% Mizar ND problem: t69_finseq_3,finseq_3,1234,53 
fof(dh_c1_66__finseq_3,definition,
    ( ( ( v1_relat_1(c1_66__finseq_3)
        & v1_funct_1(c1_66__finseq_3)
        & v1_finseq_1(c1_66__finseq_3) )
     => ! [A,B] : 
          ( v4_ordinal2(B)
         => ( B = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,A)))
           => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,A)) = k2_finseq_1(B) ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finseq_1(C) )
       => ! [D,E] : 
            ( v4_ordinal2(E)
           => ( E = k6_xcmplx_0(k3_finseq_1(C),k4_card_1(k10_relat_1(C,D)))
             => k4_finseq_1(k1_finseq_3(C,D)) = k2_finseq_1(E) ) ) ) ),
    introduced(definition,[new_symbol(c1_66__finseq_3),file(finseq_3,c1_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,c1_66__finseq_3)]).

fof(dh_c2_66__finseq_3,definition,
    ( ! [A] : 
        ( v4_ordinal2(A)
       => ( A = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
         => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(A) ) )
   => ! [B,C] : 
        ( v4_ordinal2(C)
       => ( C = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,B)))
         => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,B)) = k2_finseq_1(C) ) ) ),
    introduced(definition,[new_symbol(c2_66__finseq_3),file(finseq_3,c2_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,c2_66__finseq_3)]).

fof(dh_c3_66__finseq_3,definition,
    ( ( v4_ordinal2(c3_66__finseq_3)
     => ( c3_66__finseq_3 = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
       => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(c3_66__finseq_3) ) )
   => ! [A] : 
        ( v4_ordinal2(A)
       => ( A = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
         => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(A) ) ) ),
    introduced(definition,[new_symbol(c3_66__finseq_3),file(finseq_3,c3_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,c3_66__finseq_3)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(fc15_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc15_xreal_0)]).

fof(fc16_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc16_xreal_0)]).

fof(fc17_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc17_xreal_0)]).

fof(fc18_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc18_xreal_0)]).

fof(rc2_finset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc4_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    [interesting(0.9),axiom,file(int_1,cc4_int_1)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(fc19_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc19_xreal_0)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(fc20_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc20_xreal_0)]).

fof(fc4_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc4_int_1),
    [interesting(0.9),axiom,file(int_1,fc4_int_1)]).

fof(fc5_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc5_xreal_0)]).

fof(fc8_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v1_int_1(k6_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc8_int_1),
    [interesting(0.9),axiom,file(int_1,fc8_int_1)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc1_int_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    [interesting(0.9),axiom,file(int_1,rc1_int_1)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_int_1,theorem,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    [interesting(0.9),axiom,file(int_1,rc2_int_1)]).

fof(rc2_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc3_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

fof(dt_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc1_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(cc2_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    [interesting(0.9),axiom,file(int_1,cc2_int_1)]).

fof(cc2_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]).

fof(cc3_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    [interesting(0.9),axiom,file(int_1,cc3_int_1)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(fc18_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k10_relat_1(A,B)) ) ),
    file(finseq_1,fc18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc18_finseq_1)]).

fof(fc1_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]).

fof(fc9_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc9_int_1),
    [interesting(0.9),axiom,file(int_1,fc9_int_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(redefinition_k2_finseq_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(redefinition_k3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

fof(redefinition_k4_card_1,definition,(
    ! [A] : 
      ( v1_finset_1(A)
     => k4_card_1(A) = k1_card_1(A) ) ),
    file(card_1,k4_card_1),
    [interesting(0.9),axiom,file(card_1,k4_card_1)]).

fof(redefinition_k4_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

fof(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_1)]).

fof(dt_k1_finseq_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k1_finseq_3(A,B))
        & v1_funct_1(k1_finseq_3(A,B))
        & v1_finseq_1(k1_finseq_3(A,B)) ) ) ),
    file(finseq_3,k1_finseq_3),
    [interesting(0.9),axiom,file(finseq_3,k1_finseq_3)]).

fof(dt_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

fof(dt_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ),
    file(card_1,k4_card_1),
    [interesting(0.9),axiom,file(card_1,k4_card_1)]).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]).

fof(dt_c1_66__finseq_3,assumption,
    ( v1_relat_1(c1_66__finseq_3)
    & v1_funct_1(c1_66__finseq_3)
    & v1_finseq_1(c1_66__finseq_3) ),
    introduced(assumption,[file(finseq_3,c1_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,c1_66__finseq_3)]).

fof(dt_c2_66__finseq_3,assumption,(
    $true ),
    introduced(assumption,[file(finseq_3,c2_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,c2_66__finseq_3)]).

fof(dt_c3_66__finseq_3,assumption,(
    v4_ordinal2(c3_66__finseq_3) ),
    introduced(assumption,[file(finseq_3,c3_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,c3_66__finseq_3)]).

fof(e1_66__finseq_3,assumption,(
    c3_66__finseq_3 = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3))) ),
    introduced(assumption,[file(finseq_3,e1_66__finseq_3)]),
    [interesting(0.8),axiom,file(finseq_3,e1_66__finseq_3)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]).

fof(rc2_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(rc4_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(redefinition_m2_finseq_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k14_finseq_1,axiom,(
    ! [A] : m2_finseq_1(k14_finseq_1(A),k5_numbers) ),
    file(finseq_1,k14_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k14_finseq_1)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(fc12_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc12_finset_1)]).

fof(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(d1_finseq_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : k1_finseq_3(A,B) = k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(A),k10_relat_1(A,B))),A) ) ),
    file(finseq_3,d1_finseq_3),
    [interesting(0.9),axiom,file(finseq_3,d1_finseq_3)]).

fof(fc13_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc13_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc13_xreal_0)]).

fof(fc14_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc14_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc14_xreal_0)]).

fof(fc1_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc1_xreal_0)]).

fof(fc3_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc3_int_1),
    [interesting(0.9),axiom,file(int_1,fc3_int_1)]).

fof(fc5_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc5_int_1),
    [interesting(0.9),axiom,file(int_1,fc5_int_1)]).

fof(spc9_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ),
    file(arithm,spc9_arithm),
    [interesting(0.9),axiom,file(arithm,spc9_arithm)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(t4_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    [interesting(0.9),axiom,file(arithm,t4_arithm)]).

fof(involutiveness_k4_xcmplx_0,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,(
    k6_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,(
    k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,(
    k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,(
    k6_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,(
    k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,(
    k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,(
    k6_xcmplx_0(2,0) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,(
    k6_xcmplx_0(2,1) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,(
    k6_xcmplx_0(2,2) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]).

fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,(
    k4_xcmplx_0(0) = 0 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]).

fof(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,(
    k4_xcmplx_0(2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]).

fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(spc2_numerals,theorem,
    ( v2_xreal_0(2)
    & m2_subset_1(2,k1_numbers,k5_numbers)
    & m1_subset_1(2,k5_numbers)
    & m1_subset_1(2,k1_numbers) ),
    file(numerals,spc2_numerals),
    [interesting(0.9),axiom,file(numerals,spc2_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(spc2_boole,theorem,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    [interesting(0.9),axiom,file(boole,spc2_boole)]).

fof(t66_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) ) ),
    file(finseq_3,t66_finseq_3),
    [interesting(0.9),axiom,file(finseq_3,t66_finseq_3)]).

fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,(
    k4_xcmplx_0(1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]).

fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,(
    k6_xcmplx_0(1,1) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]).

fof(e2_66__finseq_3,plain,(
    k3_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = c3_66__finseq_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3,e1_66__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc4_finseq_1,rc4_funct_1,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_finseq_1,cc2_finset_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_ordinal2,fc1_xreal_0,fc20_xreal_0,fc2_finseq_1,fc3_int_1,fc4_int_1,fc5_xreal_0,fc8_int_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_card_1,dt_k1_numbers,dt_k4_finseq_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_relat_1,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc12_finset_1,fc18_finseq_1,fc1_funct_1,fc5_int_1,fc9_int_1,rc1_finset_1,rc2_funct_1,rc7_finseq_1,rc8_finseq_1,spc9_arithm,t1_numerals,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k4_xcmplx_0,redefinition_k3_finseq_1,redefinition_k4_card_1,dt_k10_relat_1,dt_k1_finseq_3,dt_k3_finseq_1,dt_k4_card_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,d1_finseq_3,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e1_66__finseq_3,t66_finseq_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]),
    [interesting(0.8),file(finseq_3,e2_66__finseq_3),[file(finseq_3,e2_66__finseq_3)]]).

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(0.9),axiom,file(finseq_1,d3_finseq_1)]).

fof(e3_66__finseq_3,plain,(
    k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(c3_66__finseq_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3,e1_66__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_finseq_1,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_m2_finseq_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc6_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,dt_k10_relat_1,dt_k14_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k4_xboole_0,dt_k5_ordinal2,dt_k5_relat_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc12_finset_1,fc17_finseq_1,fc18_finseq_1,fc1_finseq_1,fc1_funct_1,fc1_ordinal2,rc1_finset_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_finseq_3,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,d1_finseq_3,e2_66__finseq_3,d3_finseq_1]),
    [interesting(0.8),file(finseq_3,e3_66__finseq_3),[file(finseq_3,e3_66__finseq_3)]]).

fof(i5_66__finseq_3,theorem,(
    $true ),
    introduced(tautology,[file(finseq_3,i5_66__finseq_3)]),
    [interesting(0.8),trivial,file(finseq_3,i5_66__finseq_3)]).

fof(i4_66__finseq_3,plain,(
    k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(c3_66__finseq_3) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3,e1_66__finseq_3])],[e3_66__finseq_3,i5_66__finseq_3]),
    [interesting(0.8),file(finseq_3,i4_66__finseq_3),[file(finseq_3,i4_66__finseq_3)]]).

fof(i4_66_tmp__finseq_3,plain,
    ( c3_66__finseq_3 = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
   => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(c3_66__finseq_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3]),discharge_asm(discharge,[e1_66__finseq_3])],[e1_66__finseq_3,i4_66__finseq_3]),
    [interesting(0.8),i3_66__finseq_3]).

fof(i3_66__finseq_3,plain,
    ( c3_66__finseq_3 = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
   => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(c3_66__finseq_3) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3])],[i4_66_tmp__finseq_3,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,dt_k5_ordinal2,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc19_xreal_0,fc1_ordinal2,fc20_xreal_0,fc4_int_1,fc5_xreal_0,fc8_int_1,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc17_finseq_1,fc18_finseq_1,fc1_finseq_1,fc9_int_1,rc1_finseq_1,rc1_funct_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_card_1,redefinition_k4_finseq_1,dt_k10_relat_1,dt_k1_finseq_3,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_card_1,dt_k4_finseq_1,dt_k6_xcmplx_0,dt_c1_66__finseq_3,dt_c2_66__finseq_3,dt_c3_66__finseq_3]),
    [interesting(0.8),file(finseq_3,i3_66__finseq_3),[file(finseq_3,i3_66__finseq_3)]]).

fof(i3_66_tmp__finseq_3,plain,
    ( v4_ordinal2(c3_66__finseq_3)
   => ( c3_66__finseq_3 = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
     => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(c3_66__finseq_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3]),discharge_asm(discharge,[dt_c3_66__finseq_3])],[dt_c3_66__finseq_3,i3_66__finseq_3]),
    [interesting(0.8),i2_66__finseq_3]).

fof(i2_66__finseq_3,plain,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( A = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
       => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_66__finseq_3,dt_c2_66__finseq_3])],[i3_66_tmp__finseq_3,dh_c3_66__finseq_3]),
    [interesting(0.8),file(finseq_3,i2_66__finseq_3),[file(finseq_3,i2_66__finseq_3)]]).

fof(i2_66_tmp__finseq_3,plain,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( A = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,c2_66__finseq_3)))
       => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,c2_66__finseq_3)) = k2_finseq_1(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_66__finseq_3]),discharge_asm(discharge,[dt_c2_66__finseq_3])],[dt_c2_66__finseq_3,i2_66__finseq_3]),
    [interesting(0.8),i1_66__finseq_3]).

fof(i1_66__finseq_3,plain,(
    ! [A,B] : 
      ( v4_ordinal2(B)
     => ( B = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,A)))
       => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,A)) = k2_finseq_1(B) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_66__finseq_3])],[i2_66_tmp__finseq_3,dh_c2_66__finseq_3]),
    [interesting(0.8),file(finseq_3,i1_66__finseq_3),[file(finseq_3,i1_66__finseq_3)]]).

fof(i1_66_tmp__finseq_3,plain,
    ( ( v1_relat_1(c1_66__finseq_3)
      & v1_funct_1(c1_66__finseq_3)
      & v1_finseq_1(c1_66__finseq_3) )
   => ! [A,B] : 
        ( v4_ordinal2(B)
       => ( B = k6_xcmplx_0(k3_finseq_1(c1_66__finseq_3),k4_card_1(k10_relat_1(c1_66__finseq_3,A)))
         => k4_finseq_1(k1_finseq_3(c1_66__finseq_3,A)) = k2_finseq_1(B) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_66__finseq_3])],[dt_c1_66__finseq_3,i1_66__finseq_3]),
    [interesting(1),t69_finseq_3]).

fof(t69_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B,C] : 
          ( v4_ordinal2(C)
         => ( C = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B)))
           => k4_finseq_1(k1_finseq_3(A,B)) = k2_finseq_1(C) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_66_tmp__finseq_3,dh_c1_66__finseq_3]),
    [interesting(1),file(finseq_3,t69_finseq_3),[file(finseq_3,t69_finseq_3)]]).