% Mizar problem: t12_wellfnd1,wellfnd1,563,35 
fof(t12_wellfnd1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_wellfnd1(A)
      <=> ! [B] : 
            ( ~ v1_xboole_0(B)
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),B)),B)
                  & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),B)),B) )
               => ? [D] : 
                    ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),B)
                    & m2_relset_1(D,u1_struct_0(A),B)
                    & r1_wellfnd1(A,B,C,D) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_altcat_1,cc1_card_1,cc1_card_5,cc1_fraenkel,cc1_membered,cc1_realset1,cc1_relset_1,cc20_membered,cc2_card_5,cc2_membered,cc3_membered,cc4_membered,commutativity_k1_card_2,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k5_subset_1,connectedness_r1_ordinal1,d12_funct_1,d1_funct_2,d1_funct_4,d1_tarski,d1_wellfnd1,d1_wellord1,d1_xboole_0,d2_wellfnd1,d2_xboole_0,d3_tarski,d3_wellord1,d3_xboole_0,d4_relat_1,d4_tarski,d5_funct_1,d5_partfun1,d5_relat_1,d5_tarski,d5_wellfnd1,d6_partfun1,d7_xboole_0,dt_k1_card_1,dt_k1_card_2,dt_k1_domain_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_wellfnd1,dt_k1_wellord1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_1,dt_k2_funct_2,dt_k2_partfun1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_card_1,dt_k3_cqc_lang,dt_k3_tarski,dt_k3_xboole_0,dt_k4_partfun1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k4_tarski,dt_k5_relset_1,dt_k5_subset_1,dt_k6_ordinal2,dt_k7_ordinal2,dt_k7_relat_1,dt_k8_funct_2,dt_k8_relset_1,dt_k9_relat_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_relset_1,dt_m2_rfunct_3,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_relset_1,existence_m2_rfunct_3,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_card_1,fc1_cqc_lang,fc1_partfun1,fc1_struct_0,fc1_subset_1,fc1_wellfnd1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc2_altcat_1,fc2_card_1,fc2_card_5,fc2_subset_1,fc2_wellfnd1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_card_5,fc3_realset1,fc3_subset_1,fc4_card_5,fc4_subset_1,fc6_membered,fc7_card_5,fc7_membered,fc8_membered,fc9_membered,idempotence_k1_funct_4,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc1_card_1,rc1_card_5,rc1_fraenkel,rc1_membered,rc1_realset1,rc1_subset_1,rc1_wellfnd1,rc2_card_1,rc2_card_5,rc2_partfun1,rc2_realset1,rc2_subset_1,rc2_wellfnd1,rc3_struct_0,rc5_struct_0,redefinition_k1_domain_1,redefinition_k1_struct_0,redefinition_k1_wellfnd1,redefinition_k2_funct_2,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k5_relset_1,redefinition_k5_subset_1,redefinition_k8_funct_2,redefinition_k8_relset_1,redefinition_m2_relset_1,redefinition_m2_rfunct_3,redefinition_r1_ordinal1,reflexivity_r1_ordinal1,reflexivity_r1_partfun1,reflexivity_r1_tarski,s1_funct_7__e5_27__wellfnd1,s1_wellfnd1__e2_27_1__wellfnd1,s2_wellfnd1__e6_27_1_6__wellfnd1,s2_wellfnd1__e8_27_1_1__wellfnd1,spc0_boole,symmetry_r1_partfun1,symmetry_r1_xboole_0,t106_zfmisc_1,t119_funct_2,t119_partfun1,t11_relset_1,t120_partfun1,t12_funct_4,t14_funct_4,t18_funct_4,t1_boole,t1_subset,t1_wellfnd1,t1_xboole_1,t22_ordinal1,t22_ordinal2,t23_ordinal1,t25_ordinal2,t27_card_1,t27_ordinal2,t28_card_1,t2_boole,t2_subset,t2_tarski,t2_wellfnd1,t32_card_1,t3_subset,t3_wellfnd1,t3_xboole_0,t42_card_5,t44_partfun1,t4_subset,t5_cqc_lang,t5_subset,t5_wellfnd1,t6_boole,t6_cqc_lang,t72_card_4,t72_funct_1,t73_funct_1,t76_funct_4,t7_boole,t7_funct_2,t7_ordinal1,t8_boole,t8_funct_1,t8_grfunc_1,t91_relat_1,t92_zfmisc_1,t9_funct_1]),
    [file(wellfnd1,t12_wellfnd1)]).

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

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

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

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

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

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

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

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

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

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

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

fof(cc1_altcat_1,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    []).

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_card_5,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(card_5,cc1_card_5),
    []).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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

fof(cc2_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(card_5,cc2_card_5),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

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

fof(commutativity_k1_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => k1_card_2(A,B) = k1_card_2(B,A) ) ),
    file(card_2,k1_card_2),
    []).

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

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

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(connectedness_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(d12_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    []).

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

fof(d1_wellfnd1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v12_waybel_0(B,A)
          <=> ! [C,D] : 
                ( ( r2_hidden(C,B)
                  & r2_hidden(k4_tarski(D,C),u1_orders_2(A)) )
               => r2_hidden(D,B) ) ) ) ) ),
    file(wellfnd1,d1_wellfnd1),
    []).

fof(d1_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k1_wellord1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( D != B
                & r2_hidden(k4_tarski(D,B),A) ) ) ) ) ),
    file(wellord1,d1_wellord1),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_wellfnd1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_wellfnd1(A)
      <=> r1_wellord1(u1_orders_2(A),u1_struct_0(A)) ) ) ),
    file(wellfnd1,d2_wellfnd1),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

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

fof(d3_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_wellord1(A,B)
        <=> ! [C] : ~ ( r1_tarski(C,B)
              & C != k1_xboole_0
              & ! [D] : ~ ( r2_hidden(D,C)
                  & r1_xboole_0(k1_wellord1(A,D),C) ) ) ) ) ),
    file(wellord1,d3_wellord1),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_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_partfun1,axiom,(
    ! [A,B,C] : 
      ( C = k4_partfun1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & r1_tarski(k1_relat_1(E),A)
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(partfun1,d5_partfun1),
    []).

fof(d5_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_1,d5_relat_1),
    []).

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

fof(d5_wellfnd1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),B)),B)
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),B)),B) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r1_wellfnd1(A,B,C,D)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_funct_1(D,E) = k1_funct_1(C,k4_tarski(E,k7_relat_1(D,k1_wellord1(u1_orders_2(A),E)))) ) ) ) ) ) ) ),
    file(wellfnd1,d5_wellfnd1),
    []).

fof(d6_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ! [C] : 
                ( r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
               => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ),
    file(partfun1,d6_partfun1),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

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

fof(dt_k1_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => v1_card_1(k1_card_2(A,B)) ) ),
    file(card_2,k1_card_2),
    []).

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_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    []).

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

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

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

fof(dt_k1_wellfnd1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(C)
        & m1_relset_1(C,u1_struct_0(A),B) )
     => m1_subset_1(k1_wellfnd1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(wellfnd1,k1_wellfnd1),
    []).

fof(dt_k1_wellord1,axiom,(
    $true ),
    file(wellord1,k1_wellord1),
    []).

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_card_1,axiom,(
    ! [A] : v1_card_1(k2_card_1(A)) ),
    file(card_1,k2_card_1),
    []).

fof(dt_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_2),
    []).

fof(dt_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ),
    file(partfun1,k2_partfun1),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_card_1,axiom,(
    $true ),
    file(card_1,k3_card_1),
    []).

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_rfunct_3,axiom,(
    ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ),
    file(rfunct_3,k4_rfunct_3),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k6_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k6_ordinal2(A)) ),
    file(ordinal2,k6_ordinal2),
    []).

fof(dt_k7_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k7_ordinal2(A)) ),
    file(ordinal2,k7_ordinal2),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k8_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ),
    file(relset_1,k8_relset_1),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

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

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

fof(dt_m1_rfunct_3,axiom,(
    $true ),
    file(rfunct_3,m1_rfunct_3),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_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_rfunct_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & m1_rfunct_3(C,A,B) )
     => ! [D] : 
          ( m2_rfunct_3(D,A,B,C)
         => ( v1_funct_1(D)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(rfunct_3,m2_rfunct_3),
    []).

fof(dt_u1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

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

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

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

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

fof(existence_m1_rfunct_3,axiom,(
    ! [A,B] : 
    ? [C] : m1_rfunct_3(C,A,B) ),
    file(rfunct_3,m1_rfunct_3),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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_rfunct_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & m1_rfunct_3(C,A,B) )
     => ? [D] : m2_rfunct_3(D,A,B,C) ) ),
    file(rfunct_3,m2_rfunct_3),
    []).

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

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

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

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

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

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

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

fof(fc1_card_1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_card_1(A))
        & v2_ordinal1(k3_card_1(A))
        & v3_ordinal1(k3_card_1(A))
        & v1_card_1(k3_card_1(A)) ) ) ),
    file(card_1,fc1_card_1),
    []).

fof(fc1_cqc_lang,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(cqc_lang,fc1_cqc_lang),
    []).

fof(fc1_partfun1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    []).

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_wellfnd1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k4_partfun1(A,B))
      & v1_fraenkel(k4_partfun1(A,B)) ) ),
    file(wellfnd1,fc1_wellfnd1),
    []).

fof(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

fof(fc27_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(A,B)) ) ),
    file(membered,fc27_membered),
    []).

fof(fc28_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(B,A)) ) ),
    file(membered,fc28_membered),
    []).

fof(fc29_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc29_membered),
    []).

fof(fc2_altcat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    []).

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_card_5,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k3_card_1(A))
        & v1_ordinal1(k3_card_1(A))
        & v2_ordinal1(k3_card_1(A))
        & v3_ordinal1(k3_card_1(A))
        & ~ v1_finset_1(k3_card_1(A))
        & v1_card_1(k3_card_1(A)) ) ) ),
    file(card_5,fc2_card_5),
    []).

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

fof(fc2_wellfnd1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k2_card_1(A))
      & v1_ordinal1(k2_card_1(A))
      & v2_ordinal1(k2_card_1(A))
      & v3_ordinal1(k2_card_1(A))
      & v1_card_1(k2_card_1(A)) ) ),
    file(wellfnd1,fc2_wellfnd1),
    []).

fof(fc30_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc30_membered),
    []).

fof(fc31_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc31_membered),
    []).

fof(fc32_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc32_membered),
    []).

fof(fc33_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc33_membered),
    []).

fof(fc34_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc34_membered),
    []).

fof(fc35_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B))
        & v5_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc35_membered),
    []).

fof(fc36_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A))
        & v5_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc36_membered),
    []).

fof(fc3_card_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v1_card_1(B) )
     => ( ~ v1_xboole_0(k1_card_2(A,B))
        & v1_ordinal1(k1_card_2(A,B))
        & v2_ordinal1(k1_card_2(A,B))
        & v3_ordinal1(k1_card_2(A,B))
        & ~ v1_finset_1(k1_card_2(A,B))
        & v1_card_1(k1_card_2(A,B)) ) ) ),
    file(card_5,fc3_card_5),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

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

fof(fc4_card_5,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B) )
     => ( ~ v1_xboole_0(k1_card_2(A,B))
        & v1_ordinal1(k1_card_2(A,B))
        & v2_ordinal1(k1_card_2(A,B))
        & v3_ordinal1(k1_card_2(A,B))
        & ~ v1_finset_1(k1_card_2(A,B))
        & v1_card_1(k1_card_2(A,B)) ) ) ),
    file(card_5,fc4_card_5),
    []).

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

fof(fc7_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( ~ v1_xboole_0(k2_card_1(A))
        & v1_ordinal1(k2_card_1(A))
        & v2_ordinal1(k2_card_1(A))
        & v3_ordinal1(k2_card_1(A))
        & ~ v1_finset_1(k2_card_1(A))
        & v1_card_1(k2_card_1(A)) ) ) ),
    file(card_5,fc7_card_5),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

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

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

fof(idempotence_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

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

fof(rc1_card_5,axiom,(
    ? [A] : ~ v1_finset_1(A) ),
    file(card_5,rc1_card_5),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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_wellfnd1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A)
      & v1_card_5(A) ) ),
    file(wellfnd1,rc1_wellfnd1),
    []).

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_card_5,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_5,rc2_card_5),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

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_wellfnd1,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_wellfnd1(A) ) ),
    file(wellfnd1,rc2_wellfnd1),
    []).

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

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(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_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k1_wellfnd1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(C)
        & m1_relset_1(C,u1_struct_0(A),B) )
     => k1_wellfnd1(A,B,C) = k1_relat_1(C) ) ),
    file(wellfnd1,k1_wellfnd1),
    []).

fof(redefinition_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    []).

fof(redefinition_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k4_rfunct_3,axiom,(
    ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ),
    file(rfunct_3,k4_rfunct_3),
    []).

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_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_k8_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(relset_1,k8_relset_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_rfunct_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & m1_rfunct_3(C,A,B) )
     => ! [D] : 
          ( m2_rfunct_3(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(rfunct_3,m2_rfunct_3),
    []).

fof(redefinition_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(A,A) ) ),
    file(partfun1,r1_partfun1),
    []).

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

fof(s1_funct_7__e5_27__wellfnd1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B) )
     => ( ! [C] : 
            ( m1_subset_1(C,u1_struct_0(A))
           => ! [D] : 
                ( m1_subset_1(D,k4_rfunct_3(u1_struct_0(A),k2_card_1(B)))
               => r2_hidden(k7_ordinal2(k5_relset_1(u1_struct_0(A),k2_card_1(B),D)),k2_card_1(B)) ) )
       => ? [C] : 
            ( v1_funct_1(C)
            & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),k2_card_1(B))),k2_card_1(B))
            & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),k2_card_1(B))),k2_card_1(B))
            & ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] : 
                    ( m1_subset_1(E,k4_rfunct_3(u1_struct_0(A),k2_card_1(B)))
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),k2_card_1(B))),k2_card_1(B),C,k1_domain_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),k2_card_1(B)),D,E)) = k7_ordinal2(k5_relset_1(u1_struct_0(A),k2_card_1(B),E)) ) ) ) ) ) ),
    file(wellfnd1,s1_funct_7__e5_27__wellfnd1),
    []).

fof(s1_wellfnd1__e2_27_1__wellfnd1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),B)),B)
        & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),k4_rfunct_3(u1_struct_0(A),B)),B) )
     => ? [D] : 
          ( m1_subset_1(D,k1_zfmisc_1(k4_rfunct_3(u1_struct_0(A),B)))
          & ! [E] : 
              ( ( v1_funct_1(E)
                & m2_relset_1(E,u1_struct_0(A),B) )
             => ( r2_hidden(E,D)
              <=> ( v12_waybel_0(k1_wellfnd1(A,B,E),A)
                  & ! [F] : 
                      ( r2_hidden(F,k1_wellfnd1(A,B,E))
                     => k1_funct_1(E,F) = k1_funct_1(C,k4_tarski(F,k2_partfun1(u1_struct_0(A),B,E,k1_wellord1(u1_orders_2(A),F)))) ) ) ) ) ) ) ),
    file(wellfnd1,s1_wellfnd1__e2_27_1__wellfnd1),
    []).

fof(s2_wellfnd1__e6_27_1_6__wellfnd1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ( r2_hidden(C,u1_struct_0(A))
          & ~ r2_hidden(C,k1_relat_1(B))
          & v1_wellfnd1(A) )
       => ? [D] : 
            ( m1_subset_1(D,u1_struct_0(A))
            & r2_hidden(D,u1_struct_0(A))
            & ~ r2_hidden(D,k1_relat_1(B))
            & ! [E] : 
                ( m1_subset_1(E,u1_struct_0(A))
               => ~ ( D != E
                    & r2_hidden(E,u1_struct_0(A))
                    & ~ r2_hidden(E,k1_relat_1(B))
                    & r2_hidden(k4_tarski(E,D),u1_orders_2(A)) ) ) ) ) ) ),
    file(wellfnd1,s2_wellfnd1__e6_27_1_6__wellfnd1),
    []).

fof(s2_wellfnd1__e8_27_1_1__wellfnd1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & m2_relset_1(C,u1_struct_0(A),B)
        & v1_funct_1(D)
        & m2_relset_1(D,u1_struct_0(A),B)
        & m1_subset_1(E,u1_struct_0(A)) )
     => ( ( r2_hidden(E,k1_wellfnd1(A,B,C))
          & r2_hidden(E,k1_wellfnd1(A,B,D))
          & k1_funct_1(C,E) != k1_funct_1(D,E)
          & v1_wellfnd1(A) )
       => ? [F] : 
            ( m1_subset_1(F,u1_struct_0(A))
            & r2_hidden(F,k1_wellfnd1(A,B,C))
            & r2_hidden(F,k1_wellfnd1(A,B,D))
            & k1_funct_1(C,F) != k1_funct_1(D,F)
            & ! [G] : 
                ( m1_subset_1(G,u1_struct_0(A))
               => ~ ( F != G
                    & r2_hidden(G,k1_wellfnd1(A,B,C))
                    & r2_hidden(G,k1_wellfnd1(A,B,D))
                    & k1_funct_1(C,G) != k1_funct_1(D,G)
                    & r2_hidden(k4_tarski(G,F),u1_orders_2(A)) ) ) ) ) ) ),
    file(wellfnd1,s2_wellfnd1__e8_27_1_1__wellfnd1),
    []).

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

fof(symmetry_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_partfun1(A,B)
       => r1_partfun1(B,A) ) ) ),
    file(partfun1,r1_partfun1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

fof(t119_funct_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(F)
        & v1_funct_2(F,k2_zfmisc_1(A,B),C)
        & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
     => ( ( r2_hidden(D,A)
          & r2_hidden(E,B) )
       => ( C = k1_xboole_0
          | r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) ) ) ) ),
    file(funct_2,t119_funct_2),
    []).

fof(t119_partfun1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => r2_hidden(C,k4_partfun1(A,B)) ) ),
    file(partfun1,t119_partfun1),
    []).

fof(t11_relset_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    []).

fof(t120_partfun1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(C,k4_partfun1(A,B))
     => ( v1_funct_1(C)
        & m2_relset_1(C,A,B) ) ) ),
    file(partfun1,t120_partfun1),
    []).

fof(t12_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    []).

fof(t14_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    []).

fof(t18_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_4,t18_funct_4),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t1_wellfnd1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r1_tarski(B,C)
              & r1_tarski(A,k1_relat_1(B)) )
           => k7_relat_1(B,A) = k7_relat_1(C,A) ) ) ) ),
    file(wellfnd1,t1_wellfnd1),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t22_ordinal1,axiom,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_tarski(A,B)
                  & r2_hidden(B,C) )
               => r2_hidden(A,C) ) ) ) ) ),
    file(ordinal1,t22_ordinal1),
    []).

fof(t22_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r1_ordinal1(k6_ordinal2(B),A) ) ) ),
    file(ordinal2,t22_ordinal2),
    []).

fof(t23_ordinal1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    []).

fof(t25_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r2_hidden(k6_ordinal2(B),B) ) ) ),
    file(ordinal2,t25_ordinal2),
    []).

fof(t27_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    []).

fof(t27_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r2_hidden(A,k7_ordinal2(B)) ) ) ),
    file(ordinal2,t27_ordinal2),
    []).

fof(t28_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = B
          & r1_tarski(A,k2_relat_1(C)) ) ) ),
    file(card_1,t28_card_1),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t2_wellfnd1,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ( ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( ( r2_hidden(B,A)
                    & r2_hidden(C,A) )
                 => r1_partfun1(B,C) ) ) )
       => ( v1_relat_1(k3_tarski(A))
          & v1_funct_1(k3_tarski(A)) ) ) ) ),
    file(wellfnd1,t2_wellfnd1),
    []).

fof(t32_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => r2_hidden(A,k2_card_1(A)) ) ),
    file(card_1,t32_card_1),
    []).

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

fof(t3_wellfnd1,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v1_card_5(A) )
     => ! [B] : 
          ( ( r1_tarski(B,A)
            & r2_hidden(k1_card_1(B),A) )
         => r2_hidden(k7_ordinal2(B),A) ) ) ),
    file(wellfnd1,t3_wellfnd1),
    []).

fof(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t42_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v1_card_5(k3_card_1(0))
        & v1_card_5(k2_card_1(A)) ) ) ),
    file(card_5,t42_card_5),
    []).

fof(t44_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( v1_funct_1(k8_relset_1(A,B,D,C))
        & m2_relset_1(k8_relset_1(A,B,D,C),A,B) ) ) ),
    file(partfun1,t44_partfun1),
    []).

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_cqc_lang,axiom,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    []).

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(t5_wellfnd1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( v12_waybel_0(B,A)
                & r2_hidden(C,B) )
             => r1_tarski(k1_wellord1(u1_orders_2(A),C),B) ) ) ) ),
    file(wellfnd1,t5_wellfnd1),
    []).

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

fof(t6_cqc_lang,axiom,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    []).

fof(t72_card_4,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r1_tarski(A,k1_card_2(A,B))
            & r1_tarski(B,k1_card_2(A,B)) ) ) ) ),
    file(card_4,t72_card_4),
    []).

fof(t72_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    []).

fof(t73_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(B,k1_relat_1(C))
          & r2_hidden(B,A) )
       => r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A))) ) ) ),
    file(funct_1,t73_funct_1),
    []).

fof(t76_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( r1_xboole_0(C,k1_relat_1(B))
             => k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C) ) ) ) ),
    file(funct_4,t76_funct_4),
    []).

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

fof(t7_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    []).

fof(t7_ordinal1,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & r1_tarski(B,A) ) ),
    file(ordinal1,t7_ordinal1),
    []).

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

fof(t8_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    []).

fof(t8_grfunc_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    []).

fof(t91_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).