% Mizar ND problem: t5_finseq_3,finseq_3,60,24 
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(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(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(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_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(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(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(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(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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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

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(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(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_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(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(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(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(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_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_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_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(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(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(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(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(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(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(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(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(fc10_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]).

fof(fc11_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]).

fof(fc12_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]).

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(fc1_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_int_1(k2_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc1_int_1),
    [interesting(0.9),axiom,file(int_1,fc1_int_1)]).

fof(fc3_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]).

fof(fc3_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]).

fof(fc4_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]).

fof(fc6_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    [interesting(0.9),axiom,file(int_1,fc6_int_1)]).

fof(fc7_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]).

fof(fc8_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]).

fof(fc9_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]).

fof(fc9_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]).

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_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_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_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_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_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(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(spc6_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

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(commutativity_k1_nat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(commutativity_k2_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(redefinition_k1_nat_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_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(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(dt_k4_enumset1,axiom,(
    $true ),
    file(enumset1,k4_enumset1),
    [interesting(0.9),axiom,file(enumset1,k4_enumset1)]).

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(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(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc1_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]).

fof(fc6_finset_1,theorem,(
    ! [A,B,C,D,E,F] : v1_finset_1(k4_enumset1(A,B,C,D,E,F)) ),
    file(finset_1,fc6_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc6_finset_1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,(
    k2_xcmplx_0(1,1) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r2_r3,theorem,(
    k2_xcmplx_0(1,2) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r3_r4,theorem,(
    k2_xcmplx_0(1,3) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r3_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r3_r4)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r4_r5,theorem,(
    k2_xcmplx_0(1,4) = 5 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r4_r5),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r4_r5)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r5_r6,theorem,(
    k2_xcmplx_0(1,5) = 6 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r5_r6),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r5_r6)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r1_r3,theorem,(
    k2_xcmplx_0(2,1) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r2_r4,theorem,(
    k2_xcmplx_0(2,2) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r2_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r2_r4)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r3_r5,theorem,(
    k2_xcmplx_0(2,3) = 5 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r3_r5),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r3_r5)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r4_r6,theorem,(
    k2_xcmplx_0(2,4) = 6 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r4_r6),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r4_r6)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r5_r7,theorem,(
    k2_xcmplx_0(2,5) = 7 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r5_r7),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r5_r7)]).

fof(rqRealAdd__k2_xcmplx_0__r3_r1_r4,theorem,(
    k2_xcmplx_0(3,1) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_r1_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r1_r4)]).

fof(rqRealAdd__k2_xcmplx_0__r3_r2_r5,theorem,(
    k2_xcmplx_0(3,2) = 5 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_r2_r5),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r2_r5)]).

fof(rqRealAdd__k2_xcmplx_0__r3_r3_r6,theorem,(
    k2_xcmplx_0(3,3) = 6 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_r3_r6),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r3_r6)]).

fof(rqRealAdd__k2_xcmplx_0__r3_r4_r7,theorem,(
    k2_xcmplx_0(3,4) = 7 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_r4_r7),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r4_r7)]).

fof(rqRealAdd__k2_xcmplx_0__r4_r1_r5,theorem,(
    k2_xcmplx_0(4,1) = 5 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_r1_r5),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_r1_r5)]).

fof(rqRealAdd__k2_xcmplx_0__r4_r2_r6,theorem,(
    k2_xcmplx_0(4,2) = 6 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_r2_r6),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_r2_r6)]).

fof(rqRealAdd__k2_xcmplx_0__r4_r3_r7,theorem,(
    k2_xcmplx_0(4,3) = 7 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_r3_r7),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_r3_r7)]).

fof(rqRealAdd__k2_xcmplx_0__r5_r1_r6,theorem,(
    k2_xcmplx_0(5,1) = 6 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r5_r1_r6),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r5_r1_r6)]).

fof(rqRealAdd__k2_xcmplx_0__r5_r2_r7,theorem,(
    k2_xcmplx_0(5,2) = 7 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r5_r2_r7),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r5_r2_r7)]).

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(spc3_numerals,theorem,
    ( v2_xreal_0(3)
    & m2_subset_1(3,k1_numbers,k5_numbers)
    & m1_subset_1(3,k5_numbers)
    & m1_subset_1(3,k1_numbers) ),
    file(numerals,spc3_numerals),
    [interesting(0.9),axiom,file(numerals,spc3_numerals)]).

fof(spc4_numerals,theorem,
    ( v2_xreal_0(4)
    & m2_subset_1(4,k1_numbers,k5_numbers)
    & m1_subset_1(4,k5_numbers)
    & m1_subset_1(4,k1_numbers) ),
    file(numerals,spc4_numerals),
    [interesting(0.9),axiom,file(numerals,spc4_numerals)]).

fof(spc5_numerals,theorem,
    ( v2_xreal_0(5)
    & m2_subset_1(5,k1_numbers,k5_numbers)
    & m1_subset_1(5,k5_numbers)
    & m1_subset_1(5,k1_numbers) ),
    file(numerals,spc5_numerals),
    [interesting(0.9),axiom,file(numerals,spc5_numerals)]).

fof(spc6_numerals,theorem,
    ( v2_xreal_0(6)
    & m2_subset_1(6,k1_numbers,k5_numbers)
    & m1_subset_1(6,k5_numbers)
    & m1_subset_1(6,k1_numbers) ),
    file(numerals,spc6_numerals),
    [interesting(0.9),axiom,file(numerals,spc6_numerals)]).

fof(spc7_numerals,theorem,
    ( v2_xreal_0(7)
    & m2_subset_1(7,k1_numbers,k5_numbers)
    & m1_subset_1(7,k5_numbers)
    & m1_subset_1(7,k1_numbers) ),
    file(numerals,spc7_numerals),
    [interesting(0.9),axiom,file(numerals,spc7_numerals)]).

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(spc3_boole,theorem,(
    ~ v1_xboole_0(3) ),
    file(boole,spc3_boole),
    [interesting(0.9),axiom,file(boole,spc3_boole)]).

fof(spc4_boole,theorem,(
    ~ v1_xboole_0(4) ),
    file(boole,spc4_boole),
    [interesting(0.9),axiom,file(boole,spc4_boole)]).

fof(spc5_boole,theorem,(
    ~ v1_xboole_0(5) ),
    file(boole,spc5_boole),
    [interesting(0.9),axiom,file(boole,spc5_boole)]).

fof(spc6_boole,theorem,(
    ~ v1_xboole_0(6) ),
    file(boole,spc6_boole),
    [interesting(0.9),axiom,file(boole,spc6_boole)]).

fof(spc7_boole,theorem,(
    ~ v1_xboole_0(7) ),
    file(boole,spc7_boole),
    [interesting(0.9),axiom,file(boole,spc7_boole)]).

fof(t4_finseq_3,theorem,(
    k2_finseq_1(6) = k4_enumset1(1,2,3,4,5,6) ),
    file(finseq_3,t4_finseq_3),
    [interesting(0.9),axiom,file(finseq_3,t4_finseq_3)]).

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)) ) ),
    file(finseq_1,t11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t11_finseq_1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r6_r7,theorem,(
    k2_xcmplx_0(1,6) = 7 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r6_r7),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r6_r7)]).

fof(rqRealAdd__k2_xcmplx_0__r6_r1_r7,theorem,(
    k2_xcmplx_0(6,1) = 7 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r6_r1_r7),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r6_r1_r7)]).

fof(e1_5_1__finseq_3,plain,(
    k2_finseq_1(7) = k2_xboole_0(k4_enumset1(1,2,3,4,5,6),k1_tarski(k1_nat_1(6,1))) ),
    inference(mizar_by,[status(thm),assumptions([])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,fc1_ordinal2,fc2_finseq_1,rc2_nat_1,rc3_nat_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_int_1,cc2_nat_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,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_finseq_1,fc1_int_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc6_int_1,fc7_xreal_0,fc8_xreal_0,fc9_finset_1,fc9_xreal_0,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,spc6_arithm,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k2_xcmplx_0,redefinition_k1_nat_1,redefinition_k2_finseq_1,dt_k1_nat_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k4_enumset1,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc1_finset_1,fc1_nat_1,fc6_finset_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_r3_r4,rqRealAdd__k2_xcmplx_0__r1_r4_r5,rqRealAdd__k2_xcmplx_0__r1_r5_r6,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_r2_r4,rqRealAdd__k2_xcmplx_0__r2_r3_r5,rqRealAdd__k2_xcmplx_0__r2_r4_r6,rqRealAdd__k2_xcmplx_0__r2_r5_r7,rqRealAdd__k2_xcmplx_0__r3_r1_r4,rqRealAdd__k2_xcmplx_0__r3_r2_r5,rqRealAdd__k2_xcmplx_0__r3_r3_r6,rqRealAdd__k2_xcmplx_0__r3_r4_r7,rqRealAdd__k2_xcmplx_0__r4_r1_r5,rqRealAdd__k2_xcmplx_0__r4_r2_r6,rqRealAdd__k2_xcmplx_0__r4_r3_r7,rqRealAdd__k2_xcmplx_0__r5_r1_r6,rqRealAdd__k2_xcmplx_0__r5_r2_r7,spc1_numerals,spc2_numerals,spc3_numerals,spc4_numerals,spc5_numerals,spc6_numerals,spc7_numerals,spc1_boole,spc2_boole,spc3_boole,spc4_boole,spc5_boole,spc6_boole,spc7_boole,t4_finseq_3,t11_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r6_r7,rqRealAdd__k2_xcmplx_0__r6_r1_r7]),
    [interesting(0.65),file(finseq_3,e1_5_1__finseq_3),[file(finseq_3,e1_5_1__finseq_3)]]).

fof(dt_k5_enumset1,axiom,(
    $true ),
    file(enumset1,k5_enumset1),
    [interesting(0.9),axiom,file(enumset1,k5_enumset1)]).

fof(fc7_finset_1,theorem,(
    ! [A,B,C,D,E,F,G] : v1_finset_1(k5_enumset1(A,B,C,D,E,F,G)) ),
    file(finset_1,fc7_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc7_finset_1)]).

fof(t61_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) ),
    file(enumset1,t61_enumset1),
    [interesting(0.9),axiom,file(enumset1,t61_enumset1)]).

fof(e2_5_1__finseq_3,plain,(
    k2_xboole_0(k4_enumset1(1,2,3,4,5,6),k1_tarski(k1_nat_1(6,1))) = k5_enumset1(1,2,3,4,5,6,7) ),
    inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc2_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc6_int_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t1_boole,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_int_1,cc2_nat_1,fc9_finset_1,rc1_finset_1,spc6_arithm,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k2_xcmplx_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k1_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k4_enumset1,dt_k5_enumset1,fc1_finset_1,fc6_finset_1,fc7_finset_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_r3_r4,rqRealAdd__k2_xcmplx_0__r1_r4_r5,rqRealAdd__k2_xcmplx_0__r1_r5_r6,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_r2_r4,rqRealAdd__k2_xcmplx_0__r2_r3_r5,rqRealAdd__k2_xcmplx_0__r2_r4_r6,rqRealAdd__k2_xcmplx_0__r2_r5_r7,rqRealAdd__k2_xcmplx_0__r3_r1_r4,rqRealAdd__k2_xcmplx_0__r3_r2_r5,rqRealAdd__k2_xcmplx_0__r3_r3_r6,rqRealAdd__k2_xcmplx_0__r3_r4_r7,rqRealAdd__k2_xcmplx_0__r4_r1_r5,rqRealAdd__k2_xcmplx_0__r4_r2_r6,rqRealAdd__k2_xcmplx_0__r4_r3_r7,rqRealAdd__k2_xcmplx_0__r5_r1_r6,rqRealAdd__k2_xcmplx_0__r5_r2_r7,spc1_numerals,spc2_numerals,spc3_numerals,spc4_numerals,spc5_numerals,spc6_numerals,spc7_numerals,spc1_boole,spc2_boole,spc3_boole,spc4_boole,spc5_boole,spc6_boole,spc7_boole,t61_enumset1,rqRealAdd__k2_xcmplx_0__r6_r1_r7,rqRealAdd__k2_xcmplx_0__r1_r6_r7]),
    [interesting(0.65),file(finseq_3,e2_5_1__finseq_3),[file(finseq_3,e2_5_1__finseq_3)]]).

fof(e1_5__finseq_3,plain,(
    k2_finseq_1(7) = k5_enumset1(1,2,3,4,5,6,7) ),
    inference(iterative_eq,[status(thm),assumptions([])],[e1_5_1__finseq_3,e2_5_1__finseq_3]),
    [interesting(0.8),file(finseq_3,e1_5__finseq_3),[file(finseq_3,e1_5__finseq_3)]]).

fof(i1_5__finseq_3,theorem,(
    $true ),
    introduced(tautology,[file(finseq_3,i1_5__finseq_3)]),
    [interesting(0.8),trivial,file(finseq_3,i1_5__finseq_3)]).

fof(t5_finseq_3,theorem,(
    k2_finseq_1(7) = k5_enumset1(1,2,3,4,5,6,7) ),
    inference(conclusion,[status(thm),assumptions([])],[e1_5__finseq_3,i1_5__finseq_3]),
    [interesting(1),file(finseq_3,t5_finseq_3),[file(finseq_3,t5_finseq_3)]]).