% Mizar ND problem: t3_binarith,binarith,58,18 
fof(dh_c1_3__binarith,definition,
    ( ( m2_subset_1(c1_3__binarith,k1_numbers,k5_numbers)
     => ! [A] : 
          ( ~ v1_xboole_0(A)
         => ! [B] : 
              ( m1_subset_1(B,A)
             => ! [C] : 
                  ( m2_finseq_2(C,A,k4_finseq_2(c1_3__binarith,A))
                 => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,C,k12_finseq_1(A,B)),k23_binop_2(c1_3__binarith,1)) = B ) ) ) )
   => ! [D] : 
        ( m2_subset_1(D,k1_numbers,k5_numbers)
       => ! [E] : 
            ( ~ v1_xboole_0(E)
           => ! [F] : 
                ( m1_subset_1(F,E)
               => ! [G] : 
                    ( m2_finseq_2(G,E,k4_finseq_2(D,E))
                   => k4_finseq_4(k5_numbers,E,k8_finseq_1(E,G,k12_finseq_1(E,F)),k23_binop_2(D,1)) = F ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__binarith),file(binarith,c1_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c1_3__binarith)]).

fof(dh_c2_3__binarith,definition,
    ( ( ~ v1_xboole_0(c2_3__binarith)
     => ! [A] : 
          ( m1_subset_1(A,c2_3__binarith)
         => ! [B] : 
              ( m2_finseq_2(B,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
             => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,B,k12_finseq_1(c2_3__binarith,A)),k23_binop_2(c1_3__binarith,1)) = A ) ) )
   => ! [C] : 
        ( ~ v1_xboole_0(C)
       => ! [D] : 
            ( m1_subset_1(D,C)
           => ! [E] : 
                ( m2_finseq_2(E,C,k4_finseq_2(c1_3__binarith,C))
               => k4_finseq_4(k5_numbers,C,k8_finseq_1(C,E,k12_finseq_1(C,D)),k23_binop_2(c1_3__binarith,1)) = D ) ) ) ),
    introduced(definition,[new_symbol(c2_3__binarith),file(binarith,c2_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c2_3__binarith)]).

fof(dh_c3_3__binarith,definition,
    ( ( m1_subset_1(c3_3__binarith,c2_3__binarith)
     => ! [A] : 
          ( m2_finseq_2(A,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
         => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,A,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ) )
   => ! [B] : 
        ( m1_subset_1(B,c2_3__binarith)
       => ! [C] : 
            ( m2_finseq_2(C,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
           => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,C,k12_finseq_1(c2_3__binarith,B)),k23_binop_2(c1_3__binarith,1)) = B ) ) ),
    introduced(definition,[new_symbol(c3_3__binarith),file(binarith,c3_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c3_3__binarith)]).

fof(dh_c4_3__binarith,definition,
    ( ( m2_finseq_2(c4_3__binarith,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
     => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,c4_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith )
   => ! [A] : 
        ( m2_finseq_2(A,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
       => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,A,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ) ),
    introduced(definition,[new_symbol(c4_3__binarith),file(binarith,c4_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c4_3__binarith)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc12_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    [interesting(0.9),axiom,file(membered,fc12_membered)]).

fof(fc13_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    [interesting(0.9),axiom,file(membered,fc13_membered)]).

fof(fc14_membered,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    [interesting(0.9),axiom,file(membered,fc14_membered)]).

fof(fc15_membered,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    [interesting(0.9),axiom,file(membered,fc15_membered)]).

fof(fc16_membered,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    [interesting(0.9),axiom,file(membered,fc16_membered)]).

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

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

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

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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

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(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(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(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc1_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ),
    file(finseq_2,fc1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,fc1_finseq_2)]).

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(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(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(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_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(rc1_finseq_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_2(B,A)
      & ~ v1_xboole_0(B) ) ),
    file(finseq_2,rc1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,rc1_finseq_2)]).

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_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

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(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_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(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

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_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(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_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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_finseq_2,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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_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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k4_finseq_2)]).

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]).

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

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k7_finseq_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_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

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(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

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_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

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_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

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(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(t1_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    [interesting(0.9),axiom,file(arithm,t1_arithm)]).

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

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(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(d5_finseq_1,definition,(
    ! [A] : k5_finseq_1(A) = k1_tarski(k4_tarski(1,A)) ),
    file(finseq_1,d5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,d5_finseq_1)]).

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_k23_binop_2,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k23_binop_2(A,B) = k23_binop_2(B,A) ) ),
    file(binop_2,k23_binop_2),
    [interesting(0.9),axiom,file(binop_2,k23_binop_2)]).

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(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(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_k12_finseq_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k12_finseq_1(A,B) = k5_finseq_1(B) ) ),
    file(finseq_1,k12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]).

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_k23_binop_2,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) ),
    file(binop_2,k23_binop_2),
    [interesting(0.9),axiom,file(binop_2,k23_binop_2)]).

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

fof(redefinition_k8_finseq_1,definition,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ),
    file(finseq_1,k8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k8_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(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_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_1(k12_finseq_1(A,B),A) ) ),
    file(finseq_1,k12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k12_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_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k23_binop_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) ),
    file(binop_2,k23_binop_2),
    [interesting(0.9),axiom,file(binop_2,k23_binop_2)]).

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_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_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_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,k4_finseq_4)]).

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_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ),
    file(finseq_1,k8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]).

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(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(dt_c1_3__binarith,assumption,(
    m2_subset_1(c1_3__binarith,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(binarith,c1_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c1_3__binarith)]).

fof(dt_c2_3__binarith,assumption,(
    ~ v1_xboole_0(c2_3__binarith) ),
    introduced(assumption,[file(binarith,c2_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c2_3__binarith)]).

fof(dt_c3_3__binarith,assumption,(
    m1_subset_1(c3_3__binarith,c2_3__binarith) ),
    introduced(assumption,[file(binarith,c3_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c3_3__binarith)]).

fof(dt_c4_3__binarith,assumption,(
    m2_finseq_2(c4_3__binarith,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith)) ),
    introduced(assumption,[file(binarith,c4_3__binarith)]),
    [interesting(0.8),axiom,file(binarith,c4_3__binarith)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,(
    k2_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]).

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(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(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(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(t109_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k3_finseq_1(C) = A ) ) ) ),
    file(finseq_2,t109_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,t109_finseq_2)]).

fof(e4_3__binarith,plain,(
    k3_finseq_1(c4_3__binarith) = c1_3__binarith ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__binarith,dt_c1_3__binarith,dt_c4_3__binarith])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc4_int_1,rc1_int_1,rc1_margrel1,rc1_nat_1,rc2_int_1,rc2_nat_1,rc3_nat_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_finseq_1,dt_c2_3__binarith,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc20_membered,cc2_int_1,cc2_membered,cc2_nat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_finseq_2,fc1_margrel1,fc1_ordinal2,fc5_membered,fc6_membered,rc1_finseq_2,rc1_membered,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_2,dt_k5_numbers,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_3__binarith,dt_c4_3__binarith,cc15_membered,fc2_membered,t6_boole,t7_boole,t8_boole,t109_finseq_2]),
    [interesting(0.8),file(binarith,e4_3__binarith),[file(binarith,e4_3__binarith)]]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,(
    ~ r1_xreal_0(1,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(t5_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

fof(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_1_0_finseq_1,definition,(
    ! [A,B] : 
      ( v4_ordinal2(B)
     => ( r2_hidden(A,a_1_0_finseq_1(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & r1_xreal_0(1,C)
            & r1_xreal_0(C,B) ) ) ) ),
    file(finseq_1,a_1_0_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,a_1_0_finseq_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(d1_finseq_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k1_finseq_1(A) = a_1_0_finseq_1(A) ) ),
    file(finseq_1,d1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,d1_finseq_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_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(redefinition_k9_finseq_1,definition,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k9_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k9_finseq_1(A))
      & v1_funct_1(k9_finseq_1(A)) ) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

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) ) ) ) ),
    file(finseq_1,t56_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t56_finseq_1)]).

fof(e1_3__binarith,plain,(
    k3_finseq_1(k12_finseq_1(c2_3__binarith,c3_3__binarith)) = 1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__binarith,dt_c3_3__binarith])],[commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc1_margrel1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,cc6_membered,cc9_membered,fc10_membered,fc11_membered,fc1_margrel1,fc1_ordinal2,fc5_membered,fc6_membered,fc7_membered,fc8_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc2_int_1,rc2_nat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,fc2_membered,t2_subset,t6_boole,t7_boole,t8_boole,d5_finseq_1,redefinition_k12_finseq_1,redefinition_k3_finseq_1,redefinition_k9_finseq_1,dt_k12_finseq_1,dt_k1_tarski,dt_k2_relat_1,dt_k3_finseq_1,dt_k9_finseq_1,dt_c2_3__binarith,dt_c3_3__binarith,spc1_numerals,spc1_boole,t56_finseq_1]),
    [interesting(0.8),file(binarith,e1_3__binarith),[file(binarith,e1_3__binarith)]]).

fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,(
    k2_xcmplx_0(0,1) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,(
    k2_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]).

fof(e2_3__binarith,plain,(
    r2_hidden(k23_binop_2(0,1),k2_finseq_1(k3_finseq_1(k12_finseq_1(c2_3__binarith,c3_3__binarith)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__binarith,dt_c3_3__binarith])],[commutativity_k2_tarski,existence_m1_relset_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc1_margrel1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k4_tarski,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_int_1,cc4_membered,fc10_membered,fc11_membered,fc1_int_1,fc1_margrel1,fc1_ordinal2,fc5_membered,fc6_int_1,fc6_membered,fc7_membered,fc8_membered,rc1_int_1,rc1_membered,rc2_int_1,rc2_nat_1,rc3_nat_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,t2_tarski,fraenkel_a_1_0_finseq_1,d5_tarski,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc6_membered,cc9_membered,fc1_nat_1,fc2_membered,fc3_nat_1,fc4_nat_1,rc1_nat_1,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,d1_finseq_1,d5_finseq_1,commutativity_k23_binop_2,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k23_binop_2,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k12_finseq_1,dt_k23_binop_2,dt_k2_finseq_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_c2_3__binarith,dt_c3_3__binarith,rqLessOrEqual__r1_xreal_0__r1_r0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_3__binarith,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.8),file(binarith,e2_3__binarith),[file(binarith,e2_3__binarith)]]).

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_3__binarith,plain,(
    r2_hidden(k23_binop_2(0,1),k4_finseq_1(k12_finseq_1(c2_3__binarith,c3_3__binarith))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__binarith,dt_c3_3__binarith])],[commutativity_k2_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_relset_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc1_margrel1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k4_tarski,dt_m1_finseq_1,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_int_1,fc10_membered,fc11_membered,fc1_int_1,fc1_margrel1,fc6_int_1,fc6_membered,fc7_membered,fc8_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc2_int_1,rc2_nat_1,rc3_nat_1,t2_tarski,fraenkel_a_1_0_finseq_1,d5_tarski,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_nat_1,fc1_ordinal2,fc3_nat_1,fc4_nat_1,fc5_membered,spc6_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d1_finseq_1,d5_finseq_1,commutativity_k23_binop_2,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k23_binop_2,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k23_binop_2,dt_k2_finseq_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c2_3__binarith,dt_c3_3__binarith,fc2_membered,rqRealAdd__k2_xcmplx_0__r0_r0_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_3__binarith,d3_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1]),
    [interesting(0.8),file(binarith,e3_3__binarith),[file(binarith,e3_3__binarith)]]).

fof(t84_finseq_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,B)
             => ! [D] : 
                  ( m2_finseq_1(D,B)
                 => ( r2_hidden(A,k4_finseq_1(D))
                   => k4_finseq_4(k5_numbers,B,k8_finseq_1(B,C,D),k1_nat_1(k3_finseq_1(C),A)) = k4_finseq_4(k5_numbers,B,D,A) ) ) ) ) ) ),
    file(finseq_4,t84_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,t84_finseq_4)]).

fof(e1_3_1__binarith,plain,(
    k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,c4_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = k4_finseq_4(k5_numbers,c2_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith),1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__binarith,dt_c4_3__binarith,dt_c2_3__binarith,dt_c3_3__binarith])],[commutativity_k2_tarski,dt_k2_tarski,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,reflexivity_r1_tarski,existence_m1_finseq_2,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_finseq_2,cc1_relset_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc1_finseq_2,fc1_int_1,fc1_nat_1,fc3_nat_1,fc4_nat_1,fc6_int_1,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_2,rc1_int_1,rc1_margrel1,rc1_nat_1,rc2_int_1,rc2_nat_1,rc3_nat_1,d5_tarski,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc20_membered,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_margrel1,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,spc6_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,d5_finseq_1,commutativity_k1_nat_1,commutativity_k23_binop_2,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k23_binop_2,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k23_binop_2,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_k8_finseq_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_3__binarith,dt_c2_3__binarith,dt_c3_3__binarith,dt_c4_3__binarith,cc15_membered,fc2_membered,rqRealAdd__k2_xcmplx_0__r0_r0_r0,spc0_boole,spc1_boole,t1_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_3__binarith,e3_3__binarith,t84_finseq_4,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1]),
    [interesting(0.65),file(binarith,e1_3_1__binarith),[file(binarith,e1_3_1__binarith)]]).

fof(t25_finseq_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => k4_finseq_4(k5_numbers,A,k12_finseq_1(A,B),1) = B ) ) ),
    file(finseq_4,t25_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,t25_finseq_4)]).

fof(e2_3_1__binarith,plain,(
    k4_finseq_4(k5_numbers,c2_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith),1) = c3_3__binarith ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__binarith,dt_c3_3__binarith])],[commutativity_k2_tarski,dt_k2_tarski,dt_k2_zfmisc_1,cc1_relset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k4_tarski,dt_m1_finseq_1,dt_m2_relset_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_margrel1,d5_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_margrel1,fc1_ordinal2,fc2_membered,fc5_membered,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc2_int_1,rc2_nat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,d5_finseq_1,existence_m1_subset_1,redefinition_k12_finseq_1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_m1_subset_1,dt_c2_3__binarith,dt_c3_3__binarith,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,spc1_boole,t2_subset,t6_boole,t7_boole,t8_boole,spc1_numerals,spc1_boole,t25_finseq_4]),
    [interesting(0.65),file(binarith,e2_3_1__binarith),[file(binarith,e2_3_1__binarith)]]).

fof(e5_3__binarith,plain,(
    k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,c4_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_3__binarith,dt_c4_3__binarith,dt_c2_3__binarith,dt_c3_3__binarith])],[e1_3_1__binarith,e2_3_1__binarith]),
    [interesting(0.8),file(binarith,e5_3__binarith),[file(binarith,e5_3__binarith)]]).

fof(i5_3__binarith,theorem,(
    $true ),
    introduced(tautology,[file(binarith,i5_3__binarith)]),
    [interesting(0.8),trivial,file(binarith,i5_3__binarith)]).

fof(i4_3__binarith,plain,(
    k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,c4_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__binarith,dt_c4_3__binarith,dt_c2_3__binarith,dt_c3_3__binarith])],[e5_3__binarith,i5_3__binarith]),
    [interesting(0.8),file(binarith,i4_3__binarith),[file(binarith,i4_3__binarith)]]).

fof(i4_3_tmp__binarith,plain,
    ( m2_finseq_2(c4_3__binarith,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
   => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,c4_3__binarith,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__binarith,dt_c2_3__binarith,dt_c3_3__binarith]),discharge_asm(discharge,[dt_c4_3__binarith])],[dt_c4_3__binarith,i4_3__binarith]),
    [interesting(0.8),i3_3__binarith]).

fof(i3_3__binarith,plain,(
    ! [A] : 
      ( m2_finseq_2(A,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
     => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,A,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__binarith,dt_c2_3__binarith,dt_c3_3__binarith])],[i4_3_tmp__binarith,dh_c4_3__binarith]),
    [interesting(0.8),file(binarith,i3_3__binarith),[file(binarith,i3_3__binarith)]]).

fof(i3_3_tmp__binarith,plain,
    ( m1_subset_1(c3_3__binarith,c2_3__binarith)
   => ! [A] : 
        ( m2_finseq_2(A,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
       => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,A,k12_finseq_1(c2_3__binarith,c3_3__binarith)),k23_binop_2(c1_3__binarith,1)) = c3_3__binarith ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__binarith,dt_c2_3__binarith]),discharge_asm(discharge,[dt_c3_3__binarith])],[dt_c3_3__binarith,i3_3__binarith]),
    [interesting(0.8),i2_3__binarith]).

fof(i2_3__binarith,plain,(
    ! [A] : 
      ( m1_subset_1(A,c2_3__binarith)
     => ! [B] : 
          ( m2_finseq_2(B,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
         => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,B,k12_finseq_1(c2_3__binarith,A)),k23_binop_2(c1_3__binarith,1)) = A ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__binarith,dt_c2_3__binarith])],[i3_3_tmp__binarith,dh_c3_3__binarith]),
    [interesting(0.8),file(binarith,i2_3__binarith),[file(binarith,i2_3__binarith)]]).

fof(i2_3_tmp__binarith,plain,
    ( ~ v1_xboole_0(c2_3__binarith)
   => ! [A] : 
        ( m1_subset_1(A,c2_3__binarith)
       => ! [B] : 
            ( m2_finseq_2(B,c2_3__binarith,k4_finseq_2(c1_3__binarith,c2_3__binarith))
           => k4_finseq_4(k5_numbers,c2_3__binarith,k8_finseq_1(c2_3__binarith,B,k12_finseq_1(c2_3__binarith,A)),k23_binop_2(c1_3__binarith,1)) = A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__binarith]),discharge_asm(discharge,[dt_c2_3__binarith])],[dt_c2_3__binarith,i2_3__binarith]),
    [interesting(0.8),i1_3__binarith]).

fof(i1_3__binarith,plain,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m2_finseq_2(C,A,k4_finseq_2(c1_3__binarith,A))
             => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,C,k12_finseq_1(A,B)),k23_binop_2(c1_3__binarith,1)) = B ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__binarith])],[i2_3_tmp__binarith,dh_c2_3__binarith]),
    [interesting(0.8),file(binarith,i1_3__binarith),[file(binarith,i1_3__binarith)]]).

fof(i1_3_tmp__binarith,plain,
    ( m2_subset_1(c1_3__binarith,k1_numbers,k5_numbers)
   => ! [A] : 
        ( ~ v1_xboole_0(A)
       => ! [B] : 
            ( m1_subset_1(B,A)
           => ! [C] : 
                ( m2_finseq_2(C,A,k4_finseq_2(c1_3__binarith,A))
               => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,C,k12_finseq_1(A,B)),k23_binop_2(c1_3__binarith,1)) = B ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__binarith])],[dt_c1_3__binarith,i1_3__binarith]),
    [interesting(1),t3_binarith]).

fof(t3_binarith,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => ! [D] : 
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => k4_finseq_4(k5_numbers,B,k8_finseq_1(B,D,k12_finseq_1(B,C)),k23_binop_2(A,1)) = C ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__binarith,dh_c1_3__binarith]),
    [interesting(1),file(binarith,t3_binarith),[file(binarith,t3_binarith)]]).