% Mizar problem: t13_integra5,integra5,1049,35 
fof(t13_integra5,conjecture,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,B)
              & r2_fdiff_1(C,B)
              & r1_integra5(A,k2_fdiff_1(C,B))
              & r3_rfunct_1(k2_fdiff_1(C,B),A) )
           => k2_integra5(A,k2_fdiff_1(C,B)) = k10_binop_2(k2_seq_1(k1_numbers,k1_numbers,C,k3_pscomp_1(A)),k2_seq_1(k1_numbers,k1_numbers,C,k4_pscomp_1(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_integra1,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_integra1,cc2_membered,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,connectedness_r1_xreal_0,d11_integra1,d12_integra1,d15_integra1,d16_integra1,d17_integra1,d18_integra1,d1_integra5,d2_integra5,d3_integra5,dt_k10_binop_2,dt_k10_integra1,dt_k11_integra1,dt_k12_integra1,dt_k13_integra1,dt_k1_funct_1,dt_k1_integra1,dt_k1_integra5,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_fdiff_1,dt_k2_integra5,dt_k2_partfun1,dt_k2_relat_1,dt_k2_seq_1,dt_k2_seq_4,dt_k2_zfmisc_1,dt_k3_pscomp_1,dt_k3_seq_4,dt_k4_pscomp_1,dt_k4_relset_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relset_1,dt_k6_integra1,dt_k6_xcmplx_0,dt_k7_integra1,dt_k7_relat_1,dt_k8_integra1,dt_k9_integra1,dt_m1_finseq_1,dt_m1_integra1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_integra1,dt_m2_relset_1,dt_m3_integra1,existence_m1_finseq_1,existence_m1_integra1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_integra1,existence_m2_relset_1,existence_m3_integra1,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_integra1,fc1_ordinal2,fc1_seq_1,fc20_xreal_0,fc2_membered,fc2_seq_1,fc5_membered,fc5_xreal_0,fc6_membered,rc1_arytm_3,rc1_integra1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_integra1,rc2_xreal_0,rc3_integra1,rc3_xreal_0,rc4_xreal_0,redefinition_k10_binop_2,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k3_pscomp_1,redefinition_k4_pscomp_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k8_integra1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m3_integra1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,t12_integra5,t1_real,t1_subset,t1_xreal_1,t26_partfun1,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t60_seq_4,t62_seq_4,t65_relat_1,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(integra5,t13_integra5)]).

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_integra1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_integra1(A)
       => ( ~ v1_xboole_0(A)
          & v1_membered(A)
          & v2_membered(A)
          & v1_rcomp_1(A) ) ) ) ),
    file(integra1,cc1_integra1),
    []).

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

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_seq_1,axiom,(
    ! [A,B] : 
      ( v2_membered(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( v1_funct_1(C)
           => ( v1_funct_1(C)
              & v1_seq_1(C) ) ) ) ) ),
    file(seq_1,cc1_seq_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_integra1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_integra1(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v3_seq_4(A) ) ) ) ),
    file(integra1,cc2_integra1),
    []).

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

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

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

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

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_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

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(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d11_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k8_integra1(A),k1_numbers) )
             => ( C = k9_integra1(A,B)
              <=> ( k4_relset_1(k8_integra1(A),k1_numbers,C) = k8_integra1(A)
                  & ! [D] : 
                      ( m3_integra1(D,A,k8_integra1(A))
                     => ( r2_hidden(D,k4_relset_1(k8_integra1(A),k1_numbers,C))
                       => k2_seq_1(k8_integra1(A),k1_numbers,C,D) = k6_integra1(A,B,k8_integra1(A),D) ) ) ) ) ) ) ) ),
    file(integra1,d11_integra1),
    []).

fof(d12_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k8_integra1(A),k1_numbers) )
             => ( C = k10_integra1(A,B)
              <=> ( k4_relset_1(k8_integra1(A),k1_numbers,C) = k8_integra1(A)
                  & ! [D] : 
                      ( m3_integra1(D,A,k8_integra1(A))
                     => ( r2_hidden(D,k4_relset_1(k8_integra1(A),k1_numbers,C))
                       => k2_seq_1(k8_integra1(A),k1_numbers,C,D) = k7_integra1(A,B,k8_integra1(A),D) ) ) ) ) ) ) ) ),
    file(integra1,d12_integra1),
    []).

fof(d15_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k11_integra1(A,B) = k4_pscomp_1(k5_relset_1(k8_integra1(A),k1_numbers,k9_integra1(A,B))) ) ) ),
    file(integra1,d15_integra1),
    []).

fof(d16_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k12_integra1(A,B) = k3_pscomp_1(k5_relset_1(k8_integra1(A),k1_numbers,k10_integra1(A,B))) ) ) ),
    file(integra1,d16_integra1),
    []).

fof(d17_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r3_integra1(A,B)
          <=> ( r1_integra1(A,B)
              & r2_integra1(A,B)
              & k11_integra1(A,B) = k12_integra1(A,B) ) ) ) ) ),
    file(integra1,d17_integra1),
    []).

fof(d18_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k13_integra1(A,B) = k11_integra1(A,B) ) ) ),
    file(integra1,d18_integra1),
    []).

fof(d1_integra5,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => k1_integra5(A,B) = k2_partfun1(k1_numbers,k1_numbers,B,A) ) ) ),
    file(integra5,d1_integra5),
    []).

fof(d2_integra5,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r1_integra5(A,B)
          <=> r3_integra1(A,k1_integra5(A,B)) ) ) ) ),
    file(integra5,d2_integra5),
    []).

fof(d3_integra5,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => k2_integra5(A,B) = k13_integra1(A,k1_integra5(A,B)) ) ) ),
    file(integra5,d3_integra5),
    []).

fof(dt_k10_binop_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k10_binop_2(A,B),k1_numbers) ) ),
    file(binop_2,k10_binop_2),
    []).

fof(dt_k10_integra1,axiom,(
    ! [A,B] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k10_integra1(A,B))
        & m2_relset_1(k10_integra1(A,B),k8_integra1(A),k1_numbers) ) ) ),
    file(integra1,k10_integra1),
    []).

fof(dt_k11_integra1,axiom,(
    ! [A,B] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k11_integra1(A,B),k1_numbers) ) ),
    file(integra1,k11_integra1),
    []).

fof(dt_k12_integra1,axiom,(
    ! [A,B] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k12_integra1(A,B),k1_numbers) ) ),
    file(integra1,k12_integra1),
    []).

fof(dt_k13_integra1,axiom,(
    ! [A,B] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k13_integra1(A,B),k1_numbers) ) ),
    file(integra1,k13_integra1),
    []).

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

fof(dt_k1_integra1,axiom,(
    $true ),
    file(integra1,k1_integra1),
    []).

fof(dt_k1_integra5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,k1_numbers,k1_numbers) )
     => ( v1_funct_1(k1_integra5(A,B))
        & m2_relset_1(k1_integra5(A,B),A,k1_numbers) ) ) ),
    file(integra5,k1_integra5),
    []).

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_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_fdiff_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => ( v1_funct_1(k2_fdiff_1(A,B))
        & m2_relset_1(k2_fdiff_1(A,B),k1_numbers,k1_numbers) ) ) ),
    file(fdiff_1,k2_fdiff_1),
    []).

fof(dt_k2_integra5,axiom,(
    ! [A,B] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,k1_numbers,k1_numbers) )
     => m1_subset_1(k2_integra5(A,B),k1_numbers) ) ),
    file(integra5,k2_integra5),
    []).

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_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ),
    file(seq_1,k2_seq_1),
    []).

fof(dt_k2_seq_4,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_xreal_0(k2_seq_4(A)) ) ),
    file(seq_4,k2_seq_4),
    []).

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

fof(dt_k3_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k3_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k3_pscomp_1),
    []).

fof(dt_k3_seq_4,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_xreal_0(k3_seq_4(A)) ) ),
    file(seq_4,k3_seq_4),
    []).

fof(dt_k4_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k4_pscomp_1(A),k1_numbers) ) ),
    file(pscomp_1,k4_pscomp_1),
    []).

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_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

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

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(dt_k6_integra1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => m1_subset_1(k6_integra1(A,B,C,D),k1_numbers) ) ),
    file(integra1,k6_integra1),
    []).

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

fof(dt_k7_integra1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => m1_subset_1(k7_integra1(A,B,C,D),k1_numbers) ) ),
    file(integra1,k7_integra1),
    []).

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_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => m2_integra1(k8_integra1(A),A) ) ),
    file(integra1,k8_integra1),
    []).

fof(dt_k9_integra1,axiom,(
    ! [A,B] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k9_integra1(A,B))
        & m2_relset_1(k9_integra1(A,B),k8_integra1(A),k1_numbers) ) ) ),
    file(integra1,k9_integra1),
    []).

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_integra1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( m1_integra1(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_goboard1(B)
            & m2_finseq_1(B,k1_numbers) ) ) ) ),
    file(integra1,m1_integra1),
    []).

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_integra1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] : 
          ( m2_integra1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(integra1,m2_integra1),
    []).

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_m3_integra1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A) )
     => ! [C] : 
          ( m3_integra1(C,A,B)
         => m1_integra1(C,A) ) ) ),
    file(integra1,m3_integra1),
    []).

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

fof(existence_m1_integra1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] : m1_integra1(B,A) ) ),
    file(integra1,m1_integra1),
    []).

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_integra1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] : m2_integra1(B,A) ) ),
    file(integra1,m2_integra1),
    []).

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

fof(existence_m3_integra1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A) )
     => ? [C] : m3_integra1(C,A,B) ) ),
    file(integra1,m3_integra1),
    []).

fof(fc15_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    []).

fof(fc16_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    []).

fof(fc17_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    []).

fof(fc18_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    []).

fof(fc19_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_xreal_0),
    []).

fof(fc1_integra1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ v1_xboole_0(k1_integra1(A)) ) ),
    file(integra1,fc1_integra1),
    []).

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_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_xcmplx_0(k1_funct_1(A,B))
        & v1_xreal_0(k1_funct_1(A,B)) ) ) ),
    file(seq_1,fc1_seq_1),
    []).

fof(fc20_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc2_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_seq_1(k7_relat_1(A,B)) ) ) ),
    file(seq_1,fc2_seq_1),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc5_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    []).

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(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_integra1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & v1_membered(A)
      & v2_membered(A)
      & v1_integra1(A) ) ),
    file(integra1,rc1_integra1),
    []).

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_seq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A) ) ),
    file(seq_1,rc1_seq_1),
    []).

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

fof(rc2_integra1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_seq_4(A)
      & v1_rcomp_1(A)
      & v1_integra1(A) ) ),
    file(integra1,rc2_integra1),
    []).

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_integra1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] : 
          ( m2_integra1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(integra1,rc3_integra1),
    []).

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_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(redefinition_k10_binop_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) ),
    file(binop_2,k10_binop_2),
    []).

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

fof(redefinition_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seq_1,k2_seq_1),
    []).

fof(redefinition_k3_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k3_pscomp_1(A) = k2_seq_4(A) ) ),
    file(pscomp_1,k3_pscomp_1),
    []).

fof(redefinition_k4_pscomp_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k4_pscomp_1(A) = k3_seq_4(A) ) ),
    file(pscomp_1,k4_pscomp_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_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_k8_integra1,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => k8_integra1(A) = k1_integra1(A) ) ),
    file(integra1,k8_integra1),
    []).

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_m3_integra1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A) )
     => ! [C] : 
          ( m3_integra1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(integra1,m3_integra1),
    []).

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

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(t12_integra5,axiom,(
    ! [A] : 
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ! [D] : 
              ( m3_integra1(D,A,k8_integra1(A))
             => ( ( r1_tarski(A,B)
                  & r2_fdiff_1(C,B)
                  & r3_rfunct_1(k2_fdiff_1(C,B),A) )
               => ( r1_xreal_0(k7_integra1(A,k1_integra5(A,k2_fdiff_1(C,B)),k8_integra1(A),D),k10_binop_2(k2_seq_1(k1_numbers,k1_numbers,C,k3_pscomp_1(A)),k2_seq_1(k1_numbers,k1_numbers,C,k4_pscomp_1(A))))
                  & r1_xreal_0(k10_binop_2(k2_seq_1(k1_numbers,k1_numbers,C,k3_pscomp_1(A)),k2_seq_1(k1_numbers,k1_numbers,C,k4_pscomp_1(A))),k6_integra1(A,k1_integra5(A,k2_fdiff_1(C,B)),k8_integra1(A),D)) ) ) ) ) ) ),
    file(integra5,t12_integra5),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

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

fof(t1_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_1),
    []).

fof(t26_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ~ ( r2_hidden(C,k2_relat_1(D))
          & ! [E] : 
              ( m1_subset_1(E,A)
             => ~ ( r2_hidden(E,k4_relset_1(A,B,D))
                  & C = k1_funct_1(D,E) ) ) ) ) ),
    file(partfun1,t26_partfun1),
    []).

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

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

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

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_seq_4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_membered(A) )
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ! [C] : 
                ( v1_xreal_0(C)
               => ( r2_hidden(C,A)
                 => r1_xreal_0(B,C) ) )
           => r1_xreal_0(B,k3_seq_4(A)) ) ) ) ),
    file(seq_4,t60_seq_4),
    []).

fof(t62_seq_4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_membered(A) )
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ! [D] : 
                    ( v1_xreal_0(D)
                   => ( r2_hidden(D,A)
                     => r1_xreal_0(D,C) ) )
               => r1_xreal_0(k2_seq_4(A),C) ) ) ) ) ),
    file(seq_4,t62_seq_4),
    []).

fof(t65_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    []).

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

fof(t6_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

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

fof(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

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

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).