% Mizar ND problem: t5_trees_1,trees_1,95,64 
fof(dh_c1_4__trees_1,definition,
    ( ( ( v1_relat_1(c1_4__trees_1)
        & v1_funct_1(c1_4__trees_1)
        & v1_finseq_1(c1_4__trees_1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A)
            & v1_finseq_1(A) )
         => ( ( c1_4__trees_1 = k7_finseq_1(c1_4__trees_1,A)
              | c1_4__trees_1 = k7_finseq_1(A,c1_4__trees_1) )
           => A = k1_xboole_0 ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finseq_1(C) )
           => ( ( B = k7_finseq_1(B,C)
                | B = k7_finseq_1(C,B) )
             => C = k1_xboole_0 ) ) ) ),
    introduced(definition,[new_symbol(c1_4__trees_1),file(trees_1,c1_4__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c1_4__trees_1)]).

fof(dh_c2_4__trees_1,definition,
    ( ( ( v1_relat_1(c2_4__trees_1)
        & v1_funct_1(c2_4__trees_1)
        & v1_finseq_1(c2_4__trees_1) )
     => ( ( c1_4__trees_1 = k7_finseq_1(c1_4__trees_1,c2_4__trees_1)
          | c1_4__trees_1 = k7_finseq_1(c2_4__trees_1,c1_4__trees_1) )
       => c2_4__trees_1 = k1_xboole_0 ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => ( ( c1_4__trees_1 = k7_finseq_1(c1_4__trees_1,A)
            | c1_4__trees_1 = k7_finseq_1(A,c1_4__trees_1) )
         => A = k1_xboole_0 ) ) ),
    introduced(definition,[new_symbol(c2_4__trees_1),file(trees_1,c2_4__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c2_4__trees_1)]).

fof(e1_4__trees_1,assumption,
    ( c1_4__trees_1 = k7_finseq_1(c1_4__trees_1,c2_4__trees_1)
    | c1_4__trees_1 = k7_finseq_1(c2_4__trees_1,c1_4__trees_1) ),
    introduced(assumption,[file(trees_1,e1_4__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,e1_4__trees_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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

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

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

fof(cc2_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_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(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_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(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(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_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_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(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_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(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(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t3_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(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_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_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

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_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_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(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_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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

fof(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(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(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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_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_c2_4__trees_1,assumption,
    ( v1_relat_1(c2_4__trees_1)
    & v1_funct_1(c2_4__trees_1)
    & v1_finseq_1(c2_4__trees_1) ),
    introduced(assumption,[file(trees_1,c2_4__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c2_4__trees_1)]).

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

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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

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

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

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

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

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

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

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

fof(fc1_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(fc1_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc1_xreal_0)]).

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

fof(fc27_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc27_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc27_xreal_0)]).

fof(fc28_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(B,A))
        & v1_xreal_0(k7_xcmplx_0(B,A))
        & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc28_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc28_xreal_0)]).

fof(fc29_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc29_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc29_xreal_0)]).

fof(fc30_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc30_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc30_xreal_0)]).

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

fof(fc6_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]).

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

fof(fc13_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(A,B))
        & v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,fc13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]).

fof(fc14_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(B,A))
        & v1_relat_1(k7_finseq_1(B,A))
        & v1_funct_1(k7_finseq_1(B,A))
        & v1_finset_1(k7_finseq_1(B,A))
        & v1_finseq_1(k7_finseq_1(B,A)) ) ) ),
    file(finseq_1,fc14_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc14_finseq_1)]).

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(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__r0_rm1_rm1,theorem,(
    k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]).

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(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]).

fof(spc1_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ),
    file(arithm,spc1_arithm),
    [interesting(0.9),axiom,file(arithm,spc1_arithm)]).

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(spc8_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ),
    file(arithm,spc8_arithm),
    [interesting(0.9),axiom,file(arithm,spc8_arithm)]).

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

fof(t1_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(t4_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    [interesting(0.9),axiom,file(arithm,t4_arithm)]).

fof(t5_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(0,A) = 0 ) ),
    file(arithm,t5_arithm),
    [interesting(0.9),axiom,file(arithm,t5_arithm)]).

fof(t6_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,1) = A ) ),
    file(arithm,t6_arithm),
    [interesting(0.9),axiom,file(arithm,t6_arithm)]).

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

fof(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(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_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

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

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_k7_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k7_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]).

fof(dt_c1_4__trees_1,assumption,
    ( v1_relat_1(c1_4__trees_1)
    & v1_funct_1(c1_4__trees_1)
    & v1_finseq_1(c1_4__trees_1) ),
    introduced(assumption,[file(trees_1,c1_4__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c1_4__trees_1)]).

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

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

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

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

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

fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,(
    k7_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,(
    k7_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]).

fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,(
    k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]).

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

fof(t35_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    file(finseq_1,t35_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t35_finseq_1)]).

fof(e2_4__trees_1,plain,
    ( k3_finseq_1(k7_finseq_1(c1_4__trees_1,c2_4__trees_1)) = k1_nat_1(k3_finseq_1(c1_4__trees_1),k3_finseq_1(c2_4__trees_1))
    & k3_finseq_1(k7_finseq_1(c2_4__trees_1,c1_4__trees_1)) = k1_nat_1(k3_finseq_1(c2_4__trees_1),k3_finseq_1(c1_4__trees_1))
    & k3_finseq_1(c1_4__trees_1) = k1_nat_1(k3_finseq_1(c1_4__trees_1),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__trees_1,dt_c2_4__trees_1])],[reflexivity_r1_tarski,rc2_finset_1,rc3_finseq_1,rc6_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_nat_1,cc3_xreal_0,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_nat_1,fc1_ordinal2,fc1_xboole_0,fc2_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,spc6_arithm,t1_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc13_finseq_1,fc14_finseq_1,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,dt_k1_nat_1,dt_k3_finseq_1,dt_k7_finseq_1,dt_c1_4__trees_1,dt_c2_4__trees_1,cc1_finseq_1,rc1_finseq_1,spc0_numerals,spc0_boole,t35_finseq_1]),
    [interesting(0.8),file(trees_1,e2_4__trees_1),[file(trees_1,e2_4__trees_1)]]).

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

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

fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]).

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

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

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

fof(e3_4__trees_1,plain,(
    k3_finseq_1(c2_4__trees_1) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__trees_1,dt_c2_4__trees_1,e1_4__trees_1])],[reflexivity_r1_tarski,rc2_finset_1,rc3_finseq_1,rc6_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_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc1_xboole_0,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_finseq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc13_finseq_1,fc14_finseq_1,rc1_finseq_1,rc1_xboole_0,rc2_xboole_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,dt_k1_nat_1,dt_k3_finseq_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_finseq_1,dt_k7_xcmplx_0,dt_c1_4__trees_1,dt_c2_4__trees_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_4__trees_1,e1_4__trees_1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__r0_r0]),
    [interesting(0.8),file(trees_1,e3_4__trees_1),[file(trees_1,e3_4__trees_1)]]).

fof(t25_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) = 0
      <=> A = k1_xboole_0 ) ) ),
    file(finseq_1,t25_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t25_finseq_1)]).

fof(e4_4__trees_1,plain,(
    c2_4__trees_1 = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__trees_1,dt_c2_4__trees_1,e1_4__trees_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,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_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t7_boole,t8_boole,redefinition_k3_finseq_1,dt_k1_xboole_0,dt_k3_finseq_1,dt_c2_4__trees_1,cc1_finseq_1,fc1_xboole_0,fc2_finseq_1,rc1_finseq_1,t6_boole,spc0_numerals,spc0_boole,e3_4__trees_1,t25_finseq_1]),
    [interesting(0.8),file(trees_1,e4_4__trees_1),[file(trees_1,e4_4__trees_1)]]).

fof(i3_4__trees_1,theorem,(
    $true ),
    introduced(tautology,[file(trees_1,i3_4__trees_1)]),
    [interesting(0.8),trivial,file(trees_1,i3_4__trees_1)]).

fof(i2_4__trees_1,plain,(
    c2_4__trees_1 = k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__trees_1,dt_c2_4__trees_1,e1_4__trees_1])],[e4_4__trees_1,i3_4__trees_1]),
    [interesting(0.8),file(trees_1,i2_4__trees_1),[file(trees_1,i2_4__trees_1)]]).

fof(i1_4__trees_1,plain,
    ( ( c1_4__trees_1 = k7_finseq_1(c1_4__trees_1,c2_4__trees_1)
      | c1_4__trees_1 = k7_finseq_1(c2_4__trees_1,c1_4__trees_1) )
   => c2_4__trees_1 = k1_xboole_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__trees_1,dt_c2_4__trees_1]),discharge_asm(discharge,[e1_4__trees_1])],[e1_4__trees_1,i2_4__trees_1]),
    [interesting(0.8),file(trees_1,i1_4__trees_1),[file(trees_1,i1_4__trees_1)]]).

fof(i1_4_tmp__trees_1,plain,
    ( ( v1_relat_1(c1_4__trees_1)
      & v1_funct_1(c1_4__trees_1)
      & v1_finseq_1(c1_4__trees_1)
      & v1_relat_1(c2_4__trees_1)
      & v1_funct_1(c2_4__trees_1)
      & v1_finseq_1(c2_4__trees_1) )
   => ( ( c1_4__trees_1 = k7_finseq_1(c1_4__trees_1,c2_4__trees_1)
        | c1_4__trees_1 = k7_finseq_1(c2_4__trees_1,c1_4__trees_1) )
     => c2_4__trees_1 = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__trees_1,dt_c2_4__trees_1])],[dt_c1_4__trees_1,dt_c2_4__trees_1,i1_4__trees_1]),
    [interesting(1),t5_trees_1]).

fof(t5_trees_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( A = k7_finseq_1(A,B)
              | A = k7_finseq_1(B,A) )
           => B = k1_xboole_0 ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__trees_1,dh_c1_4__trees_1,dh_c2_4__trees_1]),
    [interesting(1),file(trees_1,t5_trees_1),[file(trees_1,t5_trees_1)]]).