% Mizar problem: t47_card_5,card_5,1438,73 
fof(t47_card_5,conjecture,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( ( ~ v1_finset_1(B)
            & v1_card_1(B) )
         => ( ( r1_tarski(k1_card_5(A),B)
              & r2_hidden(B,A) )
           => k3_card_2(A,B) = k3_card_2(k6_card_3(k2_card_5(A,B)),k1_card_5(A)) ) ) ) ),
    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_arytm_3,cc1_card_1,cc1_card_5,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_ordinal1,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_card_5,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_ordinal1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_card_2,commutativity_k2_card_2,commutativity_k2_tarski,commutativity_k2_xboole_0,connectedness_r1_ordinal1,d10_xboole_0,d1_card_3,d2_card_3,d2_funct_2,d3_card_2,d3_card_3,d3_card_5,d3_tarski,d4_card_3,d5_card_1,d5_funct_1,d5_tarski,d6_ordinal1,d7_card_3,d8_funct_1,d9_ordinal2,dt_k1_card_1,dt_k1_card_2,dt_k1_card_3,dt_k1_card_5,dt_k1_funct_1,dt_k1_funct_2,dt_k1_mcart_1,dt_k1_ordinal1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_2,dt_k2_card_3,dt_k2_card_5,dt_k2_mcart_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_card_2,dt_k3_card_3,dt_k3_tarski,dt_k4_tarski,dt_k6_card_3,dt_k7_ordinal2,dt_k8_ordinal2,dt_m1_subset_1,existence_m1_subset_1,fc10_membered,fc11_finseq_1,fc11_membered,fc12_membered,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc1_card_5,fc1_finset_1,fc1_ordinal1,fc1_ordinal3,fc1_subset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_arytm_3,fc2_card_1,fc2_finseq_1,fc2_finset_1,fc2_ordinal1,fc2_subset_1,fc3_card_5,fc3_ordinal1,fc3_ordinal2,fc3_subset_1,fc4_card_5,fc4_ordinal1,fc4_subset_1,fc5_card_5,fc5_ordinal1,fc6_card_5,fc6_membered,fc7_membered,fc8_card_5,fc8_membered,fc9_finset_1,fc9_membered,idempotence_k2_xboole_0,rc1_arytm_3,rc1_card_1,rc1_card_3,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_nat_1,rc1_ordinal1,rc1_ordinal2,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc2_ordinal2,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_funct_1,rc4_ordinal1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_r1_ordinal1,redefinition_r2_wellord2,reflexivity_r1_ordinal1,reflexivity_r1_tarski,reflexivity_r2_wellord2,s1_partfun1__e2_49_1_1__card_5,s1_zfrefle1__e5_49_1__card_5,s1_zfrefle1__e9_49__card_5,s3_funct_1__e12_49__card_5,spc0_boole,symmetry_r2_wellord2,t10_ordinal1,t10_ordinal3,t13_card_2,t15_ordinal3,t1_boole,t1_subset,t1_xboole_1,t22_ordinal1,t23_ordinal1,t26_card_1,t27_card_5,t29_ordinal2,t2_subset,t32_card_5,t33_card_3,t33_zfmisc_1,t3_subset,t41_card_5,t41_ordinal1,t43_card_2,t45_card_5,t4_subset,t54_card_3,t5_subset,t68_funct_5,t6_boole,t71_card_4,t7_boole,t7_mcart_1,t7_xboole_1,t8_boole,t9_funct_1]),
    [file(card_5,t47_card_5)]).

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_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_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_card_5,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(card_5,cc1_card_5),
    []).

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

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

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

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

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

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_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

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_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_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_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

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

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

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

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

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_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => k2_card_2(A,B) = k2_card_2(B,A) ) ),
    file(card_2,k2_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(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(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_card_3(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => v1_card_1(k1_funct_1(A,B)) ) ) ) ),
    file(card_3,d1_card_3),
    []).

fof(d2_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( B = k1_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(card_3,d2_card_3),
    []).

fof(d2_funct_2,axiom,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    []).

fof(d3_card_2,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k3_card_2(A,B) = k1_card_1(k1_funct_2(B,A)) ) ) ),
    file(card_2,d3_card_2),
    []).

fof(d3_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) ) ) ) ) ) ),
    file(card_3,d3_card_3),
    []).

fof(d3_card_5,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_card_3(C) )
             => ( C = k2_card_5(A,B)
              <=> ( ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                    <=> ( r2_hidden(D,A)
                        & v1_card_1(D) ) )
                  & ! [D] : 
                      ( v1_card_1(D)
                     => ( r2_hidden(D,A)
                       => k1_funct_1(C,D) = k3_card_2(D,B) ) ) ) ) ) ) ) ),
    file(card_5,d3_card_5),
    []).

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

fof(d4_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    []).

fof(d5_card_1,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( B = k1_card_1(A)
      <=> r2_wellord2(A,B) ) ) ),
    file(card_1,d5_card_1),
    []).

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

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

fof(d6_ordinal1,axiom,(
    ! [A] : 
      ( v4_ordinal1(A)
    <=> A = k3_tarski(A) ) ),
    file(ordinal1,d6_ordinal1),
    []).

fof(d7_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k6_card_3(A) = k1_card_1(k3_card_3(k2_card_3(A))) ) ),
    file(card_3,d7_card_3),
    []).

fof(d8_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    []).

fof(d9_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)) ) ),
    file(ordinal2,d9_ordinal2),
    []).

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_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_card_3(A))
        & v1_funct_1(k1_card_3(A))
        & v1_card_3(k1_card_3(A)) ) ) ),
    file(card_3,k1_card_3),
    []).

fof(dt_k1_card_5,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => v1_card_1(k1_card_5(A)) ) ),
    file(card_5,k1_card_5),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    []).

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

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

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

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

fof(dt_k2_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => v1_card_1(k2_card_2(A,B)) ) ),
    file(card_2,k2_card_2),
    []).

fof(dt_k2_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_card_3(A))
        & v1_funct_1(k2_card_3(A)) ) ) ),
    file(card_3,k2_card_3),
    []).

fof(dt_k2_card_5,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => ( v1_relat_1(k2_card_5(A,B))
        & v1_funct_1(k2_card_5(A,B))
        & v1_card_3(k2_card_5(A,B)) ) ) ),
    file(card_5,k2_card_5),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

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_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => v1_card_1(k3_card_2(A,B)) ) ),
    file(card_2,k3_card_2),
    []).

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

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

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

fof(dt_k6_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k6_card_3(A)) ) ),
    file(card_3,k6_card_3),
    []).

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

fof(dt_k8_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => v3_ordinal1(k8_ordinal2(A)) ) ),
    file(ordinal2,k8_ordinal2),
    []).

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

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

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_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(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_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(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(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_card_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ( v1_ordinal1(k3_card_3(A))
        & v2_ordinal1(k3_card_3(A))
        & v3_ordinal1(k3_card_3(A)) ) ) ),
    file(card_5,fc1_card_5),
    []).

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

fof(fc1_ordinal1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    []).

fof(fc1_ordinal3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k2_xboole_0(A,B))
        & v2_ordinal1(k2_xboole_0(A,B))
        & v3_ordinal1(k2_xboole_0(A,B)) ) ) ),
    file(ordinal3,fc1_ordinal3),
    []).

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

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(fc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A))
        & v4_ordinal2(k1_ordinal1(A)) ) ) ),
    file(arytm_3,fc2_arytm_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_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

fof(fc2_ordinal1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

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

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_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    []).

fof(fc3_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k1_funct_1(A,B))
        & v2_ordinal1(k1_funct_1(A,B))
        & v3_ordinal1(k1_funct_1(A,B)) ) ) ),
    file(ordinal2,fc3_ordinal2),
    []).

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_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    []).

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_card_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B) )
     => ( ~ v1_xboole_0(k2_card_2(A,B))
        & v1_ordinal1(k2_card_2(A,B))
        & v2_ordinal1(k2_card_2(A,B))
        & v3_ordinal1(k2_card_2(A,B))
        & ~ v1_finset_1(k2_card_2(A,B))
        & v1_card_1(k2_card_2(A,B)) ) ) ),
    file(card_5,fc5_card_5),
    []).

fof(fc5_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( v1_ordinal1(k1_relat_1(A))
        & v2_ordinal1(k1_relat_1(A))
        & v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,fc5_ordinal1),
    []).

fof(fc6_card_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B) )
     => ( ~ v1_xboole_0(k3_card_2(A,B))
        & v1_ordinal1(k3_card_2(A,B))
        & v2_ordinal1(k3_card_2(A,B))
        & v3_ordinal1(k3_card_2(A,B))
        & ~ v1_finset_1(k3_card_2(A,B))
        & v1_card_1(k3_card_2(A,B)) ) ) ),
    file(card_5,fc6_card_5),
    []).

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

fof(fc8_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( ~ v1_xboole_0(k1_card_5(A))
        & v1_ordinal1(k1_card_5(A))
        & v2_ordinal1(k1_card_5(A))
        & v3_ordinal1(k1_card_5(A))
        & ~ v1_finset_1(k1_card_5(A))
        & v1_card_1(k1_card_5(A)) ) ) ),
    file(card_5,fc8_card_5),
    []).

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_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

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_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

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

fof(rc1_card_3,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_card_3(A) ) ),
    file(card_3,rc1_card_3),
    []).

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

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

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

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

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_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_ordinal2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    []).

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_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

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_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

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

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

fof(rc2_ordinal2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & v1_ordinal2(A) ) ),
    file(ordinal2,rc2_ordinal2),
    []).

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_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

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

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

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

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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

fof(rc4_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    []).

fof(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

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(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(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(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(redefinition_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    []).

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

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

fof(reflexivity_r2_wellord2,axiom,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    []).

fof(s1_partfun1__e2_49_1_1__card_5,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B)
        & v1_ordinal2(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ? [E] : 
          ( v1_relat_1(E)
          & v1_funct_1(E)
          & k1_relat_1(E) = A
          & ! [F] : 
              ( r2_hidden(F,A)
             => ( ( r2_hidden(k1_funct_1(C,F),k1_funct_1(B,D))
                 => k1_funct_1(E,F) = k1_funct_1(C,F) )
                & ( ~ r2_hidden(k1_funct_1(C,F),k1_funct_1(B,D))
                 => k1_funct_1(E,F) = 0 ) ) ) ) ) ),
    file(card_5,s1_partfun1__e2_49_1_1__card_5),
    []).

fof(s1_zfrefle1__e5_49_1__card_5,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v5_ordinal1(C)
        & v1_ordinal2(C)
        & v1_relat_1(D)
        & v1_funct_1(D) )
     => ( ! [E] : ~ ( r2_hidden(E,k1_card_5(A))
            & ! [F] : ~ ? [G] : 
                  ( v1_relat_1(G)
                  & v1_funct_1(G)
                  & F = k4_tarski(G,k1_funct_1(C,E))
                  & k1_relat_1(G) = B
                  & ! [H] : 
                      ( r2_hidden(H,B)
                     => ( ( r2_hidden(k1_funct_1(D,H),k1_funct_1(C,E))
                         => k1_funct_1(G,H) = k1_funct_1(D,H) )
                        & ( ~ r2_hidden(k1_funct_1(D,H),k1_funct_1(C,E))
                         => k1_funct_1(G,H) = 0 ) ) ) ) )
       => ? [E] : 
            ( v1_relat_1(E)
            & v1_funct_1(E)
            & k1_relat_1(E) = k1_card_5(A)
            & ! [F] : 
                ( r2_hidden(F,k1_card_5(A))
               => ? [I] : 
                    ( v1_relat_1(I)
                    & v1_funct_1(I)
                    & k1_funct_1(E,F) = k4_tarski(I,k1_funct_1(C,F))
                    & k1_relat_1(I) = B
                    & ! [J] : 
                        ( r2_hidden(J,B)
                       => ( ( r2_hidden(k1_funct_1(D,J),k1_funct_1(C,F))
                           => k1_funct_1(I,J) = k1_funct_1(D,J) )
                          & ( ~ r2_hidden(k1_funct_1(D,J),k1_funct_1(C,F))
                           => k1_funct_1(I,J) = 0 ) ) ) ) ) ) ) ) ),
    file(card_5,s1_zfrefle1__e5_49_1__card_5),
    []).

fof(s1_zfrefle1__e9_49__card_5,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v5_ordinal1(C)
        & v1_ordinal2(C) )
     => ( ! [D] : ~ ( r2_hidden(D,k1_funct_2(B,A))
            & ! [E] : ~ ? [F] : 
                  ( v1_relat_1(F)
                  & v1_funct_1(F)
                  & ? [G] : 
                      ( v1_relat_1(G)
                      & v1_funct_1(G)
                      & F = D
                      & G = E
                      & k1_relat_1(F) = B
                      & r1_tarski(k2_relat_1(F),A)
                      & k1_relat_1(G) = k1_card_5(A)
                      & ! [H] : ~ ( r2_hidden(H,k1_card_5(A))
                          & ! [I] : 
                              ( ( v1_relat_1(I)
                                & v1_funct_1(I) )
                             => ~ ( k1_funct_1(G,H) = k4_tarski(I,k1_funct_1(C,H))
                                  & k1_relat_1(I) = B
                                  & ! [J] : 
                                      ( r2_hidden(J,B)
                                     => ( ( r2_hidden(k1_funct_1(F,J),k1_funct_1(C,H))
                                         => k1_funct_1(I,J) = k1_funct_1(F,J) )
                                        & ( ~ r2_hidden(k1_funct_1(F,J),k1_funct_1(C,H))
                                         => k1_funct_1(I,J) = 0 ) ) ) ) ) ) ) ) )
       => ? [D] : 
            ( v1_relat_1(D)
            & v1_funct_1(D)
            & k1_relat_1(D) = k1_funct_2(B,A)
            & ! [E] : 
                ( r2_hidden(E,k1_funct_2(B,A))
               => ? [K] : 
                    ( v1_relat_1(K)
                    & v1_funct_1(K)
                    & ? [L] : 
                        ( v1_relat_1(L)
                        & v1_funct_1(L)
                        & K = E
                        & L = k1_funct_1(D,E)
                        & k1_relat_1(K) = B
                        & r1_tarski(k2_relat_1(K),A)
                        & k1_relat_1(L) = k1_card_5(A)
                        & ! [M] : ~ ( r2_hidden(M,k1_card_5(A))
                            & ! [N] : 
                                ( ( v1_relat_1(N)
                                  & v1_funct_1(N) )
                               => ~ ( k1_funct_1(L,M) = k4_tarski(N,k1_funct_1(C,M))
                                    & k1_relat_1(N) = B
                                    & ! [O] : 
                                        ( r2_hidden(O,B)
                                       => ( ( r2_hidden(k1_funct_1(K,O),k1_funct_1(C,M))
                                           => k1_funct_1(N,O) = k1_funct_1(K,O) )
                                          & ( ~ r2_hidden(k1_funct_1(K,O),k1_funct_1(C,M))
                                           => k1_funct_1(N,O) = 0 ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(card_5,s1_zfrefle1__e9_49__card_5),
    []).

fof(s3_funct_1__e12_49__card_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B) )
     => ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = k1_relat_1(k2_card_5(A,B))
          & ! [D] : 
              ( r2_hidden(D,k1_relat_1(k2_card_5(A,B)))
             => k1_funct_1(C,D) = k1_funct_2(B,D) ) ) ) ),
    file(card_5,s3_funct_1__e12_49__card_5),
    []).

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

fof(symmetry_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(t10_ordinal1,axiom,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    []).

fof(t10_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( A != k1_xboole_0
       => r2_hidden(k1_xboole_0,A) ) ) ),
    file(ordinal3,t10_ordinal3),
    []).

fof(t13_card_2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B)))
      & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))) ) ),
    file(card_2,t13_card_2),
    []).

fof(t15_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k2_xboole_0(A,B) = A
            | k2_xboole_0(A,B) = B ) ) ) ),
    file(ordinal3,t15_ordinal3),
    []).

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

fof(t26_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(card_1,t26_card_1),
    []).

fof(t27_card_5,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( ( ~ v1_finset_1(B)
            & v1_card_1(B) )
         => ( ( r1_tarski(B,A)
              | r2_hidden(B,A) )
           => ( k1_card_2(B,A) = A
              & k1_card_2(A,B) = A
              & k2_card_2(B,A) = A
              & k2_card_2(A,B) = A ) ) ) ) ),
    file(card_5,t27_card_5),
    []).

fof(t29_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : ~ ( r2_hidden(A,k7_ordinal2(B))
          & ! [C] : 
              ( v3_ordinal1(C)
             => ~ ( r2_hidden(C,B)
                  & r1_ordinal1(A,C) ) ) ) ) ),
    file(ordinal2,t29_ordinal2),
    []).

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

fof(t32_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => k3_tarski(A) = A ) ),
    file(card_5,t32_card_5),
    []).

fof(t33_card_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(k2_card_3(B)))
      <=> ( r2_hidden(k2_mcart_1(A),k1_relat_1(B))
          & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A)))
          & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ) ) ),
    file(card_3,t33_card_3),
    []).

fof(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    []).

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

fof(t41_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ~ ( r2_hidden(k1_card_5(A),A)
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v5_ordinal1(B)
                & v1_ordinal2(B) )
             => ~ ( k1_relat_1(B) = k1_card_5(A)
                  & r1_tarski(k2_relat_1(B),A)
                  & v2_ordinal2(B)
                  & A = k8_ordinal2(B)
                  & v1_relat_1(B)
                  & v1_funct_1(B)
                  & v1_card_3(B)
                  & ~ r2_hidden(0,k2_relat_1(B)) ) ) ) ) ),
    file(card_5,t41_card_5),
    []).

fof(t41_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k1_ordinal1(B),A) ) ) ) ) ),
    file(ordinal1,t41_ordinal1),
    []).

fof(t43_card_2,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ! [C] : 
              ( v1_card_1(C)
             => k3_card_2(A,k2_card_2(B,C)) = k3_card_2(k3_card_2(A,B),C) ) ) ) ),
    file(card_2,t43_card_2),
    []).

fof(t45_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( ( ~ v1_finset_1(B)
            & v1_card_1(B) )
         => r1_tarski(k6_card_3(k2_card_5(B,A)),k3_card_2(B,A)) ) ) ),
    file(card_5,t45_card_5),
    []).

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(t54_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))) ) ),
    file(card_3,t54_card_3),
    []).

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(t68_funct_5,axiom,(
    ! [A,B,C,D] : 
      ( ( k1_card_1(A) = k1_card_1(B)
        & k1_card_1(C) = k1_card_1(D) )
     => k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) ) ),
    file(funct_5,t68_funct_5),
    []).

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

fof(t71_card_4,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ! [C] : 
              ( v1_card_1(C)
             => ~ ( ( r2_hidden(A,B)
                    | r1_tarski(A,B) )
                  & C != 0
                  & ~ ( r1_tarski(k3_card_2(C,A),k3_card_2(C,B))
                      & r1_tarski(k3_card_2(A,C),k3_card_2(B,C)) ) ) ) ) ) ),
    file(card_4,t71_card_4),
    []).

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

fof(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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

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),
    []).