15_ordinal2(B,C))
               => ( r2_hidden(k6_ordinal3(A,C),B)
                  & r2_hidden(k7_ordinal3(A,C),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_ordinal2,d7_ordinal3,t78_ordinal3,t24_ordinal3,t26_ordinal1,t27_ordinal3,t58_ordinal2,t7_ordinal1]),
    [file(ordinal3,t80_ordinal3),interesting(0.68)]).

fof(t25_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(k14_ordinal2(A,B),k14_ordinal2(A,C))
               => r2_hidden(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_ordinal1,t50_ordinal2,t7_ordinal1]),
    [file(ordinal3,t25_ordinal3),interesting(0.67)]).

fof(t29_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k14_ordinal2(A,B) = k1_xboole_0
           => ( A = k1_xboole_0
              & B = k1_xboole_0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_ordinal3,t3_xboole_1]),
    [file(ordinal3,t29_ordinal3),interesting(0.67)]).

fof(t37_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(k15_ordinal2(A,B),k15_ordinal2(C,B))
               => r2_hidden(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_ordinal1,t58_ordinal2,t7_ordinal1]),
    [file(ordinal3,t37_ordinal3),interesting(0.67)]).

fof(t10_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( A != k1_xboole_0
       => r2_hidden(k1_xboole_0,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d8_xboole_0,t21_ordinal1]),
    [file(ordinal3,t10_ordinal3),interesting(0.65)]).

fof(t17_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( r2_hidden(A,k4_ordinal2)
       => A = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t34_ordinal1,d4_ordinal2,t2_xboole_1,d10_xboole_0]),
    [file(ordinal3,t17_ordinal3),interesting(0.65)]).

fof(t39_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( A != k1_xboole_0
           => ( r1_ordinal1(B,k15_ordinal2(B,A))
              & r1_ordinal1(B,k15_ordinal2(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_ordinal3,t33_ordinal1,d4_ordinal2,t56_ordinal2,t58_ordinal2,t59_ordinal2]),
    [file(ordinal3,t39_ordinal3),interesting(0.65)]).

fof(t69_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( k5_ordinal3(A,k1_xboole_0) = A
        & k5_ordinal3(k1_xboole_0,A) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t47_ordinal2,t2_xboole_1,d6_ordinal3,d6_ordinal3,t3_xboole_1,d6_ordinal3]),
    [file(ordinal3,t69_ordinal3),interesting(0.65)]).

fof(t81_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( A != k1_xboole_0
           => k6_ordinal3(k15_ordinal2(B,A),A) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_ordinal3,t44_ordinal2,d7_ordinal3]),
    [file(ordinal3,t81_ordinal3),interesting(0.65)]).

fof(t82_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k7_ordinal3(k15_ordinal2(A,B),B) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d7_ordinal3,t67_ordinal3,t69_ordinal3,t55_ordinal2,t81_ordinal3]),
    [file(ordinal3,t82_ordinal3),interesting(0.65)]).

fof(t2_ordinal3,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_ordinal1(A),B)
     => r1_tarski(A,B) ) ),
    inference(mizar_proof,[status(thm)],[t1_ordinal3,t1_xboole_1]),
    [file(ordinal3,t2_ordinal3),interesting(0.64)]).

fof(t49_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ~ ( r2_hidden(A,k15_ordinal2(B,C))
                  & v4_ordinal1(B)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ~ ( r2_hidden(D,B)
                          & r2_hidden(A,k15_ordinal2(D,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_ordinal2,t55_ordinal2,s3_ordinal2,t54_ordinal2,t35_ordinal2,d4_tarski,t23_ordinal1,t29_ordinal2,d5_funct_1,t23_ordinal1,t41_ordinal1,t53_ordinal2,t10_ordinal3,t44_ordinal2,t49_ordinal2,t19_ordinal1]),
    [file(ordinal3,t49_ordinal3),interesting(0.64)]).

fof(t55_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( A != k1_xboole_0
              & ! [C] : 
                  ( v3_ordinal1(C)
                 => ! [D] : 
                      ( v3_ordinal1(D)
                     => ~ ( B = k14_ordinal2(k15_ordinal2(C,A),D)
                          & r2_hidden(D,A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_ordinal2,t52_ordinal2,t10_ordinal3,t45_ordinal2,t26_ordinal1,t33_ordinal1,d10_xboole_0,t44_ordinal2,t53_ordinal2,t45_ordinal2,t10_ordinal3,t10_ordinal3,t33_ordinal1,t56_ordinal2,t59_ordinal2,d4_ordinal2,t10_ordinal3,t44_ordinal2,d8_xboole_0,t21_ordinal1,t49_ordinal3,s1_ordinal1,t49_ordinal3,t19_ordinal1,t7_ordinal1,t42_ordinal1,t10_ordinal1,t7_ordinal1,t19_ordinal1,t26_ordinal1,t30_ordinal3,t53_ordinal2,t25_ordinal3,s1_ordinal2]),
    [file(ordinal3,t55_ordinal3),interesting(0.64)]).

fof(t66_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(A,B)
               => ( ( ~ r1_ordinal1(C,A)
                    & ~ r2_hidden(C,A) )
                  | r2_hidden(k5_ordinal3(A,C),k5_ordinal3(B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal1,d6_ordinal3,t1_xboole_1,d6_ordinal3,t25_ordinal3]),
    [file(ordinal3,t66_ordinal3),interesting(0.64)]).

fof(t74_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(k14_ordinal2(A,B),C)
               => r2_hidden(B,k5_ordinal3(C,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_ordinal3,t65_ordinal3,t66_ordinal3]),
    [file(ordinal3,t74_ordinal3),interesting(0.64)]).

fof(t38_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(k15_ordinal2(A,B),k15_ordinal2(C,B))
               => ( B = k1_xboole_0
                  | r1_ordinal1(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_xboole_0,t21_ordinal1,t36_ordinal3,t37_ordinal3,d2_ordinal1]),
    [file(ordinal3,t38_ordinal3),interesting(0.64)]).

fof(t7_ordinal3,theorem,(
    ! [A] : v3_ordinal1(k3_tarski(k2_ordinal2(A))) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal2,t35_ordinal1]),
    [file(ordinal3,t7_ordinal3),interesting(0.63)]).

fof(t13_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => v3_ordinal1(k1_setfam_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_ordinal3,d6_ordinal2]),
    [file(ordinal3,t13_ordinal3),interesting(0.62)]).

fof(t18_ordinal3,theorem,(
    k4_ordinal2 = k1_tarski(k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[t23_ordinal1,t17_ordinal3,t10_ordinal1,d4_ordinal2,d1_tarski]),
    [file(ordinal3,t18_ordinal3),interesting(0.62)]).

fof(t19_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ~ ( r1_ordinal1(A,k4_ordinal2)
          & A != k1_xboole_0
          & A != k4_ordinal2 ) ) ),
    inference(mizar_proof,[status(thm)],[d8_xboole_0,t21_ordinal1,t17_ordinal3]),
    [file(ordinal3,t19_ordinal3),interesting(0.62)]).

fof(t72_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(A,B)
               => r1_ordinal1(k5_ordinal3(A,C),k5_ordinal3(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal3,t1_xboole_1,d6_ordinal3,t26_ordinal3,d6_ordinal3,t2_xboole_1]),
    [file(ordinal3,t72_ordinal3),interesting(0.62)]).

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 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_ordinal1,t57_ordinal2]),
    [file(ordinal3,t36_ordinal3),interesting(0.62)]).

fof(t12_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k6_ordinal2(k1_tarski(A)) = A ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal2,t9_ordinal3,t11_setfam_1]),
    [file(ordinal3,t12_ordinal3),interesting(0.61)]).

fof(t6_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => v3_ordinal1(k3_tarski(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_ordinal1,t35_ordinal1]),
    [file(ordinal3,t6_ordinal3),interesting(0.61)]).

fof(t75_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => r1_ordinal1(A,k14_ordinal2(B,k5_ordinal3(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal3,d6_ordinal3,t26_ordinal1,t44_ordinal2,d2_ordinal1]),
    [file(ordinal3,t75_ordinal3),interesting(0.58)]).

fof(t28_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(A,B)
               => ( r2_hidden(A,k14_ordinal2(B,C))
                  & r2_hidden(A,k14_ordinal2(C,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_ordinal3]),
    [file(ordinal3,t28_ordinal3),interesting(0.56)]).

fof(t5_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
          <=> r2_hidden(k1_ordinal1(A),k1_ordinal1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t33_ordinal1,t34_ordinal1]),
    [file(ordinal3,t5_ordinal3),interesting(0.56)]).

fof(t41_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k15_ordinal2(A,B) = k4_ordinal2
           => ( A = k4_ordinal2
              & B = k4_ordinal2 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_ordinal2,t2_xboole_1,d8_xboole_0,t21_ordinal1,t33_ordinal1,d4_ordinal2,t34_ordinal1,d4_ordinal2,t3_xboole_1,t52_ordinal2,t56_ordinal2,t57_ordinal2,t7_ordinal1,t24_ordinal1,t56_ordinal2]),
    [file(ordinal3,t41_ordinal3),interesting(0.55)]).

fof(t73_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(B,k14_ordinal2(C,A))
               => ( A = k1_xboole_0
                  | r2_hidden(k5_ordinal3(B,C),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ordinal3,t65_ordinal3,t10_ordinal3,t66_ordinal3]),
    [file(ordinal3,t73_ordinal3),interesting(0.55)]).

fof(t21_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ( ( r1_ordinal1(A,B)
                      & r1_ordinal1(C,D) )
                   => r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_ordinal2,t51_ordinal2,t1_xboole_1]),
    [file(ordinal3,t21_ordinal3),interesting(0.54)]).

fof(t23_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ( ( r1_ordinal1(A,B)
                      & r1_ordinal1(C,D) )
                   => r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t58_ordinal2,t59_ordinal2,t1_xboole_1]),
    [file(ordinal3,t23_ordinal3),interesting(0.53)]).

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)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal1,t57_ordinal2,t59_ordinal2,t22_ordinal1]),
    [file(ordinal3,t22_ordinal3),interesting(0.53)]).

fof(t51_ordinal3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k1_xboole_0 != k1_relat_1(A)
           => k8_ordinal2(k1_ordinal3(B,A)) = k14_ordinal2(B,k8_ordinal2(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal3,d2_ordinal3,t47_ordinal3]),
    [file(ordinal3,t51_ordinal3),interesting(0.52)]).

fof(t15_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k2_xboole_0(A,B) = A
            | k2_xboole_0(A,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_xboole_1]),
    [file(ordinal3,t15_ordinal3),interesting(0.51)]).

fof(t16_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k3_xboole_0(A,B) = A
            | k3_xboole_0(A,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_xboole_1]),
    [file(ordinal3,t16_ordinal3),interesting(0.51)]).

fof(t68_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
           => ( k5_ordinal3(B,A) != k1_xboole_0
              & r2_hidden(k1_xboole_0,k5_ordinal3(B,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_ordinal3,t67_ordinal3]),
    [file(ordinal3,t68_ordinal3),interesting(0.51)]).

fof(t84_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( k6_ordinal3(A,k4_ordinal2) = A
        & k7_ordinal3(A,k4_ordinal2) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t10_ordinal3,t44_ordinal2,t56_ordinal2,d7_ordinal3,t56_ordinal2,t67_ordinal3]),
    [file(ordinal3,t84_ordinal3),interesting(0.50)]).

fof(t20_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ( r2_hidden(C,D)
                   => ( ( ~ r1_ordinal1(A,B)
                        & ~ r2_hidden(A,B) )
                      | r2_hidden(k14_ordinal2(A,C),k14_ordinal2(B,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal1,t49_ordinal2,t51_ordinal2,t22_ordinal1]),
    [file(ordinal3,t20_ordinal3),interesting(0.49)]).

fof(t60_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
           => B = k14_ordinal2(A,k5_ordinal3(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal1,d6_ordinal3]),
    [file(ordinal3,t60_ordinal3),interesting(0.48)]).

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 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d8_xboole_0,t21_ordinal1,t57_ordinal2]),
    [file(ordinal3,t34_ordinal3),interesting(0.47)]).

fof(t83_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( k6_ordinal3(k1_xboole_0,A) = k1_xboole_0
        & k7_ordinal3(k1_xboole_0,A) = k1_xboole_0
        & k7_ordinal3(A,k1_xboole_0) = A ) ) ),
    inference(mizar_proof,[status(thm)],[t52_ordinal2,d7_ordinal3,t81_ordinal3,t69_ordinal3,t55_ordinal2,t69_ordinal3]),
    [file(ordinal3,t83_ordinal3),interesting(0.47)]).

fof(t35_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(A,B)
               => ( C = k1_xboole_0
                  | ( r2_hidden(A,k15_ordinal2(B,C))
                    & r2_hidden(A,k15_ordinal2(C,B)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d8_xboole_0,t21_ordinal1,t33_ordinal1,d4_ordinal2,t56_ordinal2,t58_ordinal2,t59_ordinal2]),
    [file(ordinal3,t35_ordinal3),interesting(0.46)]).

fof(t79_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ! [D] : 
                  ( v3_ordinal1(D)
                 => ( ( A = k14_ordinal2(k15_ordinal2(B,C),D)
                      & r2_hidden(D,C) )
                   => ( B = k6_ordinal3(A,C)
                      & D = k7_ordinal3(A,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_ordinal3,t65_ordinal3]),
    [file(ordinal3,t79_ordinal3),interesting(0.41)]).

fof(t52_ordinal3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(k8_ordinal2(A))
           => ( k1_xboole_0 = k1_relat_1(A)
              | B = k1_xboole_0
              | k8_ordinal2(k4_ordinal3(B,A)) = k15_ordinal2(k8_ordinal2(A),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_ordinal3,d5_ordinal3,t50_ordinal3]),
    [file(ordinal3,t52_ordinal3),interesting(0.31)]).

fof(t47_ordinal3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( k1_relat_1(A) = k1_relat_1(B)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ! [E] : 
                          ( v3_ordinal1(E)
                         => ( ( r2_hidden(D,k1_relat_1(A))
                              & E = k1_funct_1(A,D) )
                           => k1_funct_1(B,D) = k14_ordinal2(C,E) ) ) ) )
               => ( k1_xboole_0 = k1_relat_1(A)
                  | k8_ordinal2(B) = k14_ordinal2(C,k8_ordinal2(A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t23_ordinal1,t29_ordinal2,d5_funct_1,t23_ordinal1,d5_funct_1,t27_ordinal2,t49_ordinal2,t22_ordinal1,t23_ordinal1,d3_tarski,t23_ordinal1,t27_ordinal3,d5_funct_1,d2_ordinal1,t27_ordinal2,t22_ordinal1,t29_ordinal2,d5_funct_1,t23_ordinal1,d5_funct_1,t50_ordinal2,t27_ordinal2,t22_ordinal1,t42_ordinal3,t35_ordinal2,d10_xboole_0]),
    [file(ordinal3,t47_ordinal3),interesting(0.15)]).

fof(t57_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( ( r2_hidden(k4_ordinal2,A)
              & v4_ordinal1(B) )
           => ( B = k1_xboole_0
              | ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v5_ordinal1(C)
                    & v1_ordinal2(C) )
                 => ( ( k1_relat_1(C) = B
                      & ! [D] : 
                          ( v3_ordinal1(D)
                         => ( r2_hidden(D,B)
                           => k1_funct_1(C,D) = k15_ordinal2(D,A) ) ) )
                   => k15_ordinal2(B,A) = k8_ordinal2(C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_ordinal2,t10_ordinal1,t35_ordinal2,t29_ordinal2,t27_ordinal2,t33_ordinal1,t1_ordinal2,d10_xboole_0,t12_ordinal1,d5_funct_1,t23_ordinal1,t41_ordinal1,t49_ordinal2,t53_ordinal2,d5_funct_1,t48_ordinal2,t27_ordinal2,t42_ordinal1,d6_ordinal1]),
    [file(ordinal3,t57_ordinal3),interesting(0.06)]).

fof(d6_ordinal2,definition,(
    ! [A] : k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A)) ),
    file(ordinal2,d6_ordinal2),
    [interesting(0.00)]).

fof(t10_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k2_ordinal2(A) = A ) ),
    file(ordinal2,t10_ordinal2),
    [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(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(t5_setfam_1,theorem,(
    ! [A] : 
      ( r2_hidden(k1_xboole_0,A)
     => k1_setfam_1(A) = k1_xboole_0 ) ),
    file(setfam_1,t5_setfam_1),
    [interesting(0.00)]).

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

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

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

fof(d2_ordinal2,definition,(
    ! [A,B] : 
      ( B = k2_ordinal2(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ( r2_hidden(C,A)
            & v3_ordinal1(C) ) ) ) ),
    file(ordinal2,d2_ordinal2),
    [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(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(t11_setfam_1,theorem,(
    ! [A] : k1_setfam_1(k1_tarski(A)) = A ),
    file(setfam_1,t11_setfam_1),
    [interesting(0.00)]).

fof(t14_ordinal3,theorem,(
    $true ),
    file(ordinal3,t14_ordinal3),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

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

fof(t34_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,k1_ordinal1(B))
          <=> r1_ordinal1(A,B) ) ) ) ),
    file(ordinal1,t34_ordinal1),
    [interesting(0.00)]).

fof(d4_ordinal2,definition,(
    k4_ordinal2 = k1_ordinal1(k1_xboole_0) ),
    file(ordinal2,d4_ordinal2),
    [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(t10_ordinal1,theorem,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    [interesting(0.00)]).

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

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

fof(t49_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(A,B)
               => r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B)) ) ) ) ) ),
    file(ordinal2,t49_ordinal2),
    [interesting(0.00)]).

fof(t51_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(A,B)
               => r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,C)) ) ) ) ) ),
    file(ordinal2,t51_ordinal2),
    [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(t50_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(A,B)
               => r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B)) ) ) ) ) ),
    file(ordinal2,t50_ordinal2),
    [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(t58_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(A,B)
               => r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,C)) ) ) ) ) ),
    file(ordinal2,t58_ordinal2),
    [interesting(0.00)]).

fof(t59_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal1(A,B)
               => r1_ordinal1(k15_ordinal2(C,A),k15_ordinal2(C,B)) ) ) ) ) ),
    file(ordinal2,t59_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(t47_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k14_ordinal2(k1_xboole_0,A) = A ) ),
    file(ordinal2,t47_ordinal2),
    [interesting(0.00)]).

fof(t57_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(B,C)
               => ( A = k1_xboole_0
                  | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A)) ) ) ) ) ) ),
    file(ordinal2,t57_ordinal2),
    [interesting(0.00)]).

fof(t33_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
          <=> r1_ordinal1(k1_ordinal1(A),B) ) ) ) ),
    file(ordinal1,t33_ordinal1),
    [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(t3_ordinal3,theorem,(
    $true ),
    file(ordinal3,t3_ordinal3),
    [interesting(0.00)]).

fof(t40_ordinal3,theorem,(
    $true ),
    file(ordinal3,t40_ordinal3),
    [interesting(0.00)]).

fof(t55_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k15_ordinal2(A,k1_xboole_0) = k1_xboole_0 ) ),
    file(ordinal2,t55_ordinal2),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.00)]).

fof(t52_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k15_ordinal2(k1_xboole_0,A) = k1_xboole_0 ) ),
    file(ordinal2,t52_ordinal2),
    [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(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(t43_ordinal3,theorem,(
    $true ),
    file(ordinal3,t43_ordinal3),
    [interesting(0.00)]).

fof(t44_ordinal3,theorem,(
    $true ),
    file(ordinal3,t44_ordinal3),
    [interesting(0.00)]).

fof(t45_ordinal3,theorem,(
    $true ),
    file(ordinal3,t45_ordinal3),
    [interesting(0.00)]).

fof(t46_ordinal3,theorem,(
    $true ),
    file(ordinal3,t46_ordinal3),
    [interesting(0.00)]).

fof(t4_ordinal3,theorem,(
    $true ),
    file(ordinal3,t4_ordinal3),
    [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(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(t53_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B) ) ) ),
    file(ordinal2,t53_ordinal2),
    [interesting(0.00)]).

fof(s3_ordinal2,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & v1_ordinal2(A)
      & k1_relat_1(A) = f1_s3_ordinal2
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(B,f1_s3_ordinal2)
           => k1_funct_1(A,B) = f2_s3_ordinal2(B) ) ) ) ),
    file(ordinal2,s3_ordinal2),
    [interesting(0.00)]).

fof(t54_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => ( A = k1_xboole_0
              | ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v5_ordinal1(C)
                    & v1_ordinal2(C) )
                 => ( ( k1_relat_1(C) = A
                      & ! [D] : 
                          ( v3_ordinal1(D)
                         => ( r2_hidden(D,A)
                           => k1_funct_1(C,D) = k15_ordinal2(D,B) ) ) )
                   => k15_ordinal2(A,B) = k3_tarski(k8_ordinal2(C)) ) ) ) ) ) ) ),
    file(ordinal2,t54_ordinal2),
    [interesting(0.00)]).

fof(t35_ordinal2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A))
        & k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)) ) ) ),
    file(ordinal2,t35_ordinal2),
    [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(t29_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : ~ ( r2_hidden(A,k7_ordinal2(B))
          & ! [C] : 
              ( v3_ordinal1(C)
             => ~ ( r2_hidden(C,B)
                  & r1_ordinal1(A,C) ) ) ) ) ),
    file(ordinal2,t29_ordinal2),
    [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(t41_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k1_ordinal1(B),A) ) ) ) ) ),
    file(ordinal1,t41_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(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(t42_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ ( ~ v4_ordinal1(A)
            & ! [B] : 
                ( v3_ordinal1(B)
               => A != k1_ordinal1(B) ) )
        & ~ ( ? [B] : 
                ( v3_ordinal1(B)
                & A = k1_ordinal1(B) )
            & v4_ordinal1(A) ) ) ) ),
    file(ordinal1,t42_ordinal1),
    [interesting(0.00)]).

fof(t46_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => ( A = k1_xboole_0
              | ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v5_ordinal1(C)
                    & v1_ordinal2(C) )
                 => ( ( k1_relat_1(C) = A
                      & ! [D] : 
                          ( v3_ordinal1(D)
                         => ( r2_hidden(D,A)
                           => k1_funct_1(C,D) = k14_ordinal2(B,D) ) ) )
                   => k14_ordinal2(B,A) = k8_ordinal2(C) ) ) ) ) ) ) ),
    file(ordinal2,t46_ordinal2),
    [interesting(0.00)]).

fof(t28_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(C,B)
               => r2_hidden(C,A) ) )
         => r1_ordinal1(k7_ordinal2(B),A) ) ) ),
    file(ordinal2,t28_ordinal2),
    [interesting(0.00)]).

fof(s1_ordinal2,theorem,
    ( ( p1_s1_ordinal2(k1_xboole_0)
      & ! [A] : 
          ( v3_ordinal1(A)
         => ( p1_s1_ordinal2(A)
           => p1_s1_ordinal2(k1_ordinal1(A)) ) )
      & ! [A] : 
          ( v3_ordinal1(A)
         => ( ( v4_ordinal1(A)
              & ! [B] : 
                  ( v3_ordinal1(B)
                 => ( r2_hidden(B,A)
                   => p1_s1_ordinal2(B) ) ) )
           => ( A = k1_xboole_0
              | p1_s1_ordinal2(A) ) ) ) )
   => ! [A] : 
        ( v3_ordinal1(A)
       => p1_s1_ordinal2(A) ) ),
    file(ordinal2,s1_ordinal2),
    [interesting(0.00)]).

fof(t27_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r2_hidden(A,k7_ordinal2(B)) ) ) ),
    file(ordinal2,t27_ordinal2),
    [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(t30_ordinal2,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_ordinal1(k7_ordinal2(A),k7_ordinal2(B)) ) ),
    file(ordinal2,t30_ordinal2),
    [interesting(0.00)]).

fof(d2_ordinal3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v5_ordinal1(C)
                & v1_ordinal2(C) )
             => ( C = k1_ordinal3(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(B)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,k1_relat_1(B))
                       => k1_funct_1(C,D) = k14_ordinal2(A,k1_funct_1(B,D)) ) ) ) ) ) ) ) ),
    file(ordinal3,d2_ordinal3),
    [interesting(0.00)]).

fof(d5_ordinal3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v5_ordinal1(C)
                & v1_ordinal2(C) )
             => ( C = k4_ordinal3(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(B)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,k1_relat_1(B))
                       => k1_funct_1(C,D) = k15_ordinal2(k1_funct_1(B,D),A) ) ) ) ) ) ) ) ),
    file(ordinal3,d5_ordinal3),
    [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(t50_ordinal3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( k1_relat_1(A) = k1_relat_1(B)
                  & v4_ordinal1(k8_ordinal2(A))
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ! [E] : 
                          ( v3_ordinal1(E)
                         => ( ( r2_hidden(D,k1_relat_1(A))
                              & E = k1_funct_1(A,D) )
                           => k1_funct_1(B,D) = k15_ordinal2(E,C) ) ) ) )
               => ( k1_xboole_0 = k1_relat_1(A)
                  | C = k1_xboole_0
                  | k8_ordinal2(B) = k15_ordinal2(k8_ordinal2(A),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t23_ordinal1,t29_ordinal2,d5_funct_1,t23_ordinal1,d5_funct_1,t27_ordinal2,t57_ordinal2,t22_ordinal1,t35_ordinal2,d3_tarski,t23_ordinal1,t49_ordinal3,t29_ordinal2,d5_funct_1,t23_ordinal1,d5_funct_1,t27_ordinal2,t58_ordinal2,t19_ordinal1,d10_xboole_0]),
    [file(ordinal3,t50_ordinal3),interesting(0.00)]).

fof(d6_ordinal1,definition,(
    ! [A] : 
      ( v4_ordinal1(A)
    <=> A = k3_tarski(A) ) ),
    file(ordinal1,d6_ordinal1),
    [interesting(0.00)]).

fof(t2_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k3_tarski(k1_ordinal1(A)) = A ) ),
    file(ordinal2,t2_ordinal2),
    [interesting(0.00)]).

fof(t48_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A) ) ),
    file(ordinal2,t48_ordinal2),
    [interesting(0.00)]).

fof(t1_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
          <=> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B)) ) ) ) ),
    file(ordinal2,t1_ordinal2),
    [interesting(0.00)]).

fof(t12_ordinal1,theorem,(
    ! [A,B] : 
      ( k1_ordinal1(A) = k1_ordinal1(B)
     => A = B ) ),
    file(ordinal1,t12_ordinal1),
    [interesting(0.00)]).

fof(t59_ordinal3,theorem,(
    $true ),
    file(ordinal3,t59_ordinal3),
    [interesting(0.00)]).

fof(d6_ordinal3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_ordinal1(B,A)
                 => ( C = k5_ordinal3(A,B)
                  <=> A = k14_ordinal2(B,C) ) )
                & ( ~ r1_ordinal1(B,A)
                 => ( C = k5_ordinal3(A,B)
                  <=> C = k1_xboole_0 ) ) ) ) ) ) ),
    file(ordinal3,d6_ordinal3),
    [interesting(0.00)]).

fof(t61_ordinal3,theorem,(
    $true ),
    file(ordinal3,t61_ordinal3),
    [interesting(0.00)]).

fof(t62_ordinal3,theorem,(
    $true ),
    file(ordinal3,t62_ordinal3),
    [interesting(0.00)]).

fof(t63_ordinal3,theorem,(
    $true ),
    file(ordinal3,t63_ordinal3),
    [interesting(0.00)]).

fof(t64_ordinal3,theorem,(
    $true ),
    file(ordinal3,t64_ordinal3),
    [interesting(0.00)]).

fof(t35_ordinal1,theorem,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,A)
         => v3_ordinal1(B) )
     => v3_ordinal1(k3_tarski(A)) ) ),
    file(ordinal1,t35_ordinal1),
    [interesting(0.00)]).

fof(d7_ordinal3,definition,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( B != k1_xboole_0
                 => ( C = k6_ordinal3(A,B)
                  <=> ? [D] : 
                        ( v3_ordinal1(D)
                        & A = k14_ordinal2(k15_ordinal2(C,B),D)
                        & r2_hidden(D,B) ) ) )
                & ( B = k1_xboole_0
                 => ( C = k6_ordinal3(A,B)
                  <=> C = k1_xboole_0 ) ) ) ) ) ) ),
    file(ordinal3,d7_ordinal3),
    [interesting(0.00)]).