% Mizar problem: t33_hilbert3,hilbert3,962,34 
fof(t33_hilbert3,conjecture,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => ! [B] : 
          ( m1_hilbert3(B,A)
         => k5_hilbert3(A,B,k2_hilbert1) = k6_partfun1(k3_hilbert3(A,k2_hilbert1)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_abian,cc1_fraenkel,cc1_funct_1,cc1_funct_2,cc1_hilbert1,cc1_hilbert3,cc1_partfun1,cc1_pboole,cc1_relat_1,cc1_relset_1,cc1_tex_2,cc2_funct_1,cc2_funct_2,cc2_hilbert3,cc2_int_1,cc2_pboole,cc2_tex_2,cc3_funct_2,cc3_hilbert1,cc3_hilbert3,cc3_int_1,cc3_pboole,cc3_tex_2,cc4_funct_2,cc4_int_1,cc4_tex_2,cc5_funct_2,cc5_tex_2,cc6_funct_2,cc6_tex_2,cc7_tex_2,d3_hilbert3,d5_hilbert3,d6_hilbert3,d7_hilbert1,d8_hilbert1,d9_hilbert1,dt_k12_finseq_1,dt_k15_funct_3,dt_k16_funct_3,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_hilbert1,dt_k1_hilbert2,dt_k1_hilbert3,dt_k1_msualg_3,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_hilbert1,dt_k2_hilbert3,dt_k2_zfmisc_1,dt_k3_hilbert1,dt_k3_hilbert3,dt_k4_hilbert1,dt_k4_hilbert3,dt_k5_finseq_1,dt_k5_hilbert3,dt_k5_numbers,dt_k5_ordinal2,dt_k6_partfun1,dt_k6_relat_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_hilbert3,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,existence_m1_finseq_1,existence_m1_fraenkel,existence_m1_hilbert3,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,fc12_relat_1,fc16_abian,fc17_abian,fc1_fraenkel,fc1_funct_2,fc1_hilbert1,fc1_hilbert3,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc2_fraenkel,fc2_funct_1,fc2_funct_2,fc2_hilbert1,fc2_hilbert3,fc2_partfun1,fc2_pboole,fc3_hilbert3,fc4_hilbert3,fc4_relat_1,fc4_subset_1,fc5_hilbert3,fc7_funcop_1,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_hilbert1,rc1_hilbert3,rc1_int_1,rc1_partfun1,rc1_pboole,rc1_relat_1,rc1_subset_1,rc1_tex_2,rc2_funct_1,rc2_funct_2,rc2_hilbert3,rc2_int_1,rc2_partfun1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc2_tex_2,rc3_funct_1,rc3_partfun1,rc3_pboole,rc3_relat_1,rc3_tex_2,rc4_funct_1,rc4_pboole,rc4_tex_2,rc5_funct_1,rc5_tex_2,rc6_abian,rc6_tex_2,rc7_tex_2,redefinition_k12_finseq_1,redefinition_k16_funct_3,redefinition_k1_fraenkel,redefinition_k1_msualg_3,redefinition_k5_numbers,redefinition_k6_partfun1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t1_numerals,t1_subset,t29_hilbert3,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(hilbert3,t33_hilbert3)]).

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

fof(cc1_abian,axiom,(
    ! [A] : 
      ( v2_setfam_1(A)
     => v1_realset1(A) ) ),
    file(abian,cc1_abian),
    []).

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

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_hilbert1,axiom,(
    ! [A] : 
      ( v5_hilbert1(A)
     => ( ~ v1_xboole_0(A)
        & v1_hilbert1(A)
        & v2_hilbert1(A)
        & v3_hilbert1(A)
        & v4_hilbert1(A) ) ) ),
    file(hilbert1,cc1_hilbert1),
    []).

fof(cc1_hilbert3,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(D,A,k1_funct_2(B,C))
     => ( ( v1_funct_1(D)
          & v1_funct_2(D,A,k1_funct_2(B,C)) )
       => ( v1_funct_1(D)
          & v1_funct_2(D,A,k1_funct_2(B,C))
          & v1_funcop_1(D) ) ) ) ),
    file(hilbert3,cc1_hilbert3),
    []).

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

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

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

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

fof(cc1_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    []).

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_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    []).

fof(cc2_hilbert3,axiom,(
    ! [A,B] : 
      ( v1_fraenkel(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v1_funcop_1(C) ) ) ) ) ),
    file(hilbert3,cc2_hilbert3),
    []).

fof(cc2_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    []).

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

fof(cc2_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    []).

fof(cc3_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    []).

fof(cc3_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_hilbert1)
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A) ) ) ),
    file(hilbert1,cc3_hilbert1),
    []).

fof(cc3_hilbert3,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_subset_1(B,k1_hilbert1)
        & m1_subset_1(C,k1_hilbert1)
        & m1_subset_1(D,k1_hilbert1) )
     => ! [E] : 
          ( m1_subset_1(E,k3_hilbert3(A,k3_hilbert1(B,k3_hilbert1(C,D))))
         => ( v1_relat_1(E)
            & v1_funct_1(E)
            & v1_funcop_1(E) ) ) ) ),
    file(hilbert3,cc3_hilbert3),
    []).

fof(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    []).

fof(cc3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    []).

fof(cc3_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_2),
    []).

fof(cc4_funct_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( ( v1_funct_1(B)
          & v1_partfun1(B,A,A)
          & v1_relat_2(B)
          & v1_funct_2(B,A,A) )
       => ( v1_funct_1(B)
          & v2_funct_1(B)
          & v1_funct_2(B,A,A)
          & v2_funct_2(B,A,A)
          & v3_funct_2(B,A,A) ) ) ) ),
    file(funct_2,cc4_funct_2),
    []).

fof(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

fof(cc4_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc5_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(cc6_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    []).

fof(cc7_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    []).

fof(d3_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => ! [B] : 
          ( m1_subset_1(B,k1_hilbert1)
         => k3_hilbert3(A,B) = k1_funct_1(k2_hilbert3(A),B) ) ) ),
    file(hilbert3,d3_hilbert3),
    []).

fof(d5_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => ! [B] : 
          ( m1_hilbert3(B,A)
         => ! [C] : 
              ( m3_pboole(C,k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A))
             => ( C = k4_hilbert3(A,B)
              <=> ( k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,k2_hilbert1) = k6_partfun1(1)
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,k1_hilbert2(D)) = k1_funct_1(B,D) )
                  & ! [D] : 
                      ( m1_subset_1(D,k1_hilbert1)
                     => ! [E] : 
                          ( m1_subset_1(E,k1_hilbert1)
                         => ? [F] : 
                              ( v1_funct_1(F)
                              & v1_funct_2(F,k3_hilbert3(A,D),k3_hilbert3(A,D))
                              & v3_funct_2(F,k3_hilbert3(A,D),k3_hilbert3(A,D))
                              & m2_relset_1(F,k3_hilbert3(A,D),k3_hilbert3(A,D))
                              & ? [G] : 
                                  ( v1_funct_1(G)
                                  & v1_funct_2(G,k3_hilbert3(A,E),k3_hilbert3(A,E))
                                  & v3_funct_2(G,k3_hilbert3(A,E),k3_hilbert3(A,E))
                                  & m2_relset_1(G,k3_hilbert3(A,E),k3_hilbert3(A,E))
                                  & F = k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,D)
                                  & G = k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,E)
                                  & k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,k4_hilbert1(D,E)) = k16_funct_3(k3_hilbert3(A,D),k3_hilbert3(A,E),k3_hilbert3(A,D),k3_hilbert3(A,E),F,G)
                                  & k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,k3_hilbert1(D,E)) = k1_hilbert3(k3_hilbert3(A,D),k3_hilbert3(A,E),F,G) ) ) ) ) ) ) ) ) ) ),
    file(hilbert3,d5_hilbert3),
    []).

fof(d6_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => ! [B] : 
          ( m1_hilbert3(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_hilbert1)
             => k5_hilbert3(A,B,C) = k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),k4_hilbert3(A,B),C) ) ) ) ),
    file(hilbert3,d6_hilbert3),
    []).

fof(d7_hilbert1,axiom,(
    k2_hilbert1 = k12_finseq_1(k5_numbers,0) ),
    file(hilbert1,d7_hilbert1),
    []).

fof(d8_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] : 
          ( m1_subset_1(B,k1_hilbert1)
         => k3_hilbert1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,1),A),B) ) ) ),
    file(hilbert1,d8_hilbert1),
    []).

fof(d9_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] : 
          ( m1_subset_1(B,k1_hilbert1)
         => k4_hilbert1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,2),A),B) ) ) ),
    file(hilbert1,d9_hilbert1),
    []).

fof(dt_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_1(k12_finseq_1(A,B),A) ) ),
    file(finseq_1,k12_finseq_1),
    []).

fof(dt_k15_funct_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k15_funct_3(A,B))
        & v1_funct_1(k15_funct_3(A,B)) ) ) ),
    file(funct_3,k15_funct_3),
    []).

fof(dt_k16_funct_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,D)
        & m1_relset_1(F,B,D) )
     => ( v1_funct_1(k16_funct_3(A,B,C,D,E,F))
        & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
        & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) ) ) ),
    file(funct_3,k16_funct_3),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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_hilbert1,axiom,(
    $true ),
    file(hilbert1,k1_hilbert1),
    []).

fof(dt_k1_hilbert2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k1_hilbert2(A),k1_hilbert1) ) ),
    file(hilbert2,k1_hilbert2),
    []).

fof(dt_k1_hilbert3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B) )
     => ( v1_funct_1(k1_hilbert3(A,B,C,D))
        & v1_funct_2(k1_hilbert3(A,B,C,D),k1_fraenkel(A,B),k1_fraenkel(A,B))
        & m2_relset_1(k1_hilbert3(A,B,C,D),k1_fraenkel(A,B),k1_fraenkel(A,B)) ) ) ),
    file(hilbert3,k1_hilbert3),
    []).

fof(dt_k1_msualg_3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k1_msualg_3(A,B,C,D,E))
        & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E))
        & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ),
    file(msualg_3,k1_msualg_3),
    []).

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

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_hilbert1,axiom,(
    m1_subset_1(k2_hilbert1,k1_hilbert1) ),
    file(hilbert1,k2_hilbert1),
    []).

fof(dt_k2_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => m1_pboole(k2_hilbert3(A),k1_hilbert1) ) ),
    file(hilbert3,k2_hilbert3),
    []).

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

fof(dt_k3_hilbert1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_hilbert1)
        & m1_subset_1(B,k1_hilbert1) )
     => m1_subset_1(k3_hilbert1(A,B),k1_hilbert1) ) ),
    file(hilbert1,k3_hilbert1),
    []).

fof(dt_k3_hilbert3,axiom,(
    $true ),
    file(hilbert3,k3_hilbert3),
    []).

fof(dt_k4_hilbert1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_hilbert1)
        & m1_subset_1(B,k1_hilbert1) )
     => m1_subset_1(k4_hilbert1(A,B),k1_hilbert1) ) ),
    file(hilbert1,k4_hilbert1),
    []).

fof(dt_k4_hilbert3,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_hilbert3(B,A) )
     => m3_pboole(k4_hilbert3(A,B),k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A)) ) ),
    file(hilbert3,k4_hilbert3),
    []).

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

fof(dt_k5_hilbert3,axiom,(
    ! [A,B,C] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_hilbert3(B,A)
        & m1_subset_1(C,k1_hilbert1) )
     => ( v1_funct_1(k5_hilbert3(A,B,C))
        & v1_funct_2(k5_hilbert3(A,B,C),k3_hilbert3(A,C),k3_hilbert3(A,C))
        & m2_relset_1(k5_hilbert3(A,B,C),k3_hilbert3(A,C),k3_hilbert3(A,C)) ) ) ),
    file(hilbert3,k5_hilbert3),
    []).

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

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

fof(dt_k6_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_m1_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => ! [B] : 
          ( m1_hilbert3(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(hilbert3,m1_hilbert3),
    []).

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

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

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

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

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

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

fof(dt_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

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

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(existence_m1_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => ? [B] : m1_hilbert3(B,A) ) ),
    file(hilbert3,m1_hilbert3),
    []).

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

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

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

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

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

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

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

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

fof(fc16_abian,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_setfam_1(B)
        & v2_relat_1(C)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => ~ v1_xboole_0(k1_funct_1(C,D)) ) ),
    file(abian,fc16_abian),
    []).

fof(fc17_abian,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_zfmisc_1(A))
        & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ),
    file(abian,fc17_abian),
    []).

fof(fc1_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

fof(fc1_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

fof(fc1_hilbert1,axiom,
    ( ~ v1_xboole_0(k1_hilbert1)
    & v1_hilbert1(k1_hilbert1)
    & v2_hilbert1(k1_hilbert1)
    & v3_hilbert1(k1_hilbert1)
    & v4_hilbert1(k1_hilbert1)
    & v5_hilbert1(k1_hilbert1) ),
    file(hilbert1,fc1_hilbert1),
    []).

fof(fc1_hilbert3,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_funcop_1(k1_xboole_0) ),
    file(hilbert3,fc1_hilbert3),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

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

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

fof(fc2_fraenkel,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => ( v1_finset_1(k1_funct_2(A,B))
        & v1_fraenkel(k1_funct_2(A,B)) ) ) ),
    file(fraenkel,fc2_fraenkel),
    []).

fof(fc2_funct_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    []).

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

fof(fc2_hilbert1,axiom,
    ( ~ v1_xboole_0(k1_hilbert1)
    & v1_fraenkel(k1_hilbert1)
    & v1_hilbert1(k1_hilbert1)
    & v2_hilbert1(k1_hilbert1)
    & v3_hilbert1(k1_hilbert1)
    & v4_hilbert1(k1_hilbert1)
    & v5_hilbert1(k1_hilbert1) ),
    file(hilbert1,fc2_hilbert1),
    []).

fof(fc2_hilbert3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v2_funct_1(B) )
     => ( v1_relat_1(k15_funct_3(A,B))
        & v1_funct_1(k15_funct_3(A,B))
        & v2_funct_1(k15_funct_3(A,B)) ) ) ),
    file(hilbert3,fc2_hilbert3),
    []).

fof(fc2_partfun1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(partfun1,fc2_partfun1),
    []).

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

fof(fc3_hilbert3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & v3_funct_2(D,B,B)
        & m1_relset_1(D,B,B) )
     => ( ~ v1_xboole_0(k1_hilbert3(A,B,C,D))
        & v1_relat_1(k1_hilbert3(A,B,C,D))
        & v1_funct_1(k1_hilbert3(A,B,C,D))
        & v2_funct_1(k1_hilbert3(A,B,C,D))
        & v1_funct_2(k1_hilbert3(A,B,C,D),k1_fraenkel(A,B),k1_fraenkel(A,B))
        & v2_funct_2(k1_hilbert3(A,B,C,D),k1_fraenkel(A,B),k1_fraenkel(A,B))
        & v3_funct_2(k1_hilbert3(A,B,C,D),k1_fraenkel(A,B),k1_fraenkel(A,B))
        & v1_funcop_1(k1_hilbert3(A,B,C,D))
        & v1_partfun1(k1_hilbert3(A,B,C,D),k1_fraenkel(A,B),k1_fraenkel(A,B)) ) ) ),
    file(hilbert3,fc3_hilbert3),
    []).

fof(fc4_hilbert3,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_subset_1(B,k1_hilbert1) )
     => ~ v1_xboole_0(k3_hilbert3(A,B)) ) ),
    file(hilbert3,fc4_hilbert3),
    []).

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_hilbert3,axiom,(
    ! [A,B,C] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_subset_1(B,k1_hilbert1)
        & m1_subset_1(C,k1_hilbert1) )
     => ( ~ v1_xboole_0(k3_hilbert3(A,k3_hilbert1(B,C)))
        & v1_fraenkel(k3_hilbert3(A,k3_hilbert1(B,C))) ) ) ),
    file(hilbert3,fc5_hilbert3),
    []).

fof(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

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

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    []).

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

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_hilbert1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_hilbert1(A)
      & v2_hilbert1(A)
      & v3_hilbert1(A)
      & v4_hilbert1(A)
      & v5_hilbert1(A) ) ),
    file(hilbert1,rc1_hilbert1),
    []).

fof(rc1_hilbert3,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_subset_1(B,k1_hilbert1)
        & m1_subset_1(C,k1_hilbert1)
        & m1_subset_1(D,k1_hilbert1) )
     => ? [E] : 
          ( m1_relset_1(E,k3_hilbert3(A,k3_hilbert1(B,C)),k3_hilbert3(A,k3_hilbert1(B,D)))
          & ~ v1_xboole_0(E)
          & v1_relat_1(E)
          & v1_funct_1(E)
          & v1_funct_2(E,k3_hilbert3(A,k3_hilbert1(B,C)),k3_hilbert3(A,k3_hilbert1(B,D)))
          & v1_funcop_1(E)
          & v1_partfun1(E,k3_hilbert3(A,k3_hilbert1(B,C)),k3_hilbert3(A,k3_hilbert1(B,D))) ) ) ),
    file(hilbert3,rc1_hilbert3),
    []).

fof(rc1_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

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

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

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

fof(rc1_tex_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    []).

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_funct_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    []).

fof(rc2_hilbert3,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers)
        & m1_subset_1(B,k1_hilbert1)
        & m1_subset_1(C,k1_hilbert1)
        & m1_subset_1(D,k1_hilbert1) )
     => ? [E] : 
          ( m1_subset_1(E,k3_hilbert3(A,k3_hilbert1(B,k3_hilbert1(C,D))))
          & v1_relat_1(E)
          & v1_funct_1(E)
          & v1_funcop_1(E) ) ) ),
    file(hilbert3,rc2_hilbert3),
    []).

fof(rc2_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

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

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

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

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

fof(rc2_tex_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    []).

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_partfun1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) ),
    file(partfun1,rc3_partfun1),
    []).

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

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

fof(rc3_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    []).

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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    []).

fof(rc4_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    []).

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

fof(rc5_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    []).

fof(rc6_abian,axiom,(
    ! [A,B] : 
      ( ~ v2_setfam_1(B)
     => ? [C] : 
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ),
    file(abian,rc6_abian),
    []).

fof(rc6_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    []).

fof(rc7_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    []).

fof(redefinition_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k12_finseq_1(A,B) = k5_finseq_1(B) ) ),
    file(finseq_1,k12_finseq_1),
    []).

fof(redefinition_k16_funct_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,D)
        & m1_relset_1(F,B,D) )
     => k16_funct_3(A,B,C,D,E,F) = k15_funct_3(E,F) ) ),
    file(funct_3,k16_funct_3),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k1_msualg_3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C)
        & m1_subset_1(E,A) )
     => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ),
    file(msualg_3,k1_msualg_3),
    []).

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

fof(redefinition_k6_partfun1,axiom,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) ),
    file(partfun1,k6_partfun1),
    []).

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

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

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

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

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

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

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

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

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

fof(t1_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(t29_hilbert3,axiom,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,k5_numbers) )
     => k3_hilbert3(A,k2_hilbert1) = 1 ) ),
    file(hilbert3,t29_hilbert3),
    []).

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

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

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

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

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

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

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