fof(l15_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r2_wellord2(k2_finseq_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[t4_finseq_1,t11_finseq_1,t52_card_1,d1_ordinal1,t48_card_1,t3_xboole_0,d1_tarski,t3_xboole_0,d1_tarski,t38_nat_1,t3_finseq_1,t58_card_1,s1_nat_1]),
    [file(finseq_1,l15_finseq_1),interesting(1.00)]).

fof(t75_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r2_wellord2(k2_finseq_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[l15_finseq_1]),
    [file(finseq_1,t75_finseq_1),interesting(0.93)]).

fof(l16_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_card_1(k2_finseq_1(A)) = k1_card_1(A) ) ),
    inference(mizar_proof,[status(thm)],[l15_finseq_1,t21_card_1]),
    [file(finseq_1,l16_finseq_1),interesting(0.90)]).

fof(t77_finseq_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ r2_wellord2(A,k2_finseq_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t74_card_1,l15_finseq_1,t22_wellord2]),
    [file(finseq_1,t77_finseq_1),interesting(0.87)]).

fof(t8_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_finseq_1(A) = k2_finseq_1(B)
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_finseq_1,t1_xreal_1]),
    [file(finseq_1,t8_finseq_1),interesting(0.81)]).

fof(t60_finseq_1,theorem,(
    ! [A,B,C] : 
      ( k11_finseq_1(A,B,C) = k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C))
      & k11_finseq_1(A,B,C) = k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) ) ),
    inference(mizar_proof,[status(thm)],[t45_finseq_1]),
    [file(finseq_1,t60_finseq_1),interesting(0.80)]).

fof(t65_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k2_relat_1(A) = k2_relat_1(B)
              & v2_funct_1(A)
              & v2_funct_1(B) )
           => k3_finseq_1(A) = k3_finseq_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t64_relat_1,t44_finseq_1,t55_finseq_1,d1_tarski,d2_xboole_0,d5_funct_1,d3_finseq_1,t3_finseq_1,t28_nat_1,t3_finseq_1,t28_nat_1,t19_finseq_1,s1_finseq_1,t37_nat_1,t2_xreal_1,t21_finseq_1,d3_tarski,t44_finseq_1,t144_relat_1,t148_relat_1,d5_funct_1,t70_funct_1,d3_finseq_1,t3_finseq_1,t31_xreal_1,t7_finseq_1,t21_finseq_1,d3_finseq_1,d8_funct_1,d1_tarski,d4_xboole_0,d5_funct_1,t37_nat_1,t3_finseq_1,t9_xreal_1,d3_finseq_1,d5_funct_1,t3_finseq_1,d8_funct_1,d1_tarski,d4_xboole_0,d2_xboole_0,d10_xboole_0,d3_tarski,d4_xboole_0,d5_funct_1,d3_finseq_1,d4_xboole_0,d1_tarski,t28_nat_1,t59_nat_1,t3_finseq_1,t8_xreal_1,d5_funct_1,t3_finseq_1,t38_nat_1,t21_finseq_1,t70_funct_1,d5_funct_1,d5_real_1,d2_xboole_0,t44_finseq_1,t33_finseq_1,d3_tarski,t76_funct_1,d5_funct_1,d3_finseq_1,t59_finseq_1,t70_funct_1,t3_finseq_1,t31_xreal_1,t3_finseq_1,t2_xreal_1,t5_finseq_1,t57_finseq_1,d7_finseq_1,d8_funct_1,d1_tarski,d4_xboole_0,d10_xboole_0,d3_tarski,d4_xboole_0,t44_finseq_1,d1_tarski,d2_xboole_0,t55_finseq_1,d1_tarski,d8_funct_1,t84_funct_1,d7_finseq_1,d8_funct_1,d7_finseq_1,t70_funct_1,t76_funct_1,t3_finseq_1,t37_nat_1,t3_finseq_1,t9_xreal_1,d3_finseq_1,t21_finseq_1,t3_finseq_1,t31_xreal_1,t2_xreal_1,t37_nat_1,d8_funct_1,d7_finseq_1,t70_funct_1,t76_funct_1,t3_finseq_1,t37_nat_1,t3_finseq_1,t9_xreal_1,d3_finseq_1,t21_finseq_1,t3_finseq_1,t31_xreal_1,t2_xreal_1,t37_nat_1,d8_funct_1,d7_finseq_1,t3_finseq_1,t37_nat_1,t3_finseq_1,t9_xreal_1,d3_finseq_1,d8_funct_1,t38_finseq_1,t35_finseq_1,t56_finseq_1,d3_finseq_1,d3_finseq_1,d7_finseq_1,t70_funct_1,t4_finseq_1,t55_finseq_1,d1_tarski,t59_finseq_1,t38_finseq_1,t56_finseq_1,t35_finseq_1,d7_finseq_1,t35_finseq_1,t35_finseq_1,t57_finseq_1,t35_finseq_1,t35_finseq_1,t57_finseq_1,t84_funct_1,s3_finseq_1]),
    [file(finseq_1,t65_finseq_1),interesting(0.80)]).

fof(t76_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_card_1(k2_finseq_1(A)) = k1_card_1(A) ) ),
    inference(mizar_proof,[status(thm)],[l16_finseq_1]),
    [file(finseq_1,t76_finseq_1),interesting(0.80)]).

fof(t7_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
          <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t3_finseq_1,t2_xreal_1,t5_finseq_1,t3_finseq_1]),
    [file(finseq_1,t7_finseq_1),interesting(0.78)]).

fof(t29_finseq_1,theorem,(
    ! [A] : m2_finseq_1(k1_xboole_0,A) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d4_finseq_1]),
    [file(finseq_1,t29_finseq_1),interesting(0.78)]).

fof(t63_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( A != k1_xboole_0
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ! [C] : A != k7_finseq_1(B,k9_finseq_1(C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l32_finseq_1,t22_nat_1,t19_finseq_1,t90_relat_1,d3_finseq_1,t29_nat_1,t7_finseq_1,t28_xboole_1,d3_finseq_1,t35_finseq_1,t56_finseq_1,d3_finseq_1,d3_finseq_1,d3_finseq_1,t11_finseq_1,t70_funct_1,d7_finseq_1,d8_finseq_1,d1_tarski,d3_finseq_1,d7_finseq_1,d8_finseq_1,d1_tarski,d2_xboole_0,t9_funct_1]),
    [file(finseq_1,t63_finseq_1),interesting(0.78)]).

fof(t5_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( A = 0
        | r2_hidden(A,k2_finseq_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_nat_1,d21_ordinal2,t29_nat_1]),
    [file(finseq_1,t5_finseq_1),interesting(0.76)]).

fof(t23_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_finseq_1,d4_finseq_1,t76_funct_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_1,t23_finseq_1),interesting(0.75)]).

fof(t73_finseq_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & A = k2_relat_1(B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_finset_1,t2_xcmplx_1,t3_finseq_1,t28_nat_1,s2_funct_1,t30_axioms,d3_tarski,d5_funct_1,t3_finseq_1,t38_nat_1,d10_xboole_0,d3_tarski,t29_nat_1,t38_nat_1,d5_funct_1,t46_relat_1,d2_finseq_1,t47_relat_1,d2_finseq_1,t30_axioms,s2_funct_1,d1_finset_1,d3_tarski,d5_funct_1,t29_nat_1,t38_nat_1,d10_xboole_0,d3_tarski,t3_finseq_1,t28_nat_1,t3_finseq_1,t38_nat_1,d5_funct_1,t47_relat_1,t46_relat_1]),
    [file(finseq_1,t73_finseq_1),interesting(0.74)]).

fof(t83_finseq_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k13_finseq_1(A),k13_finseq_1(B)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d11_finseq_1,d4_finseq_1,t1_xboole_1,d4_finseq_1,d11_finseq_1]),
    [file(finseq_1,t83_finseq_1),interesting(0.74)]).

fof(l60_finseq_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k1_tarski(k4_tarski(A,B)))
      & v1_funct_1(k1_tarski(k4_tarski(A,B))) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_tarski,t33_zfmisc_1,t2_funct_1]),
    [file(finseq_1,l60_finseq_1),interesting(0.72)]).

fof(t43_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,t41_finseq_1,d7_finseq_1,d5_funct_1,d3_tarski]),
    [file(finseq_1,t43_finseq_1),interesting(0.72)]).

fof(t66_finseq_1,theorem,(
    ! [A] : r2_hidden(k1_xboole_0,k13_finseq_1(A)) ),
    inference(mizar_proof,[status(thm)],[d11_finseq_1]),
    [file(finseq_1,t66_finseq_1),interesting(0.72)]).

fof(l32_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A = k1_xboole_0
      <=> k3_finseq_1(A) = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[t5_finseq_1,d3_finseq_1,d4_funct_1,d3_finseq_1,t4_finseq_1,d1_relat_1,d4_relat_1]),
    [file(finseq_1,l32_finseq_1),interesting(0.71)]).

fof(t39_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_nat_1,t7_finseq_1,d7_finseq_1,d3_finseq_1]),
    [file(finseq_1,t39_finseq_1),interesting(0.71)]).

fof(t42_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,t39_finseq_1,d7_finseq_1,d5_funct_1,d3_tarski]),
    [file(finseq_1,t42_finseq_1),interesting(0.71)]).

fof(t44_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,d7_finseq_1,t3_finseq_1,t36_finseq_1,t28_nat_1,t9_xreal_1,t8_xreal_1,d3_finseq_1,d5_funct_1,t26_nat_1,d3_finseq_1,d7_finseq_1,d5_funct_1,d2_xboole_0,d3_tarski,t42_finseq_1,t43_finseq_1,t8_xboole_1,d10_xboole_0]),
    [file(finseq_1,t44_finseq_1),interesting(0.71)]).

fof(l28_finseq_1,theorem,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_funct_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t11_relset_1]),
    [file(finseq_1,l28_finseq_1),interesting(0.70)]).

fof(t24_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ? [C] : 
              ( m2_finseq_1(C,B)
              & k3_finseq_1(C) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t19_funcop_1,d2_finseq_1,t19_funcop_1,t37_zfmisc_1,t1_xboole_1,d4_finseq_1,d3_finseq_1]),
    [file(finseq_1,t24_finseq_1),interesting(0.70)]).

fof(t62_finseq_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D)
        & v1_finseq_1(D) )
     => ( D = k11_finseq_1(A,B,C)
      <=> ( k3_finseq_1(D) = 3
          & k1_funct_1(D,1) = A
          & k1_funct_1(D,2) = B
          & k1_funct_1(D,3) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_finseq_1,t61_finseq_1,t56_finseq_1,d1_tarski,d8_finseq_1,t4_finseq_1,t60_finseq_1,d7_finseq_1,d8_finseq_1,t61_finseq_1,d3_finseq_1,d7_finseq_1,t61_finseq_1,d8_finseq_1,t4_finseq_1,t61_finseq_1,d7_finseq_1,d8_finseq_1,d3_finseq_1,t61_finseq_1,t56_finseq_1,t61_finseq_1,d3_finseq_1,t61_finseq_1,t61_finseq_1,t4_finseq_1,d2_tarski,d8_finseq_1,t4_finseq_1,d1_tarski,t61_finseq_1,d8_finseq_1,d7_finseq_1]),
    [file(finseq_1,t62_finseq_1),interesting(0.70)]).

fof(t33_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d7_finseq_1,t37_nat_1,t9_finseq_1,d7_finseq_1,t68_funct_1]),
    [file(finseq_1,t33_finseq_1),interesting(0.70)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2]),
    [file(finseq_1,t3_finseq_1),interesting(0.69)]).

fof(t9_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
           => k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_finseq_1,t28_xboole_1]),
    [file(finseq_1,t9_finseq_1),interesting(0.69)]).

fof(t14_finseq_1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[d2_finseq_1,t4_finseq_1]),
    [file(finseq_1,t14_finseq_1),interesting(0.69)]).

fof(l61_finseq_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k1_tarski(k4_tarski(C,D)))
     => ( A = C
        & B = D ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t33_zfmisc_1]),
    [file(finseq_1,l61_finseq_1),interesting(0.68)]).

fof(t11_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,1))) = k2_finseq_1(k2_xcmplx_0(A,1)) ) ),
    inference(mizar_proof,[status(thm)],[t9_xreal_1,t7_finseq_1,d3_tarski,d2_xboole_0,d1_tarski,t5_finseq_1,d10_xboole_0,d3_tarski,t3_finseq_1,t26_nat_1,d1_tarski,d2_xboole_0]),
    [file(finseq_1,t11_finseq_1),interesting(0.68)]).

fof(t50_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_finseq_1(k7_finseq_1(A,B),C)
             => ( m2_finseq_1(A,C)
                & m2_finseq_1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t44_finseq_1,t7_xboole_1,t1_xboole_1,d4_finseq_1,t7_xboole_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_1,t50_finseq_1),interesting(0.68)]).

fof(s3_finseq_1,theorem,
    ( ( p1_s3_finseq_1(k1_xboole_0)
      & ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A)
            & v1_finseq_1(A) )
         => ! [B] : 
              ( p1_s3_finseq_1(A)
             => p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))) ) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => p1_s3_finseq_1(A) ) ),
    inference(mizar_proof,[status(thm)],[s1_real_1,l32_finseq_1,l32_finseq_1,t63_finseq_1,t35_finseq_1,t56_finseq_1,s1_nat_1]),
    [file(finseq_1,s3_finseq_1),interesting(0.68)]).

fof(t47_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t35_finseq_1,l32_finseq_1,d3_finseq_1,d7_finseq_1,t17_finseq_1,d3_finseq_1,t35_finseq_1,l32_finseq_1,d3_finseq_1,l32_finseq_1,d7_finseq_1,t17_finseq_1]),
    [file(finseq_1,t47_finseq_1),interesting(0.66)]).

fof(t68_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d12_finseq_1]),
    [file(finseq_1,t68_finseq_1),interesting(0.66)]).

fof(t74_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_wellord2(k2_finseq_1(A),k2_finseq_1(B))
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[s5_nat_1,d4_wellord2,t4_finseq_1,t65_relat_1,t8_finseq_1,t22_nat_1,t4_finseq_1,t65_relat_1,t8_finseq_1,t22_nat_1,t5_finseq_1,t61_card_1,t38_nat_1,t3_finseq_1,d3_tarski,d3_xboole_0,d1_tarski,d3_tarski,d3_xboole_0,d1_tarski,t11_finseq_1,t3_xboole_1,t40_xboole_1,d7_xboole_0,t83_xboole_1]),
    [file(finseq_1,t74_finseq_1),interesting(0.66)]).

fof(t19_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( v1_relat_1(k7_relat_1(B,k2_finseq_1(A)))
            & v1_funct_1(k7_relat_1(B,k2_finseq_1(A)))
            & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t90_relat_1,d3_finseq_1,t9_finseq_1,d2_finseq_1]),
    [file(finseq_1,t19_finseq_1),interesting(0.64)]).

fof(t45_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_finseq_1,t35_finseq_1,t35_finseq_1,t39_finseq_1,d7_finseq_1,d7_finseq_1,t41_finseq_1,d7_finseq_1,d7_finseq_1,d7_finseq_1,t38_finseq_1,t35_finseq_1,d7_finseq_1,d7_finseq_1,d7_finseq_1]),
    [file(finseq_1,t45_finseq_1),interesting(0.64)]).

fof(t26_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A = k1_xboole_0
      <=> k4_finseq_1(A) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t60_relat_1,t64_relat_1]),
    [file(finseq_1,t26_finseq_1),interesting(0.63)]).

fof(t27_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t60_relat_1,t64_relat_1]),
    [file(finseq_1,t27_finseq_1),interesting(0.63)]).

fof(t35_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_finseq_1,d3_finseq_1]),
    [file(finseq_1,t35_finseq_1),interesting(0.62)]).

fof(t79_finseq_1,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ! [C] : 
          ( v4_ordinal2(C)
         => ( r1_xreal_0(k3_finseq_1(B),C)
           => k16_finseq_1(A,B,C) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_finseq_1,d3_finseq_1,t97_relat_1]),
    [file(finseq_1,t79_finseq_1),interesting(0.62)]).

fof(t61_finseq_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_finseq_1,t56_finseq_1,t56_finseq_1,d1_tarski,d8_finseq_1,t4_finseq_1,d7_finseq_1,d8_finseq_1,d8_finseq_1,t4_finseq_1,t56_finseq_1,d7_finseq_1,d8_finseq_1,d3_finseq_1,t56_finseq_1,t56_finseq_1,d8_finseq_1,t4_finseq_1,d1_tarski,d8_finseq_1,d8_finseq_1,t4_finseq_1,t56_finseq_1,d1_tarski,d8_finseq_1,d1_tarski,d7_finseq_1]),
    [file(finseq_1,t61_finseq_1),interesting(0.61)]).

fof(t32_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( A = k6_finseq_1(B)
        <=> k3_finseq_1(A) = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[l32_finseq_1]),
    [file(finseq_1,t32_finseq_1),interesting(0.60)]).

fof(t6_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ),
    inference(mizar_proof,[status(thm)],[t5_finseq_1]),
    [file(finseq_1,t6_finseq_1),interesting(0.60)]).

fof(t80_finseq_1,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ! [C] : 
          ( v4_ordinal2(C)
         => ( r1_xreal_0(C,k3_finseq_1(B))
           => k3_finseq_1(k16_finseq_1(A,B,C)) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t7_finseq_1,d3_finseq_1,t91_relat_1,d3_finseq_1]),
    [file(finseq_1,t80_finseq_1),interesting(0.60)]).

fof(t25_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) = 0
      <=> A = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[l32_finseq_1]),
    [file(finseq_1,t25_finseq_1),interesting(0.59)]).

fof(t78_finseq_1,theorem,
    ( ! [A] : 
        ( v4_ordinal2(A)
       => k4_card_1(k2_finseq_1(A)) = A )
    & ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( k4_card_1(A) = A
          & k4_card_1(k1_card_1(A)) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,l15_finseq_1,t81_card_1,d11_card_1,l15_finseq_1,t81_card_1,d11_card_1]),
    [file(finseq_1,t78_finseq_1),interesting(0.58)]).

fof(t10_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B))
           => r1_xreal_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_finseq_1,t8_finseq_1]),
    [file(finseq_1,t10_finseq_1),interesting(0.57)]).

fof(t57_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d8_finseq_1]),
    [file(finseq_1,t57_finseq_1),interesting(0.57)]).

fof(t12_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,1)),k1_tarski(k2_xcmplx_0(A,1))) ) ),
    inference(mizar_proof,[status(thm)],[t11_finseq_1,d7_xboole_0,d3_xboole_0,d3_xboole_0,d1_tarski,t3_finseq_1,t31_xreal_1,t88_xboole_1]),
    [file(finseq_1,t12_finseq_1),interesting(0.56)]).

fof(t48_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k7_finseq_1(A,B) = k1_xboole_0
           => ( A = k1_xboole_0
              & B = k1_xboole_0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l32_finseq_1,t35_finseq_1,t23_nat_1,l32_finseq_1]),
    [file(finseq_1,t48_finseq_1),interesting(0.56)]).

fof(t56_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t55_finseq_1]),
    [file(finseq_1,t56_finseq_1),interesting(0.56)]).

fof(t59_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A ) ),
    inference(mizar_proof,[status(thm)],[d8_finseq_1,d7_finseq_1,d8_finseq_1]),
    [file(finseq_1,t59_finseq_1),interesting(0.54)]).

fof(t72_finseq_1,theorem,(
    ! [A] : 
      ( ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & r1_tarski(A,k2_finseq_1(B)) )
     => ( k14_finseq_1(A) = k1_xboole_0
      <=> A = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d13_finseq_1,d13_finseq_1,t4_finseq_1,t65_relat_1,d3_finseq_1,l32_finseq_1]),
    [file(finseq_1,t72_finseq_1),interesting(0.54)]).

fof(t81_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r2_hidden(B,k2_finseq_1(A))
               => r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_finseq_1,t29_nat_1,t2_xreal_1,t9_xreal_1,t3_finseq_1]),
    [file(finseq_1,t81_finseq_1),interesting(0.54)]).

fof(t58_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ),
    inference(mizar_proof,[status(thm)],[d8_finseq_1,d7_finseq_1,d8_finseq_1]),
    [file(finseq_1,t58_finseq_1),interesting(0.53)]).

fof(t55_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_finseq_1,d8_finseq_1,t4_finseq_1,t14_funct_1,d8_finseq_1,d5_funct_1,d1_tarski,d8_finseq_1]),
    [file(finseq_1,t55_finseq_1),interesting(0.53)]).

fof(t71_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => k2_relat_1(k14_finseq_1(k1_relat_1(A))) = k1_relat_1(A) ) ),
    inference(mizar_proof,[status(thm)],[d12_finseq_1,d13_finseq_1]),
    [file(finseq_1,t71_finseq_1),interesting(0.53)]).

fof(t84_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(A,B)
           => r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_card_1,t56_card_1]),
    [file(finseq_1,t84_finseq_1),interesting(0.52)]).

fof(s4_finseq_1,theorem,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finseq_1(C)
          & r2_hidden(C,k13_finseq_1(f1_s4_finseq_1))
          & p1_s4_finseq_1(C)
          & B = C ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0]),
    [file(finseq_1,s4_finseq_1),interesting(0.45)]).

fof(t20_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(k2_relat_1(B),k1_relat_1(A))
           => ( v1_relat_1(k5_relat_1(B,A))
              & v1_funct_1(k5_relat_1(B,A))
              & v1_finseq_1(k5_relat_1(B,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t46_relat_1,d3_finseq_1,d2_finseq_1]),
    [file(finseq_1,t20_finseq_1),interesting(0.44)]).

fof(t15_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ~ ( ? [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
              & r1_tarski(k1_relat_1(A),k2_finseq_1(B)) )
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ~ r1_tarski(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d2_finseq_1,d3_relat_1,d4_relat_1,d4_funct_1,t8_funct_1]),
    [file(finseq_1,t15_finseq_1),interesting(0.43)]).

fof(t41_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(B))
               => r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_finseq_1]),
    [file(finseq_1,t41_finseq_1),interesting(0.43)]).

fof(t21_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r1_xreal_0(A,k3_finseq_1(B))
                  & C = k7_relat_1(B,k2_finseq_1(A)) )
               => ( k3_finseq_1(C) = A
                  & k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t7_finseq_1,d3_finseq_1,t91_relat_1,d3_finseq_1]),
    [file(finseq_1,t21_finseq_1),interesting(0.41)]).

fof(t40_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ~ ( r2_hidden(A,k4_finseq_1(B))
              & ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( D = A
                      & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t3_finseq_1,t29_nat_1,t2_xreal_1,t9_xreal_1,d7_finseq_1]),
    [file(finseq_1,t40_finseq_1),interesting(0.37)]).

fof(t38_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B)))
                  & ~ r2_hidden(C,k4_finseq_1(A))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_finseq_1(B))
                          & C = k1_nat_1(k3_finseq_1(A),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t35_finseq_1,t3_finseq_1,t26_nat_1,d3_finseq_1,t28_nat_1,t3_finseq_1,t8_xreal_1,t29_nat_1,d3_finseq_1]),
    [file(finseq_1,t38_finseq_1),interesting(0.30)]).

fof(t36_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( r1_xreal_0(k1_nat_1(k3_finseq_1(A),1),C)
                  & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) )
               => k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_nat_1,t21_xreal_1,t22_xreal_1,d3_finseq_1,d7_finseq_1]),
    [file(finseq_1,t36_finseq_1),interesting(0.28)]).

fof(t37_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B)))
               => ( r1_xreal_0(C,k3_finseq_1(A))
                  | k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_nat_1,t35_finseq_1,t36_finseq_1]),
    [file(finseq_1,t37_finseq_1),interesting(0.25)]).

fof(t16_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ~ ( r2_hidden(A,B)
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(B))
                  & A = k4_tarski(C,k1_funct_1(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_relat_1,t8_funct_1,t8_funct_1]),
    [file(finseq_1,t16_finseq_1),interesting(0.24)]).

fof(s1_finseq_1,theorem,
    ( ( ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B,C] : 
              ( ( r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))
                & p1_s1_finseq_1(A,B)
                & p1_s1_finseq_1(A,C) )
             => B = C ) )
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))
              & ! [B] : ~ p1_s1_finseq_1(A,B) ) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f1_s1_finseq_1))
             => p1_s1_finseq_1(B,k1_funct_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s2_funct_1,d2_finseq_1]),
    [file(finseq_1,s1_finseq_1),interesting(0.14)]).

fof(t85_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(1,C)
                  & r1_xreal_0(C,k3_finseq_1(A)) )
               => k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d7_finseq_1]),
    [file(finseq_1,t85_finseq_1),interesting(0.14)]).

fof(s2_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A)
      & k3_finseq_1(A) = f1_s2_finseq_1
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(f1_s2_finseq_1))
           => k1_funct_1(A,B) = f2_s2_finseq_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d2_finseq_1,d3_finseq_1]),
    [file(finseq_1,s2_finseq_1),interesting(0.12)]).

fof(t18_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t3_finseq_1,t9_funct_1]),
    [file(finseq_1,t18_finseq_1),interesting(0.12)]).

fof(t86_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(1,C)
                  & r1_xreal_0(C,k3_finseq_1(B)) )
               => k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_xreal_1,t36_finseq_1]),
    [file(finseq_1,t86_finseq_1),interesting(0.07)]).

fof(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

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

fof(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(t2_funct_1,theorem,(
    ! [A] : 
      ( ( ! [B] : ~ ( r2_hidden(B,A)
            & ! [C,D] : k4_tarski(C,D) != B )
        & ! [B,C,D] : 
            ( ( r2_hidden(k4_tarski(B,C),A)
              & r2_hidden(k4_tarski(B,D),A) )
           => C = D ) )
     => ( v1_relat_1(A)
        & v1_funct_1(A) ) ) ),
    file(funct_1,t2_funct_1),
    [interesting(0.00)]).

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

fof(d2_finseq_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ),
    file(finseq_1,d2_finseq_1),
    [interesting(0.00)]).

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

fof(s1_xboole_0,theorem,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,f1_s1_xboole_0)
        & p1_s1_xboole_0(B) ) ) ),
    file(xboole_0,s1_xboole_0),
    [interesting(0.00)]).

fof(s1_wellord2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_wellord2)
        & ! [B] : ~ ( r2_hidden(B,f2_s1_wellord2)
            & p1_s1_wellord2(A,B) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s1_wellord2
        & r1_tarski(k2_relat_1(A),f2_s1_wellord2)
        & ! [B] : 
            ( r2_hidden(B,f1_s1_wellord2)
           => p1_s1_wellord2(B,k1_funct_1(A,B)) ) ) ),
    file(wellord2,s1_wellord2),
    [interesting(0.00)]).

fof(s5_finseq_1,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))
            & ! [B] : 
                ( m1_subset_1(B,f1_s5_finseq_1)
               => ~ p1_s5_finseq_1(A,B) ) ) )
   => ? [A] : 
        ( m2_finseq_1(A,f1_s5_finseq_1)
        & k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f2_s5_finseq_1))
             => p1_s5_finseq_1(B,k1_funct_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_wellord2,d2_finseq_1,d4_finseq_1]),
    [file(finseq_1,s5_finseq_1),interesting(0.00)]).

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

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [interesting(0.00)]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.00)]).

fof(t22_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( A != 0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => A != k1_nat_1(B,1) ) ) ) ),
    file(nat_1,t22_nat_1),
    [interesting(0.00)]).

fof(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

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

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

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

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

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t31_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ),
    file(xreal_1,t31_xreal_1),
    [interesting(0.00)]).

fof(t88_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => k4_xboole_0(k2_xboole_0(A,B),B) = A ) ),
    file(xboole_1,t88_xboole_1),
    [interesting(0.00)]).

fof(t13_finseq_1,theorem,(
    $true ),
    file(finseq_1,t13_finseq_1),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t27_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(B,k2_xcmplx_0(A,1))
              & A != B
              & B != k2_xcmplx_0(A,1) ) ) ) ),
    file(nat_1,t27_nat_1),
    [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(t4_finseq_1,theorem,
    ( k2_finseq_1(0) = k1_xboole_0
    & k2_finseq_1(1) = k1_tarski(1)
    & k2_finseq_1(2) = k2_tarski(1,2) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t3_finseq_1,t1_xreal_1,d1_tarski,d1_tarski,t2_tarski,t27_nat_1,d2_tarski,d2_tarski,t2_tarski]),
    [file(finseq_1,t4_finseq_1),interesting(0.00)]).

fof(d3_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    [interesting(0.00)]).

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

fof(d4_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> r2_hidden(k4_tarski(B,C),A) ) )
          & ( ~ r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> C = k1_xboole_0 ) ) ) ) ),
    file(funct_1,d4_funct_1),
    [interesting(0.00)]).

fof(t8_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    [interesting(0.00)]).

fof(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    [interesting(0.00)]).

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

fof(t1_finseq_1,theorem,(
    $true ),
    file(finseq_1,t1_finseq_1),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

fof(t22_finseq_1,theorem,(
    $true ),
    file(finseq_1,t22_finseq_1),
    [interesting(0.00)]).

fof(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    [interesting(0.00)]).

fof(t76_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B))
        & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ) ),
    file(funct_1,t76_funct_1),
    [interesting(0.00)]).

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

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

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

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

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

fof(t28_finseq_1,theorem,(
    $true ),
    file(finseq_1,t28_finseq_1),
    [interesting(0.00)]).

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

fof(t2_finseq_1,theorem,(
    $true ),
    file(finseq_1,t2_finseq_1),
    [interesting(0.00)]).

fof(t30_finseq_1,theorem,(
    $true ),
    file(finseq_1,t30_finseq_1),
    [interesting(0.00)]).

fof(t31_finseq_1,theorem,(
    $true ),
    file(finseq_1,t31_finseq_1),
    [interesting(0.00)]).

fof(t34_finseq_1,theorem,(
    $true ),
    file(finseq_1,t34_finseq_1),
    [interesting(0.00)]).

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

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

fof(t28_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    [interesting(0.00)]).

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

fof(t22_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,k2_xcmplx_0(B,C))
              <=> r1_xreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) ),
    file(xreal_1,t22_xreal_1),
    [interesting(0.00)]).

fof(t17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k4_finseq_1(A) = k4_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_funct_1]),
    [file(finseq_1,t17_finseq_1),interesting(0.00)]).

fof(t46_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k7_finseq_1(A,B) = k7_finseq_1(C,B)
                  | k7_finseq_1(B,A) = k7_finseq_1(B,C) )
               => A = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_finseq_1,t35_finseq_1,d3_finseq_1,d3_finseq_1,d7_finseq_1,d7_finseq_1,t17_finseq_1,t35_finseq_1,t35_finseq_1,d3_finseq_1,d3_finseq_1,d7_finseq_1,d7_finseq_1,t17_finseq_1]),
    [file(finseq_1,t46_finseq_1),interesting(0.00)]).

fof(t23_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_xcmplx_0(A,B) = 0
           => ( A = 0
              & B = 0 ) ) ) ) ),
    file(nat_1,t23_nat_1),
    [interesting(0.00)]).

fof(t49_finseq_1,theorem,(
    $true ),
    file(finseq_1,t49_finseq_1),
    [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(t8_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t8_xreal_1),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

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

fof(t51_finseq_1,theorem,(
    $true ),
    file(finseq_1,t51_finseq_1),
    [interesting(0.00)]).

fof(t52_finseq_1,theorem,(
    ! [A] : k9_finseq_1(A) = k1_tarski(k4_tarski(1,A)) ),
    file(finseq_1,t52_finseq_1),
    [interesting(0.00)]).

fof(t53_finseq_1,theorem,(
    $true ),
    file(finseq_1,t53_finseq_1),
    [interesting(0.00)]).

fof(t54_finseq_1,theorem,(
    $true ),
    file(finseq_1,t54_finseq_1),
    [interesting(0.00)]).

fof(d8_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k1_relat_1(B) = k2_finseq_1(1)
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,d8_finseq_1),
    [interesting(0.00)]).

fof(t14_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_tarski(A)
       => k2_relat_1(B) = k1_tarski(k1_funct_1(B,A)) ) ) ),
    file(funct_1,t14_funct_1),
    [interesting(0.00)]).

fof(s1_real_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( r2_hidden(B,A)
          <=> p1_s1_real_1(B) ) ) ) ),
    file(real_1,s1_real_1),
    [interesting(0.00)]).

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

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

fof(t64_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ~ ( k7_finseq_1(A,B) = k7_finseq_1(C,D)
                      & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C))
                      & ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => k7_finseq_1(A,E) != C ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l32_finseq_1,t47_finseq_1,l32_finseq_1,d3_finseq_1,d3_finseq_1,d7_finseq_1,d7_finseq_1,t47_finseq_1,t17_finseq_1,t35_finseq_1,t56_finseq_1,t35_finseq_1,t56_finseq_1,t26_nat_1,t45_finseq_1,t45_finseq_1,s3_finseq_1]),
    [file(finseq_1,t64_finseq_1),interesting(0.00)]).

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

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

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

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

fof(t148_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ),
    file(relat_1,t148_relat_1),
    [interesting(0.00)]).

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

fof(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(t59_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(A,B),A)
          <=> r1_xreal_0(1,B) ) ) ) ),
    file(nat_1,t59_nat_1),
    [interesting(0.00)]).

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

fof(t68_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( B = k7_relat_1(C,A)
          <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)
              & ! [D] : 
                  ( r2_hidden(D,k1_relat_1(B))
                 => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ),
    file(funct_1,t68_funct_1),
    [interesting(0.00)]).

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

fof(d11_finseq_1,definition,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    [interesting(0.00)]).

fof(t67_finseq_1,theorem,(
    $true ),
    file(finseq_1,t67_finseq_1),
    [interesting(0.00)]).

fof(d12_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & r1_tarski(k1_relat_1(A),k2_finseq_1(B)) ) ) ) ),
    file(finseq_1,d12_finseq_1),
    [interesting(0.00)]).

fof(t89_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B))
        & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)) ) ) ),
    file(funct_1,t89_funct_1),
    [interesting(0.00)]).

fof(t69_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_relat_1(B,A))
        & v1_funct_1(k7_relat_1(B,A))
        & v2_finseq_1(k7_relat_1(B,A))
        & v1_relat_1(k8_relat_1(A,B))
        & v1_funct_1(k8_relat_1(A,B))
        & v2_finseq_1(k8_relat_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t76_funct_1,t89_funct_1,d12_finseq_1]),
    [file(finseq_1,t69_finseq_1),interesting(0.00)]).

fof(t70_finseq_1,theorem,(
    $true ),
    file(finseq_1,t70_finseq_1),
    [interesting(0.00)]).

fof(d13_finseq_1,definition,(
    ! [A] : 
      ( ? [B] : 
          ( v4_ordinal2(B)
          & r1_tarski(A,k2_finseq_1(B)) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( B = k14_finseq_1(A)
          <=> ( k2_relat_1(B) = A
              & ! [C] : 
                  ( v4_ordinal2(C)
                 => ! [D] : 
                      ( v4_ordinal2(D)
                     => ! [E] : 
                          ( v4_ordinal2(E)
                         => ! [F] : 
                              ( v4_ordinal2(F)
                             => ~ ( r1_xreal_0(1,C)
                                  & ~ r1_xreal_0(D,C)
                                  & r1_xreal_0(D,k3_finseq_1(B))
                                  & E = k1_funct_1(B,C)
                                  & F = k1_funct_1(B,D)
                                  & r1_xreal_0(F,E) ) ) ) ) ) ) ) ) ) ),
    file(finseq_1,d13_finseq_1),
    [interesting(0.00)]).

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

fof(d1_finset_1,definition,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & k2_relat_1(B) = A
          & r2_hidden(k1_relat_1(B),k5_ordinal2) ) ) ),
    file(finset_1,d1_finset_1),
    [interesting(0.00)]).

fof(t2_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B)
               => A = C ) ) ) ) ),
    file(xcmplx_1,t2_xcmplx_1),
    [interesting(0.00)]).

fof(t30_axioms,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => A = a_1_0_axioms(A) ) ),
    file(axioms,t30_axioms),
    [interesting(0.00)]).

fof(t47_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
           => k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) ) ) ) ),
    file(relat_1,t47_relat_1),
    [interesting(0.00)]).

fof(s5_nat_1,theorem,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s5_nat_1(A) )
   => ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s5_nat_1(A)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( p1_s5_nat_1(B)
             => r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,s5_nat_1),
    [interesting(0.00)]).

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

fof(t61_card_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r2_wellord2(A,B)
        & r2_hidden(C,A)
        & r2_hidden(D,B) )
     => r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))) ) ),
    file(card_1,t61_card_1),
    [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(t40_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) ),
    file(xboole_1,t40_xboole_1),
    [interesting(0.00)]).

fof(t83_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    [interesting(0.00)]).

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

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

fof(t48_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,k1_tarski(B))
    <=> ? [C] : A = k1_tarski(C) ) ),
    file(card_1,t48_card_1),
    [interesting(0.00)]).

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

fof(t58_card_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_xboole_0(A,B)
        & r1_xboole_0(C,D)
        & r2_wellord2(A,C)
        & r2_wellord2(B,D) )
     => r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)) ) ),
    file(card_1,t58_card_1),
    [interesting(0.00)]).

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

fof(t74_card_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ r2_wellord2(A,B) ) ) ),
    file(card_1,t74_card_1),
    [interesting(0.00)]).

fof(t22_wellord2,theorem,(
    ! [A,B,C] : 
      ( ( r2_wellord2(A,B)
        & r2_wellord2(B,C) )
     => r2_wellord2(A,C) ) ),
    file(wellord2,t22_wellord2),
    [interesting(0.00)]).

fof(t81_card_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r2_wellord2(A,B)
           => k4_card_1(A) = k4_card_1(B) ) ) ) ),
    file(card_1,t81_card_1),
    [interesting(0.00)]).

fof(d11_card_1,definition,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k4_card_1(A)
          <=> k1_card_1(B) = k1_card_1(A) ) ) ) ),
    file(card_1,d11_card_1),
    [interesting(0.00)]).

fof(t97_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k7_relat_1(B,A) = B ) ) ),
    file(relat_1,t97_relat_1),
    [interesting(0.00)]).

fof(t82_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C)))
               => ( r1_xreal_0(B,0)
                  | ( r2_hidden(B,k2_finseq_1(A))
                    & r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_nat_1,t3_finseq_1,t8_xreal_1,t3_finseq_1,t29_nat_1,t2_xreal_1,t3_finseq_1]),
    [file(finseq_1,t82_finseq_1),interesting(0.00)]).

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

fof(t56_card_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
          <=> r1_ordinal1(A,B) ) ) ) ),
    file(card_1,t56_card_1),
    [interesting(0.00)]).