% Mizar problem: t15_msafree3,msafree3,595,22 
fof(t15_msafree3,conjecture,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => r2_pboole(u1_struct_0(A),k2_msafree3(A,C),B) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,antisymmetry_r2_hidden,cc10_trees_3,cc1_card_1,cc1_finseq_1,cc1_funct_1,cc1_index_1,cc1_msaterm,cc1_pboole,cc1_relat_1,cc1_relset_1,cc1_trees_9,cc2_card_1,cc2_funct_1,cc2_index_1,cc2_instalg1,cc2_pboole,cc2_trees_9,cc3_card_1,cc3_instalg1,cc3_trees_9,cc4_instalg1,cc4_msafree3,cc4_trees_3,cc4_trees_9,cc5_instalg1,cc5_trees_3,cc5_trees_9,cc6_trees_9,commutativity_k2_tarski,d3_tarski,d5_funct_1,d5_pboole,d5_tarski,dt_g1_lang1,dt_k13_finseq_1,dt_k1_card_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_msaterm,dt_k1_msualg_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_msafree3,dt_k2_msaterm,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_4,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k4_finseq_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_msafree,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relset_1,dt_k5_trees_3,dt_k6_domain_1,dt_k6_lang1,dt_k6_msafree,dt_k7_dtconstr,dt_l1_lang1,dt_l1_msualg_1,dt_l1_struct_0,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_msaterm,dt_m1_pboole,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m1_trees_4,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_trees_2,dt_m4_trees_3,dt_m5_trees_3,dt_u1_lang1,dt_u1_msualg_1,dt_u1_struct_0,existence_l1_lang1,existence_l1_msualg_1,existence_l1_struct_0,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_msaterm,existence_m1_pboole,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m1_trees_4,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc11_finseq_1,fc12_relat_1,fc16_finseq_1,fc17_finseq_1,fc1_msaterm,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_trees_9,fc26_trees_3,fc2_card_1,fc2_finseq_1,fc2_msaterm,fc2_pboole,fc2_subset_1,fc2_trees_2,fc2_trees_9,fc3_msafree,fc3_subset_1,fc3_trees_9,fc4_msafree,fc4_relat_1,fc4_subset_1,fc5_msafree,fc5_relat_1,fc5_trees_2,fc6_funct_1,fc6_relat_1,fc6_trees_3,fc7_relat_1,fc8_relat_1,fc9_finseq_1,fc9_trees_9,free_g1_lang1,rc1_card_1,rc1_finseq_1,rc1_funct_1,rc1_index_1,rc1_instalg1,rc1_pboole,rc1_relat_1,rc1_subset_1,rc1_trees_2,rc1_trees_9,rc2_card_1,rc2_catalg_1,rc2_finseq_1,rc2_funct_1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc2_trees_3,rc2_trees_9,rc3_finseq_1,rc3_funct_1,rc3_pboole,rc3_relat_1,rc3_struct_0,rc3_trees_9,rc4_finseq_1,rc4_funct_1,rc4_trees_3,rc4_trees_9,rc5_funct_1,rc5_struct_0,rc5_trees_2,rc5_trees_9,rc6_finseq_1,rc6_trees_2,rc6_trees_3,rc6_trees_9,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc8_trees_3,rc9_trees_2,redefinition_k1_domain_1,redefinition_k2_msaterm,redefinition_k2_trees_4,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k6_domain_1,redefinition_k7_dtconstr,redefinition_m1_dtconstr,redefinition_m1_struct_0,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,reflexivity_r1_tarski,reflexivity_r2_pboole,s1_msaterm__e3_25__msafree3,t11_msafree3,t12_msafree3,t1_subset,t22_msaterm,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(msafree3,t15_msafree3)]).

fof(abstractness_v1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => ( v1_lang1(A)
       => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) ),
    file(lang1,v1_lang1),
    []).

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

fof(cc10_trees_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v3_trees_3(A) )
     => ! [B] : 
          ( m1_finseq_1(B,A)
         => v6_trees_3(B) ) ) ),
    file(trees_3,cc10_trees_3),
    []).

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(index_1,cc1_index_1),
    []).

fof(cc1_msaterm,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C] : 
          ( m1_subset_1(C,k1_msaterm(A,B))
         => v1_finset_1(C) ) ) ),
    file(msaterm,cc1_msaterm),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_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_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_card_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)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    []).

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

fof(cc2_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(index_1,cc2_index_1),
    []).

fof(cc2_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( ~ v3_struct_0(A)
       => v1_instalg1(A) ) ) ),
    file(instalg1,cc2_instalg1),
    []).

fof(cc2_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc2_trees_9,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v1_trees_9(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v3_trees_2(A) ) ) ),
    file(trees_9,cc2_trees_9),
    []).

fof(cc3_card_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_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    []).

fof(cc3_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
       => v1_instalg1(A) ) ) ),
    file(instalg1,cc3_instalg1),
    []).

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_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( ( v3_struct_0(A)
          & v1_instalg1(A) )
       => v2_msualg_1(A) ) ) ),
    file(instalg1,cc4_instalg1),
    []).

fof(cc4_msafree3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) ) ) ),
    file(msafree3,cc4_msafree3),
    []).

fof(cc4_trees_3,axiom,(
    ! [A] : 
      ( v3_trees_3(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v3_trees_3(B) ) ) ),
    file(trees_3,cc4_trees_3),
    []).

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_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( ( ~ v2_msualg_1(A)
          & v1_instalg1(A) )
       => ~ v3_struct_0(A) ) ) ),
    file(instalg1,cc5_instalg1),
    []).

fof(cc5_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m4_trees_3(B,A)
         => v3_trees_3(B) ) ) ),
    file(trees_3,cc5_trees_3),
    []).

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(cc6_trees_9,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A))) )
     => ! [C] : 
          ( m1_subset_1(C,B)
         => v1_finset_1(C) ) ) ),
    file(trees_9,cc6_trees_9),
    []).

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

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

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(d5_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_g1_lang1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k3_finseq_2(A))
     => ( v1_lang1(g1_lang1(A,B))
        & l1_lang1(g1_lang1(A,B)) ) ) ),
    file(lang1,g1_lang1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

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

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_msaterm,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => m1_subset_1(k1_msaterm(A,B),k1_zfmisc_1(k5_trees_3(u1_struct_0(k5_msafree(A,B))))) ) ),
    file(msaterm,k1_msaterm),
    []).

fof(dt_k1_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ),
    file(msualg_1,k1_msualg_1),
    []).

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

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_trees_4,axiom,(
    ! [A] : 
      ( v1_relat_1(k1_trees_4(A))
      & v1_funct_1(k1_trees_4(A))
      & v3_trees_2(k1_trees_4(A)) ) ),
    file(trees_4,k1_trees_4),
    []).

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_k2_msafree3,axiom,(
    ! [A,B] : 
      ( ( l1_msualg_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B) )
     => m1_pboole(k2_msafree3(A,B),u1_struct_0(A)) ) ),
    file(msafree3,k2_msafree3),
    []).

fof(dt_k2_msaterm,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => m1_struct_0(k2_msaterm(A,B,C),k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B))) ) ),
    file(msaterm,k2_msaterm),
    []).

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_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m5_trees_3(k2_trees_4(A,B),A,k5_trees_3(A)) ) ),
    file(trees_4,k2_trees_4),
    []).

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_finseq_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_trees_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k4_trees_4(A,B))
        & v1_funct_1(k4_trees_4(A,B))
        & v3_trees_2(k4_trees_4(A,B)) ) ) ),
    file(trees_4,k4_trees_4),
    []).

fof(dt_k5_msafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => l1_lang1(k5_msafree(A,B)) ) ),
    file(msafree,k5_msafree),
    []).

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_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(dt_k5_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m4_trees_3(k5_trees_3(A),A) ) ),
    file(trees_3,k5_trees_3),
    []).

fof(dt_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(dt_k6_lang1,axiom,(
    $true ),
    file(lang1,k6_lang1),
    []).

fof(dt_k6_msafree,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => m1_subset_1(k6_msafree(A,B,C),u1_struct_0(k5_msafree(A,B))) ) ),
    file(msafree,k6_msafree),
    []).

fof(dt_k7_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k7_dtconstr(A))
        & m1_subset_1(k7_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(dtconstr,k7_dtconstr),
    []).

fof(dt_l1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => l1_struct_0(A) ) ),
    file(lang1,l1_lang1),
    []).

fof(dt_l1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] : 
          ( m1_dtconstr(D,A,B,C)
         => m5_trees_3(D,A,B) ) ) ),
    file(dtconstr,m1_dtconstr),
    []).

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_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

fof(dt_m1_msaterm,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) )
     => ! [D] : 
          ( m1_msaterm(D,A,B,C)
         => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ),
    file(msaterm,m1_msaterm),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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

fof(dt_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m1_struct_0(C,A,B)
         => m1_subset_1(C,u1_struct_0(A)) ) ) ),
    file(struct_0,m1_struct_0),
    []).

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

fof(dt_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m1_trees_4(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(trees_4,m1_trees_4),
    []).

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_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),
    []).

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_3,axiom,(
    $true ),
    file(trees_3,m4_trees_3),
    []).

fof(dt_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m5_trees_3(C,A,B)
         => ( v1_funct_1(C)
            & v3_trees_2(C)
            & m3_trees_2(C,A) ) ) ) ),
    file(trees_3,m5_trees_3),
    []).

fof(dt_u1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => m2_relset_1(u1_lang1(A),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ),
    file(lang1,u1_lang1),
    []).

fof(dt_u1_msualg_1,axiom,(
    $true ),
    file(msualg_1,u1_msualg_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_lang1,axiom,(
    ? [A] : l1_lang1(A) ),
    file(lang1,l1_lang1),
    []).

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ? [D] : m1_dtconstr(D,A,B,C) ) ),
    file(dtconstr,m1_dtconstr),
    []).

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

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

fof(existence_m1_msaterm,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) )
     => ? [D] : m1_msaterm(D,A,B,C) ) ),
    file(msaterm,m1_msaterm),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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

fof(existence_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [C] : m1_struct_0(C,A,B) ) ),
    file(struct_0,m1_struct_0),
    []).

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

fof(existence_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m1_trees_4(C,A,B) ) ),
    file(trees_4,m1_trees_4),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_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),
    []).

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_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m4_trees_3(B,A) ) ),
    file(trees_3,m4_trees_3),
    []).

fof(existence_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ? [C] : m5_trees_3(C,A,B) ) ),
    file(trees_3,m5_trees_3),
    []).

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_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc16_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & v1_fraenkel(k13_finseq_1(A)) ) ),
    file(finseq_1,fc16_finseq_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_msaterm,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(msaterm,fc1_msaterm),
    []).

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_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc1_trees_9,axiom,(
    ! [A] : 
      ( v1_relat_1(k1_trees_4(A))
      & v1_funct_1(k1_trees_4(A))
      & v1_finset_1(k1_trees_4(A))
      & v3_trees_2(k1_trees_4(A))
      & v1_trees_9(k1_trees_4(A)) ) ),
    file(trees_9,fc1_trees_9),
    []).

fof(fc26_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_trees_3(A)) )
     => ( ~ v1_xboole_0(k1_relat_1(B))
        & v1_finset_1(k1_relat_1(B))
        & v1_trees_1(k1_relat_1(B)) ) ) ),
    file(trees_3,fc26_trees_3),
    []).

fof(fc2_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_1,fc2_card_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_msaterm,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k1_msaterm(A,B))
        & v3_trees_3(k1_msaterm(A,B)) ) ) ),
    file(msaterm,fc2_msaterm),
    []).

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

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_msafree,axiom,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ~ v1_xboole_0(u1_msualg_1(A)) ) ),
    file(msafree,fc3_msafree),
    []).

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_msafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_msafree(A,B))
        & v1_lang1(k5_msafree(A,B)) ) ) ),
    file(msafree,fc4_msafree),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_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_msafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_msafree(A,B))
        & v1_lang1(k5_msafree(A,B))
        & v1_dtconstr(k5_msafree(A,B))
        & v2_dtconstr(k5_msafree(A,B))
        & v3_dtconstr(k5_msafree(A,B)) ) ) ),
    file(msafree,fc5_msafree),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_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(fc6_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => v1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_1,fc6_funct_1),
    []).

fof(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

fof(fc6_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k5_trees_3(A))
        & v3_trees_3(k5_trees_3(A)) ) ) ),
    file(trees_3,fc6_trees_3),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

fof(fc9_finseq_1,axiom,(
    ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ),
    file(finseq_1,fc9_finseq_1),
    []).

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(free_g1_lang1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k3_finseq_2(A))
     => ! [C,D] : 
          ( g1_lang1(A,B) = g1_lang1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(lang1,g1_lang1),
    []).

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & ~ v3_relat_1(B)
          & v1_funct_1(B) ) ) ),
    file(index_1,rc1_index_1),
    []).

fof(rc1_instalg1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A)
      & v1_instalg1(A) ) ),
    file(instalg1,rc1_instalg1),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_trees_1(A)
      & v1_trees_2(A) ) ),
    file(trees_2,rc1_trees_2),
    []).

fof(rc1_trees_9,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v3_trees_2(A)
      & v1_trees_9(A) ) ),
    file(trees_9,rc1_trees_9),
    []).

fof(rc2_card_1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    []).

fof(rc2_catalg_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & ~ v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(catalg_1,rc2_catalg_1),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_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_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v3_trees_3(A) ) ),
    file(trees_3,rc2_trees_3),
    []).

fof(rc2_trees_9,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v3_trees_2(A)
      & ~ v1_trees_9(A) ) ),
    file(trees_9,rc2_trees_9),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc4_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m4_trees_3(B,A)
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v3_trees_3(B) ) ) ),
    file(trees_3,rc4_trees_3),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

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_3,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v6_trees_3(A) ) ),
    file(trees_3,rc6_trees_3),
    []).

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(rc8_trees_3,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v6_trees_3(A) ) ),
    file(trees_3,rc8_trees_3),
    []).

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_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k2_msaterm,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => k2_msaterm(A,B,C) = k6_msafree(A,B,C) ) ),
    file(msaterm,k2_msaterm),
    []).

fof(redefinition_k2_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k2_trees_4(A,B) = k1_trees_4(B) ) ),
    file(trees_4,k2_trees_4),
    []).

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_finseq_2,axiom,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_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_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(redefinition_k7_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_dtconstr(A)
        & l1_lang1(A) )
     => k7_dtconstr(A) = k6_lang1(A) ) ),
    file(dtconstr,k7_dtconstr),
    []).

fof(redefinition_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] : 
          ( m1_dtconstr(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(dtconstr,m1_dtconstr),
    []).

fof(redefinition_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m1_struct_0(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(struct_0,m1_struct_0),
    []).

fof(redefinition_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m1_trees_4(C,A,B)
        <=> m1_finseq_1(C,B) ) ) ),
    file(trees_4,m1_trees_4),
    []).

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_finseq_2,axiom,(
    ! [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),
    []).

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(redefinition_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m5_trees_3(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(trees_3,m5_trees_3),
    []).

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

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    []).

fof(s1_msaterm__e3_25__msafree3,axiom,(
    ! [A,B] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ( ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_funct_1(B,C))
                 => r2_pboole(u1_struct_0(A),k2_msafree3(A,k1_trees_4(k4_tarski(D,C))),B) ) )
          & ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
                 => ( ! [E] : 
                        ( m1_dtconstr(E,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                       => ( r2_hidden(E,k2_relat_1(D))
                         => r2_pboole(u1_struct_0(A),k2_msafree3(A,E),B) ) )
                   => r2_pboole(u1_struct_0(A),k2_msafree3(A,k4_trees_4(k4_tarski(C,u1_struct_0(A)),D)),B) ) ) ) )
       => ! [C] : 
            ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
           => r2_pboole(u1_struct_0(A),k2_msafree3(A,C),B) ) ) ) ),
    file(msafree3,s1_msaterm__e3_25__msafree3),
    []).

fof(t11_msafree3,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B,C] : 
          ( ( r2_hidden(B,u1_struct_0(A))
           => k1_funct_1(k2_msafree3(A,k1_trees_4(k4_tarski(C,B))),B) = k1_tarski(C) )
          & ! [D] : 
              ( ~ ( D = B
                  & r2_hidden(B,u1_struct_0(A)) )
             => k1_funct_1(k2_msafree3(A,k1_trees_4(k4_tarski(C,B))),D) = k1_xboole_0 ) ) ) ),
    file(msafree3,t11_msafree3),
    []).

fof(t12_msafree3,axiom,(
    ! [A,B,C] : 
      ( l1_msualg_1(C)
     => ! [D] : 
          ( r2_hidden(D,u1_struct_0(C))
         => ! [E] : 
              ( ( v1_relat_1(E)
                & v1_funct_1(E)
                & v1_finseq_1(E)
                & v6_trees_3(E) )
             => ( r2_hidden(A,k1_funct_1(k2_msafree3(C,k4_trees_4(k4_tarski(B,u1_struct_0(C)),E)),D))
              <=> ? [F] : 
                    ( v1_relat_1(F)
                    & v1_funct_1(F)
                    & v3_trees_2(F)
                    & r2_hidden(F,k2_relat_1(E))
                    & r2_hidden(A,k1_funct_1(k2_msafree3(C,F),D)) ) ) ) ) ) ),
    file(msafree3,t12_msafree3),
    []).

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

fof(t22_msaterm,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
                 => ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
                    & k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C))
                    & ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k4_finseq_1(D))
                         => m1_dtconstr(k1_funct_1(D,E),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ) ) ) ),
    file(msaterm,t22_msaterm),
    []).

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

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

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(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(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),
    []).