% Mizar problem: t58_qc_lang4,qc_lang4,2144,43 
fof(t58_qc_lang4,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(A)))
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ( ( r2_hidden(D,k3_qc_lang4(A,B))
                          & r2_hidden(k7_finseq_1(D,E),k3_qc_lang4(A,C)) )
                       => r2_hidden(E,k3_qc_lang4(B,C)) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc1_trees_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,cc3_nat_1,cc3_trees_9,cc4_trees_9,cc5_trees_9,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,d1_tarski,d2_qc_lang4,d3_qc_lang4,d4_finseq_1,d5_funct_1,d8_finseq_1,dt_k11_qc_lang1,dt_k12_finseq_1,dt_k17_qc_lang1,dt_k18_qc_lang1,dt_k19_qc_lang1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_qc_lang4,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_qc_lang1,dt_k2_finseq_1,dt_k2_qc_lang4,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_9,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_qc_lang4,dt_k3_trees_2,dt_k4_finseq_1,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_finseq_1,dt_k7_finseq_1,dt_k8_finseq_1,dt_k8_qc_lang1,dt_k9_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_trees_2,dt_m4_trees_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_trees_2,existence_m4_trees_1,fc11_finseq_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_finset_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_finset_1,fc2_subset_1,fc2_trees_2,fc2_trees_9,fc3_finseq_1,fc3_nat_1,fc3_subset_1,fc3_trees_9,fc4_finseq_1,fc4_nat_1,fc4_subset_1,fc5_trees_2,fc9_trees_9,fraenkel_a_2_8_qc_lang4,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_qc_lang4,rc1_subset_1,rc1_trees_1,rc1_trees_2,rc1_trees_a,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_subset_1,rc2_trees_1,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc3_trees_1,rc3_trees_9,rc4_finseq_1,rc4_finset_1,rc4_trees_9,rc5_trees_2,rc5_trees_9,rc6_finseq_1,rc6_trees_2,rc6_trees_9,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k3_trees_2,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_k9_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_nat_1__e4_58__qc_lang4,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t1_arithm,t1_numerals,t1_subset,t25_finseq_1,t2_subset,t2_tarski,t33_qc_lang1,t36_qc_lang4,t3_subset,t45_finseq_1,t45_trees_1,t47_finseq_1,t47_trees_1,t49_qc_lang4,t4_finseq_1,t4_subset,t4_trees_2,t50_finseq_1,t51_qc_lang4,t52_qc_lang4,t53_qc_lang4,t54_qc_lang4,t55_qc_lang4,t56_qc_lang4,t58_qc_lang2,t5_subset,t64_qc_lang2,t6_boole,t7_boole,t8_boole,t8_trees_1]),
    [file(qc_lang4,t58_qc_lang4)]).

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

fof(cc1_finseq_1,axiom,(
    ! [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),
    []).

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

fof(cc1_nat_1,axiom,(
    ! [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),
    []).

fof(cc1_relset_1,axiom,(
    ! [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),
    []).

fof(cc1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m4_trees_1(B,A)
         => v1_finset_1(B) ) ) ),
    file(trees_1,cc1_trees_1),
    []).

fof(cc1_trees_9,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A) ) ) ),
    file(trees_9,cc1_trees_9),
    []).

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

fof(cc2_nat_1,axiom,(
    ! [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),
    []).

fof(cc3_nat_1,axiom,(
    ! [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),
    []).

fof(cc3_trees_9,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A) )
     => ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v2_trees_9(A) ) ) ),
    file(trees_9,cc3_trees_9),
    []).

fof(cc4_trees_9,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v3_trees_2(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v3_trees_9(A) ) ) ),
    file(trees_9,cc4_trees_9),
    []).

fof(cc5_trees_9,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v3_trees_9(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v4_trees_9(A) ) ) ),
    file(trees_9,cc5_trees_9),
    []).

fof(commutativity_k1_nat_1,axiom,(
    ! [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),
    []).

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

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [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),
    []).

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

fof(d2_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,k8_qc_lang1) )
         => ( B = k2_qc_lang4(A)
          <=> ( k1_funct_1(B,k1_xboole_0) = A
              & ! [C] : 
                  ( m1_trees_1(C,k1_relat_1(B))
                 => k2_trees_9(B,C) = k1_qc_lang4(k3_trees_2(k8_qc_lang1,B,C)) ) ) ) ) ) ),
    file(qc_lang4,d2_qc_lang4),
    []).

fof(d3_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m4_trees_1(C,k1_relat_1(k2_qc_lang4(A)))
             => ( C = k3_qc_lang4(A,B)
              <=> ! [D] : 
                    ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(A)))
                   => ( r2_hidden(D,C)
                    <=> k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),D) = B ) ) ) ) ) ) ),
    file(qc_lang4,d3_qc_lang4),
    []).

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

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

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

fof(dt_k11_qc_lang1,axiom,(
    m1_subset_1(k11_qc_lang1,k8_qc_lang1) ),
    file(qc_lang1,k11_qc_lang1),
    []).

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),
    []).

fof(dt_k17_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k17_qc_lang1(A),k8_qc_lang1) ) ),
    file(qc_lang1,k17_qc_lang1),
    []).

fof(dt_k18_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k18_qc_lang1(A),k8_qc_lang1) ) ),
    file(qc_lang1,k18_qc_lang1),
    []).

fof(dt_k19_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k19_qc_lang1(A),k8_qc_lang1) ) ),
    file(qc_lang1,k19_qc_lang1),
    []).

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

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

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_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),
    []).

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

fof(dt_k1_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m2_finseq_1(k1_qc_lang4(A),k8_qc_lang1) ) ),
    file(qc_lang4,k1_qc_lang4),
    []).

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

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

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

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

fof(dt_k21_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k21_qc_lang1(A),k8_qc_lang1) ) ),
    file(qc_lang1,k21_qc_lang1),
    []).

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),
    []).

fof(dt_k2_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v1_funct_1(k2_qc_lang4(A))
        & v1_finset_1(k2_qc_lang4(A))
        & v3_trees_2(k2_qc_lang4(A))
        & m3_trees_2(k2_qc_lang4(A),k8_qc_lang1) ) ) ),
    file(qc_lang4,k2_qc_lang4),
    []).

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

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

fof(dt_k2_trees_9,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v4_trees_9(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k2_trees_9(A,B))
        & v1_funct_1(k2_trees_9(A,B))
        & v1_finseq_1(k2_trees_9(A,B)) ) ) ),
    file(trees_9,k2_trees_9),
    []).

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

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

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

fof(dt_k3_qc_lang4,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m4_trees_1(k3_qc_lang4(A,B),k1_relat_1(k2_qc_lang4(A))) ) ),
    file(qc_lang4,k3_qc_lang4),
    []).

fof(dt_k3_trees_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m3_trees_2(B,A)
        & m1_subset_1(C,k1_relat_1(B)) )
     => m1_subset_1(k3_trees_2(A,B,C),A) ) ),
    file(trees_2,k3_trees_2),
    []).

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),
    []).

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

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

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

fof(dt_k6_finseq_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k6_finseq_1(A))
      & m2_finseq_1(k6_finseq_1(A),A) ) ),
    file(finseq_1,k6_finseq_1),
    []).

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),
    []).

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),
    []).

fof(dt_k8_qc_lang1,axiom,(
    ~ v1_xboole_0(k8_qc_lang1) ),
    file(qc_lang1,k8_qc_lang1),
    []).

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),
    []).

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),
    []).

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

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

fof(dt_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => m2_finseq_1(B,k5_numbers) ) ) ),
    file(trees_1,m1_trees_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),
    []).

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),
    []).

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),
    []).

fof(dt_m3_trees_2,axiom,(
    ! [A,B] : 
      ( m3_trees_2(B,A)
     => v1_relat_1(B) ) ),
    file(trees_2,m3_trees_2),
    []).

fof(dt_m4_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m4_trees_1(B,A)
         => v2_trees_1(B) ) ) ),
    file(trees_1,m4_trees_1),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    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),
    []).

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

fof(existence_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : m1_trees_1(B,A) ) ),
    file(trees_1,m1_trees_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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),
    []).

fof(existence_m3_trees_2,axiom,(
    ! [A] : 
    ? [B] : m3_trees_2(B,A) ),
    file(trees_2,m3_trees_2),
    []).

fof(existence_m4_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : m4_trees_1(B,A) ) ),
    file(trees_1,m4_trees_1),
    []).

fof(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc12_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    []).

fof(fc13_finseq_1,axiom,(
    ! [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),
    []).

fof(fc14_finseq_1,axiom,(
    ! [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),
    []).

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

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

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

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

fof(fc1_nat_1,axiom,(
    ! [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),
    []).

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

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_finseq_1,axiom,
    ( 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),
    []).

fof(fc2_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_trees_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( ~ v1_xboole_0(k1_relat_1(A))
        & v1_trees_1(k1_relat_1(A)) ) ) ),
    file(trees_2,fc2_trees_2),
    []).

fof(fc2_trees_9,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v3_trees_9(A) )
     => ( ~ v1_xboole_0(k1_relat_1(A))
        & v1_trees_1(k1_relat_1(A))
        & v1_trees_2(k1_relat_1(A))
        & v2_trees_9(k1_relat_1(A)) ) ) ),
    file(trees_9,fc2_trees_9),
    []).

fof(fc3_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    []).

fof(fc3_nat_1,axiom,(
    ! [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),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_trees_9,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v4_trees_9(A) )
     => ( ~ v1_xboole_0(k1_relat_1(A))
        & v1_trees_1(k1_relat_1(A))
        & v2_trees_9(k1_relat_1(A)) ) ) ),
    file(trees_9,fc3_trees_9),
    []).

fof(fc4_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_1),
    []).

fof(fc4_nat_1,axiom,(
    ! [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),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_trees_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(trees_2,fc5_trees_2),
    []).

fof(fc9_trees_9,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v3_trees_3(k1_tarski(A)) ) ) ),
    file(trees_9,fc9_trees_9),
    []).

fof(fraenkel_a_2_8_qc_lang4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k8_qc_lang1)
        & m1_subset_1(C,k8_qc_lang1) )
     => ( r2_hidden(A,a_2_8_qc_lang4(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(B)))
            & A = D
            & k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D) = C ) ) ) ),
    file(qc_lang4,a_2_8_qc_lang4),
    []).

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

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

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

fof(rc1_qc_lang4,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m3_trees_2(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v3_trees_2(B)
          & v3_trees_9(B)
          & v4_trees_9(B) ) ) ),
    file(qc_lang4,rc1_qc_lang4),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_trees_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_trees_1(A) ) ),
    file(trees_1,rc1_trees_1),
    []).

fof(rc1_trees_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_trees_1(A)
      & v1_trees_2(A) ) ),
    file(trees_2,rc1_trees_2),
    []).

fof(rc1_trees_a,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : 
          ( m4_trees_1(B,A)
          & ~ v1_xboole_0(B)
          & v2_trees_1(B) ) ) ),
    file(trees_a,rc1_trees_a),
    []).

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

fof(rc2_finset_1,axiom,(
    ! [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),
    []).

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

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_trees_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_1(A) ) ),
    file(trees_1,rc2_trees_1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [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),
    []).

fof(rc3_finset_1,axiom,(
    ! [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),
    []).

fof(rc3_nat_1,axiom,(
    ? [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),
    []).

fof(rc3_trees_1,axiom,(
    ? [A] : v2_trees_1(A) ),
    file(trees_1,rc3_trees_1),
    []).

fof(rc3_trees_9,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_1(A)
      & v1_trees_2(A)
      & v2_trees_9(A) ) ),
    file(trees_9,rc3_trees_9),
    []).

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

fof(rc4_finset_1,axiom,(
    ! [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),
    []).

fof(rc4_trees_9,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v3_trees_2(A)
      & v3_trees_9(A)
      & v4_trees_9(A) ) ),
    file(trees_9,rc4_trees_9),
    []).

fof(rc5_trees_2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v3_trees_2(A) ) ),
    file(trees_2,rc5_trees_2),
    []).

fof(rc5_trees_9,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_xboole_0(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(trees_9,rc5_trees_9),
    []).

fof(rc6_finseq_1,axiom,(
    ? [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),
    []).

fof(rc6_trees_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m3_trees_2(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v3_trees_2(B) ) ) ),
    file(trees_2,rc6_trees_2),
    []).

fof(rc6_trees_9,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_finseq_1(B) ) ) ),
    file(trees_9,rc6_trees_9),
    []).

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

fof(rc7_trees_2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v3_trees_2(A) ) ),
    file(trees_2,rc7_trees_2),
    []).

fof(rc8_finseq_1,axiom,(
    ? [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),
    []).

fof(rc8_trees_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m3_trees_2(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v3_trees_2(B) ) ) ),
    file(trees_2,rc8_trees_2),
    []).

fof(rc9_trees_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & ~ v1_xboole_0(C) ) ) ),
    file(trees_2,rc9_trees_2),
    []).

fof(redefinition_k12_finseq_1,axiom,(
    ! [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),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [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),
    []).

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

fof(redefinition_k3_finseq_1,axiom,(
    ! [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),
    []).

fof(redefinition_k3_trees_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m3_trees_2(B,A)
        & m1_subset_1(C,k1_relat_1(B)) )
     => k3_trees_2(A,B,C) = k1_funct_1(B,C) ) ),
    file(trees_2,k3_trees_2),
    []).

fof(redefinition_k4_finseq_1,axiom,(
    ! [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),
    []).

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

fof(redefinition_k8_finseq_1,axiom,(
    ! [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),
    []).

fof(redefinition_k9_finseq_1,axiom,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_1),
    []).

fof(redefinition_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
        <=> m1_subset_1(B,A) ) ) ),
    file(trees_1,m1_trees_1),
    []).

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

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

fof(redefinition_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,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(s1_nat_1__e4_58__qc_lang4,axiom,
    ( ( ! [A] : 
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] : 
              ( m1_subset_1(B,k8_qc_lang1)
             => ! [C] : 
                  ( m1_subset_1(C,k8_qc_lang1)
                 => ! [D] : 
                      ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(A)))
                     => ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ( ( B = k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),D)
                              & r2_hidden(k7_finseq_1(D,E),k3_qc_lang4(A,C))
                              & k3_finseq_1(E) = 0 )
                           => r2_hidden(E,k3_qc_lang4(B,C)) ) ) ) ) ) )
      & ! [F] : 
          ( m2_subset_1(F,k1_numbers,k5_numbers)
         => ( ! [G] : 
                ( m1_subset_1(G,k8_qc_lang1)
               => ! [H] : 
                    ( m1_subset_1(H,k8_qc_lang1)
                   => ! [I] : 
                        ( m1_subset_1(I,k8_qc_lang1)
                       => ! [J] : 
                            ( m1_trees_1(J,k1_relat_1(k2_qc_lang4(G)))
                           => ! [K] : 
                                ( ( v1_relat_1(K)
                                  & v1_funct_1(K)
                                  & v1_finseq_1(K) )
                               => ( ( H = k3_trees_2(k8_qc_lang1,k2_qc_lang4(G),J)
                                    & r2_hidden(k7_finseq_1(J,K),k3_qc_lang4(G,I))
                                    & k3_finseq_1(K) = F )
                                 => r2_hidden(K,k3_qc_lang4(H,I)) ) ) ) ) ) )
           => ! [L] : 
                ( m1_subset_1(L,k8_qc_lang1)
               => ! [M] : 
                    ( m1_subset_1(M,k8_qc_lang1)
                   => ! [N] : 
                        ( m1_subset_1(N,k8_qc_lang1)
                       => ! [O] : 
                            ( m1_trees_1(O,k1_relat_1(k2_qc_lang4(L)))
                           => ! [P] : 
                                ( ( v1_relat_1(P)
                                  & v1_funct_1(P)
                                  & v1_finseq_1(P) )
                               => ( ( M = k3_trees_2(k8_qc_lang1,k2_qc_lang4(L),O)
                                    & r2_hidden(k7_finseq_1(O,P),k3_qc_lang4(L,N))
                                    & k3_finseq_1(P) = k1_nat_1(F,1) )
                                 => r2_hidden(P,k3_qc_lang4(M,N)) ) ) ) ) ) ) ) ) )
   => ! [F] : 
        ( m2_subset_1(F,k1_numbers,k5_numbers)
       => ! [Q] : 
            ( m1_subset_1(Q,k8_qc_lang1)
           => ! [R] : 
                ( m1_subset_1(R,k8_qc_lang1)
               => ! [S] : 
                    ( m1_subset_1(S,k8_qc_lang1)
                   => ! [T] : 
                        ( m1_trees_1(T,k1_relat_1(k2_qc_lang4(Q)))
                       => ! [U] : 
                            ( ( v1_relat_1(U)
                              & v1_funct_1(U)
                              & v1_finseq_1(U) )
                           => ( ( R = k3_trees_2(k8_qc_lang1,k2_qc_lang4(Q),T)
                                & r2_hidden(k7_finseq_1(T,U),k3_qc_lang4(Q,S))
                                & k3_finseq_1(U) = F )
                             => r2_hidden(U,k3_qc_lang4(R,S)) ) ) ) ) ) ) ) ),
    file(qc_lang4,s1_nat_1__e4_58__qc_lang4),
    []).

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

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

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

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

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

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

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

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

fof(t25_finseq_1,axiom,(
    ! [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),
    []).

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

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

fof(t33_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ~ ( A != k11_qc_lang1
          & ~ v2_qc_lang1(A)
          & ~ v3_qc_lang1(A)
          & ~ v4_qc_lang1(A)
          & ~ v5_qc_lang1(A) ) ) ),
    file(qc_lang1,t33_qc_lang1),
    []).

fof(t36_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(k2_qc_lang4(B)))
             => ( r1_qc_lang2(A,k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),C))
              <=> ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)),k1_relat_1(k2_qc_lang4(B)))
                    & A = k1_funct_1(k2_qc_lang4(B),k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D))) ) ) ) ) ) ),
    file(qc_lang4,t36_qc_lang4),
    []).

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

fof(t45_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ),
    file(finseq_1,t45_finseq_1),
    []).

fof(t45_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r1_tarski(C,B) )
               => r2_hidden(C,A) ) ) ) ) ),
    file(trees_1,t45_trees_1),
    []).

fof(t47_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    file(finseq_1,t47_finseq_1),
    []).

fof(t47_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( r2_hidden(k1_xboole_0,A)
        & r2_hidden(k6_finseq_1(k5_numbers),A) ) ) ),
    file(trees_1,t47_trees_1),
    []).

fof(t49_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k3_qc_lang4(A,B) = a_2_8_qc_lang4(A,B) ) ) ),
    file(qc_lang4,t49_qc_lang4),
    []).

fof(t4_finseq_1,axiom,
    ( k2_finseq_1(0) = k1_xboole_0
    & k2_finseq_1(1) = k1_tarski(1)
    & k2_finseq_1(2) = k2_tarski(1,2) ),
    file(finseq_1,t4_finseq_1),
    []).

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

fof(t4_trees_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ~ ( k3_finseq_1(B) = k1_nat_1(A,1)
              & ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v1_finseq_1(C) )
                 => ! [D] : ~ ( B = k7_finseq_1(C,k9_finseq_1(D))
                      & k3_finseq_1(C) = A ) ) ) ) ) ),
    file(trees_2,t4_trees_2),
    []).

fof(t50_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_finseq_1(k7_finseq_1(A,B),C)
             => ( m2_finseq_1(A,C)
                & m2_finseq_1(B,C) ) ) ) ) ),
    file(finseq_1,t50_finseq_1),
    []).

fof(t51_qc_lang4,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(k2_qc_lang4(B)))
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(B)))
                 => ( ( C = k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,A))
                      & v3_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D)) )
                   => ( k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),C) = k17_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D))
                      & A = 0 ) ) ) ) ) ) ),
    file(qc_lang4,t51_qc_lang4),
    []).

fof(t52_qc_lang4,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(k2_qc_lang4(B)))
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(B)))
                 => ~ ( C = k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,A))
                      & v4_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D))
                      & ~ ( k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),C) = k18_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D))
                          & A = 0 )
                      & ~ ( k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),C) = k19_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D))
                          & A = 1 ) ) ) ) ) ) ),
    file(qc_lang4,t52_qc_lang4),
    []).

fof(t53_qc_lang4,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(k2_qc_lang4(B)))
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(k2_qc_lang4(B)))
                 => ( ( C = k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,A))
                      & v5_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D)) )
                   => ( k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),C) = k21_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(B),D))
                      & A = 0 ) ) ) ) ) ) ),
    file(qc_lang4,t53_qc_lang4),
    []).

fof(t54_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_trees_1(B,k1_relat_1(k2_qc_lang4(A)))
         => ( v3_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B))
           => ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0)),k1_relat_1(k2_qc_lang4(A)))
              & k1_funct_1(k2_qc_lang4(A),k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0))) = k17_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B)) ) ) ) ) ),
    file(qc_lang4,t54_qc_lang4),
    []).

fof(t55_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_trees_1(B,k1_relat_1(k2_qc_lang4(A)))
         => ( v4_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B))
           => ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0)),k1_relat_1(k2_qc_lang4(A)))
              & k1_funct_1(k2_qc_lang4(A),k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0))) = k18_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B))
              & r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,1)),k1_relat_1(k2_qc_lang4(A)))
              & k1_funct_1(k2_qc_lang4(A),k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,1))) = k19_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B)) ) ) ) ) ),
    file(qc_lang4,t55_qc_lang4),
    []).

fof(t56_qc_lang4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_trees_1(B,k1_relat_1(k2_qc_lang4(A)))
         => ( v5_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B))
           => ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0)),k1_relat_1(k2_qc_lang4(A)))
              & k1_funct_1(k2_qc_lang4(A),k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0))) = k21_qc_lang1(k3_trees_2(k8_qc_lang1,k2_qc_lang4(A),B)) ) ) ) ) ),
    file(qc_lang4,t56_qc_lang4),
    []).

fof(t58_qc_lang2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ~ r1_qc_lang2(A,k11_qc_lang1) ) ),
    file(qc_lang2,t58_qc_lang2),
    []).

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

fof(t64_qc_lang2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( v2_qc_lang1(A)
              & r1_qc_lang2(B,A) ) ) ) ),
    file(qc_lang2,t64_qc_lang2),
    []).

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

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

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

fof(t8_trees_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & B = k7_finseq_1(A,C) ) ) ) ) ),
    file(trees_1,t8_trees_1),
    []).