% Mizar problem: t1_cat_4,cat_4,59,26 
fof(t1_cat_4,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_4(A)
      <=> ( ? [B] : 
              ( m1_subset_1(B,u1_cat_1(A))
              & v6_cat_1(B,A) )
          & ! [B] : 
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ? [D] : 
                      ( m1_subset_1(D,u1_cat_1(A))
                      & ? [E] : 
                          ( m1_subset_1(E,u2_cat_1(A))
                          & ? [F] : 
                              ( m1_subset_1(F,u2_cat_1(A))
                              & k2_cat_1(A,E) = D
                              & k2_cat_1(A,F) = D
                              & k3_cat_1(A,E) = B
                              & k3_cat_1(A,F) = C
                              & r2_cat_3(A,D,E,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,cc2_nat_1,cc3_nat_1,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,d14_cat_3,d15_cat_3,d16_cat_3,d1_cat_3,d1_funct_2,d1_funct_4,d1_tarski,d2_cat_1,d2_cqc_lang,d2_tarski,d3_cat_1,d3_cat_3,d3_cat_4,d4_cat_3,d4_xboole_0,d6_cat_1,d7_cat_3,dt_k1_card_1,dt_k1_cat_3,dt_k1_funct_1,dt_k1_funct_4,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_cat_3,dt_k2_funcop_1,dt_k2_partfun1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k3_cat_3,dt_k3_cqc_lang,dt_k4_card_1,dt_k4_cat_1,dt_k4_cat_3,dt_k4_finseq_4,dt_k4_funct_4,dt_k4_relset_1,dt_k4_xboole_0,dt_k5_funct_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k6_cat_1,dt_k6_xcmplx_0,dt_k7_cat_3,dt_k7_relat_1,dt_k8_funct_2,dt_l1_cat_1,dt_m1_cat_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_cat_1,dt_u2_cat_1,dt_u3_cat_1,dt_u4_cat_1,existence_l1_cat_1,existence_m1_cat_3,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc12_finset_1,fc12_relat_1,fc13_relat_1,fc14_finset_1,fc1_cqc_lang,fc1_finset_1,fc1_nat_1,fc1_subset_1,fc2_finset_1,fc2_relat_1,fc2_subset_1,fc3_nat_1,fc3_relat_1,fc3_subset_1,fc4_funct_1,fc4_nat_1,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_finset_1,fraenkel_a_3_0_cat_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,rc1_finset_1,rc1_funct_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc2_finset_1,rc2_funct_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_relat_1,rc4_finset_1,rc4_funct_1,redefinition_k1_cat_3,redefinition_k1_nat_1,redefinition_k2_cat_3,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k5_funct_4,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_nat_1__e7_4__cat_4,spc0_boole,spc1_boole,spc1_numerals,t11_relset_1,t12_relset_1,t13_funcop_1,t14_funct_4,t18_cat_1,t18_funct_2,t18_funct_4,t1_boole,t1_cat_3,t1_numerals,t1_subset,t1_xboole_1,t20_cat_3,t26_xcmplx_1,t2_cat_3,t2_subset,t2_tarski,t36_xboole_1,t37_zfmisc_1,t38_funct_2,t39_xboole_1,t3_boole,t3_subset,t42_cat_1,t43_cat_1,t45_cat_3,t46_cat_3,t46_zfmisc_1,t47_card_1,t4_boole,t4_subset,t55_cat_3,t55_funct_2,t59_card_2,t59_cat_3,t5_subset,t60_relat_1,t63_card_2,t64_zfmisc_1,t69_funct_4,t6_boole,t72_funct_1,t79_card_1,t7_boole,t7_cat_3,t8_boole,t8_xboole_1]),
    [file(cat_4,t1_cat_4)]).

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

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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

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

fof(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

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

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

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(d14_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( m1_cat_3(D,A,B,C)
              <=> k3_cat_3(A,C,D) = k1_cat_3(u1_cat_1(A),C,B) ) ) ) ) ),
    file(cat_3,d14_cat_3),
    []).

fof(d15_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( r1_cat_3(A,B,C,D)
              <=> ( m1_cat_3(D,A,B,C)
                  & ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_cat_3(F,A,E,C)
                         => ~ ( k4_cat_3(A,C,D) = k4_cat_3(A,C,F)
                              & ! [G] : 
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(G,k6_cat_1(A,E,B))
                                      & ! [H] : 
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ( r2_hidden(H,k6_cat_1(A,E,B))
                                           => ( ! [I] : 
                                                  ( r2_hidden(I,C)
                                                 => k4_cat_1(A,H,k4_finseq_4(C,u2_cat_1(A),D,I)) = k4_finseq_4(C,u2_cat_1(A),F,I) )
                                            <=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(cat_3,d15_cat_3),
    []).

fof(d16_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_cat_3(A,B,C,D)
                  <=> ( k2_cat_1(A,C) = B
                      & k2_cat_1(A,D) = B
                      & ! [E] : 
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] : 
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ! [G] : 
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(F,k6_cat_1(A,E,k3_cat_1(A,C)))
                                      & r2_hidden(G,k6_cat_1(A,E,k3_cat_1(A,D)))
                                      & ! [H] : 
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ~ ( r2_hidden(H,k6_cat_1(A,E,B))
                                              & ! [I] : 
                                                  ( m1_subset_1(I,u2_cat_1(A))
                                                 => ( r2_hidden(I,k6_cat_1(A,E,B))
                                                   => ( ( k4_cat_1(A,I,C) = F
                                                        & k4_cat_1(A,I,D) = G )
                                                    <=> H = I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(cat_3,d16_cat_3),
    []).

fof(d1_cat_3,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] : 
              ( r2_hidden(D,A)
             => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ) ),
    file(cat_3,d1_cat_3),
    []).

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(d2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) ) ) ),
    file(cat_1,d2_cat_1),
    []).

fof(d2_cqc_lang,axiom,(
    ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ),
    file(cqc_lang,d2_cqc_lang),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) ),
    file(cat_1,d3_cat_1),
    []).

fof(d3_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u1_cat_1(A))
                & m2_relset_1(D,B,u1_cat_1(A)) )
             => ( D = k3_cat_3(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u1_cat_1(A),D,E) = k2_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ),
    file(cat_3,d3_cat_3),
    []).

fof(d3_cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_4(A)
      <=> ! [B] : 
            ( v1_finset_1(B)
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,B,u1_cat_1(A))
                  & m2_relset_1(C,B,u1_cat_1(A)) )
               => ? [D] : 
                    ( m1_subset_1(D,u1_cat_1(A))
                    & ? [E] : 
                        ( m1_cat_3(E,A,D,B)
                        & k4_cat_3(A,B,E) = C
                        & r1_cat_3(A,D,B,E) ) ) ) ) ) ) ),
    file(cat_4,d3_cat_4),
    []).

fof(d4_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u1_cat_1(A))
                & m2_relset_1(D,B,u1_cat_1(A)) )
             => ( D = k4_cat_3(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u1_cat_1(A),D,E) = k3_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ),
    file(cat_3,d4_cat_3),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C) ) ) ) ),
    file(cat_1,d6_cat_1),
    []).

fof(d7_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] : 
              ( m1_subset_1(D,u2_cat_1(A))
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,u2_cat_1(A))
                    & m2_relset_1(E,B,u2_cat_1(A)) )
                 => ( E = k7_cat_3(A,B,C,D)
                  <=> ! [F] : 
                        ( r2_hidden(F,B)
                       => k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,D,k4_finseq_4(B,u2_cat_1(A),C,F)) ) ) ) ) ) ) ),
    file(cat_3,d7_cat_3),
    []).

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

fof(dt_k1_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k1_cat_3(A,B,C))
        & v1_funct_2(k1_cat_3(A,B,C),B,A)
        & m2_relset_1(k1_cat_3(A,B,C),B,A) ) ) ),
    file(cat_3,k1_cat_3),
    []).

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_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

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

fof(dt_k1_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_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)) ) ),
    file(cat_1,k2_cat_1),
    []).

fof(dt_k2_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k2_cat_3(A,B,C))
        & v1_funct_2(k2_cat_3(A,B,C),k1_tarski(B),A)
        & m2_relset_1(k2_cat_3(A,B,C),k1_tarski(B),A) ) ) ),
    file(cat_3,k2_cat_3),
    []).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

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_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)) ) ),
    file(cat_1,k3_cat_1),
    []).

fof(dt_k3_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k3_cat_3(A,B,C))
        & v1_funct_2(k3_cat_3(A,B,C),B,u1_cat_1(A))
        & m2_relset_1(k3_cat_3(A,B,C),B,u1_cat_1(A)) ) ) ),
    file(cat_3,k3_cat_3),
    []).

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

fof(dt_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ),
    file(card_1,k4_card_1),
    []).

fof(dt_k4_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)) ) ),
    file(cat_1,k4_cat_1),
    []).

fof(dt_k4_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k4_cat_3(A,B,C))
        & v1_funct_2(k4_cat_3(A,B,C),B,u1_cat_1(A))
        & m2_relset_1(k4_cat_3(A,B,C),B,u1_cat_1(A)) ) ) ),
    file(cat_3,k4_cat_3),
    []).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    []).

fof(dt_k4_funct_4,axiom,(
    $true ),
    file(funct_4,k4_funct_4),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_funct_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k5_funct_4(A,B,C,D,E))
        & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A)
        & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) ) ) ),
    file(funct_4,k5_funct_4),
    []).

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

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

fof(dt_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ),
    file(real_1,k5_real_1),
    []).

fof(dt_k6_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))) ) ),
    file(cat_1,k6_cat_1),
    []).

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

fof(dt_k7_cat_3,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(A)) )
     => ( v1_funct_1(k7_cat_3(A,B,C,D))
        & v1_funct_2(k7_cat_3(A,B,C,D),B,u2_cat_1(A))
        & m2_relset_1(k7_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) ),
    file(cat_3,k7_cat_3),
    []).

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_l1_cat_1,axiom,(
    $true ),
    file(cat_1,l1_cat_1),
    []).

fof(dt_m1_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ! [D] : 
          ( m1_cat_3(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,C,u2_cat_1(A))
            & m2_relset_1(D,C,u2_cat_1(A)) ) ) ) ),
    file(cat_3,m1_cat_3),
    []).

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

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_u1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) ),
    file(cat_1,u1_cat_1),
    []).

fof(dt_u2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u2_cat_1(A)) ) ),
    file(cat_1,u2_cat_1),
    []).

fof(dt_u3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u3_cat_1(A))
        & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u3_cat_1),
    []).

fof(dt_u4_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u4_cat_1(A))
        & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u4_cat_1),
    []).

fof(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_cat_1),
    []).

fof(existence_m1_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ? [D] : m1_cat_3(D,A,B,C) ) ),
    file(cat_3,m1_cat_3),
    []).

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

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

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

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

fof(fc13_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    []).

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

fof(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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

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

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

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

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

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

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

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

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

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

fof(fc9_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(fraenkel_a_3_0_cat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(B))
        & m1_subset_1(D,u1_cat_1(B)) )
     => ( r2_hidden(A,a_3_0_cat_1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u2_cat_1(B))
            & A = E
            & k2_cat_1(B,E) = C
            & k3_cat_1(B,E) = D ) ) ) ),
    file(cat_1,a_3_0_cat_1),
    []).

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(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_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_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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

fof(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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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

fof(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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

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

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

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

fof(redefinition_k1_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k1_cat_3(A,B,C) = k2_funcop_1(B,C) ) ),
    file(cat_3,k1_cat_3),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k2_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k2_cat_3(A,B,C) = k3_cqc_lang(B,C) ) ),
    file(cat_3,k2_cat_3),
    []).

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_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => k4_card_1(A) = k1_card_1(A) ) ),
    file(card_1,k4_card_1),
    []).

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_k5_funct_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E) ) ),
    file(funct_4,k5_funct_4),
    []).

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

fof(redefinition_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(real_1,k5_real_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_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(s1_nat_1__e7_4__cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( ( ! [B] : 
              ( v1_finset_1(B)
             => ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,B,u1_cat_1(A))
                    & m2_relset_1(C,B,u1_cat_1(A)) )
                 => ~ ( k4_card_1(B) = 0
                      & ! [D] : 
                          ( m1_subset_1(D,u1_cat_1(A))
                         => ! [E] : 
                              ( m1_cat_3(E,A,D,B)
                             => ~ ( k4_cat_3(A,B,E) = C
                                  & r1_cat_3(A,D,B,E) ) ) ) ) ) )
          & ! [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
             => ( ! [G] : 
                    ( v1_finset_1(G)
                   => ! [H] : 
                        ( ( v1_funct_1(H)
                          & v1_funct_2(H,G,u1_cat_1(A))
                          & m2_relset_1(H,G,u1_cat_1(A)) )
                       => ~ ( k4_card_1(G) = F
                            & ! [I] : 
                                ( m1_subset_1(I,u1_cat_1(A))
                               => ! [J] : 
                                    ( m1_cat_3(J,A,I,G)
                                   => ~ ( k4_cat_3(A,G,J) = H
                                        & r1_cat_3(A,I,G,J) ) ) ) ) ) )
               => ! [K] : 
                    ( v1_finset_1(K)
                   => ! [L] : 
                        ( ( v1_funct_1(L)
                          & v1_funct_2(L,K,u1_cat_1(A))
                          & m2_relset_1(L,K,u1_cat_1(A)) )
                       => ~ ( k4_card_1(K) = k1_nat_1(F,1)
                            & ! [M] : 
                                ( m1_subset_1(M,u1_cat_1(A))
                               => ! [N] : 
                                    ( m1_cat_3(N,A,M,K)
                                   => ~ ( k4_cat_3(A,K,N) = L
                                        & r1_cat_3(A,M,K,N) ) ) ) ) ) ) ) ) )
       => ! [F] : 
            ( m2_subset_1(F,k1_numbers,k5_numbers)
           => ! [O] : 
                ( v1_finset_1(O)
               => ! [P] : 
                    ( ( v1_funct_1(P)
                      & v1_funct_2(P,O,u1_cat_1(A))
                      & m2_relset_1(P,O,u1_cat_1(A)) )
                   => ~ ( k4_card_1(O) = F
                        & ! [Q] : 
                            ( m1_subset_1(Q,u1_cat_1(A))
                           => ! [R] : 
                                ( m1_cat_3(R,A,Q,O)
                               => ~ ( k4_cat_3(A,O,R) = P
                                    & r1_cat_3(A,Q,O,R) ) ) ) ) ) ) ) ) ) ),
    file(cat_4,s1_nat_1__e7_4__cat_4),
    []).

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

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

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

fof(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(t12_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    []).

fof(t13_funcop_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    []).

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_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) ),
    file(cat_1,t18_cat_1),
    []).

fof(t18_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( r2_hidden(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t18_funct_2),
    []).

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_cat_3,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ( ! [E] : 
                    ( r2_hidden(E,A)
                   => k4_finseq_4(A,B,C,E) = k4_finseq_4(A,B,D,E) )
               => C = D ) ) ) ) ),
    file(cat_3,t1_cat_3),
    []).

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

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

fof(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(t20_cat_3,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( k3_cat_3(B,A,D) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C))
               => ( k3_cat_3(B,A,k7_cat_3(B,A,D,C)) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C))
                  & k4_cat_3(B,A,k7_cat_3(B,A,D,C)) = k4_cat_3(B,A,D) ) ) ) ) ) ),
    file(cat_3,t20_cat_3),
    []).

fof(t26_xcmplx_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => A = k6_xcmplx_0(k2_xcmplx_0(A,B),B) ) ) ),
    file(xcmplx_1,t26_xcmplx_1),
    []).

fof(t2_cat_3,axiom,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(C)
     => ! [D] : 
          ( m1_subset_1(D,C)
         => ( r2_hidden(B,A)
           => k4_finseq_4(A,C,k1_cat_3(C,A,D),B) = D ) ) ) ),
    file(cat_3,t2_cat_3),
    []).

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(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

fof(t38_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(C,A)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(k2_partfun1(A,B,D,C))
            & v1_funct_2(k2_partfun1(A,B,D,C),C,B)
            & m2_relset_1(k2_partfun1(A,B,D,C),C,B) ) ) ) ) ),
    file(funct_2,t38_funct_2),
    []).

fof(t39_xboole_1,axiom,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t42_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => ( k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)
                  & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) ) ) ) ) ) ),
    file(cat_1,t42_cat_1),
    []).

fof(t43_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
                      & k2_cat_1(A,C) = k3_cat_1(A,B) )
                   => k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D)) ) ) ) ) ) ),
    file(cat_1,t43_cat_1),
    []).

fof(t45_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] : 
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] : 
              ( m1_cat_3(E,C,D,A)
             => ( r2_hidden(B,A)
               => k2_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) ),
    file(cat_3,t45_cat_3),
    []).

fof(t46_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
                & m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
             => m1_cat_3(C,A,B,k1_xboole_0) ) ) ) ),
    file(cat_3,t46_cat_3),
    []).

fof(t46_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    []).

fof(t47_card_1,axiom,(
    k1_card_1(k1_xboole_0) = k1_xboole_0 ),
    file(card_1,t47_card_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t55_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
                & m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
             => ( r1_cat_3(A,B,k1_xboole_0,C)
              <=> v6_cat_1(B,A) ) ) ) ) ),
    file(cat_3,t55_cat_3),
    []).

fof(t55_funct_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_xboole_0
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_xboole_0,A)
          & m2_relset_1(B,k1_xboole_0,A) ) ) ) ),
    file(funct_2,t55_funct_2),
    []).

fof(t59_card_2,axiom,(
    ! [A] : 
      ( k1_card_1(A) = 0
     => A = k1_xboole_0 ) ),
    file(card_2,t59_card_2),
    []).

fof(t59_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] : 
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] : 
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] : 
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( A != B
                   => ( r2_cat_3(C,D,E,F)
                    <=> r1_cat_3(C,D,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F)) ) ) ) ) ) ) ),
    file(cat_3,t59_cat_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(t60_relat_1,axiom,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    []).

fof(t63_card_2,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_tarski(B,A)
           => k4_card_1(k4_xboole_0(A,B)) = k5_real_1(k4_card_1(A),k4_card_1(B)) ) ) ) ),
    file(card_2,t63_card_2),
    []).

fof(t64_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) ),
    file(zfmisc_1,t64_zfmisc_1),
    []).

fof(t69_funct_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ( k1_relat_1(E) = k2_tarski(A,B)
          & k1_funct_1(E,A) = C
          & k1_funct_1(E,B) = D )
       => E = k4_funct_4(A,B,C,D) ) ) ),
    file(funct_4,t69_funct_4),
    []).

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

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(t79_card_1,axiom,(
    ! [A] : k4_card_1(k1_tarski(A)) = 1 ),
    file(card_1,t79_card_1),
    []).

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

fof(t7_cat_3,axiom,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(C)
     => ( A != B
       => ! [D] : 
            ( m1_subset_1(D,C)
           => ! [E] : 
                ( m1_subset_1(E,C)
               => ( k4_finseq_4(k2_tarski(A,B),C,k5_funct_4(C,A,B,D,E),A) = D
                  & k4_finseq_4(k2_tarski(A,B),C,k5_funct_4(C,A,B,D,E),B) = E ) ) ) ) ) ),
    file(cat_3,t7_cat_3),
    []).

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

fof(t8_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    []).