% Mizar problem: t70_prob_3,prob_3,1619,61 
fof(t70_prob_3,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( m1_prob_3(D,A,B)
                 => ( r1_xreal_0(k1_funct_1(C,k8_prob_3(A,D)),k15_rvsum_1(k13_prob_3(A,B,D,C)))
                    & ( v1_prob_2(D)
                     => k1_funct_1(C,k8_prob_3(A,D)) = k15_rvsum_1(k13_prob_3(A,B,D,C)) ) ) ) ) ) ) ),
    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_funct_1,cc1_membered,cc1_prob_1,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_funct_1,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,d3_prob_2,d4_prob_2,dt_k11_prob_3,dt_k13_prob_3,dt_k15_rvsum_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_kurato_2,dt_k1_numbers,dt_k1_pcomps_1,dt_k1_prob_1,dt_k1_prob_2,dt_k1_relat_1,dt_k1_series_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_series_1,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_finseq_1,dt_k4_relset_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k7_kurato_2,dt_k7_prob_3,dt_k8_funct_2,dt_k8_prob_3,dt_k9_prob_1,dt_m1_finseq_1,dt_m1_prob_1,dt_m1_prob_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_prob_1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_prob_1,dt_m4_prob_1,existence_m1_finseq_1,existence_m1_prob_1,existence_m1_prob_3,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_prob_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_prob_1,existence_m4_prob_1,fc1_funct_1,fc1_ordinal2,fc1_seq_1,fc1_subset_1,fc2_membered,fc4_subset_1,fc5_membered,fc6_membered,rc1_arytm_3,rc1_funct_1,rc1_membered,rc1_prob_1,rc1_seq_1,rc1_subset_1,rc1_xreal_0,rc2_funct_1,rc2_prob_1,rc2_subset_1,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,redefinition_k11_prob_3,redefinition_k13_prob_3,redefinition_k1_kurato_2,redefinition_k1_pcomps_1,redefinition_k1_prob_1,redefinition_k1_prob_2,redefinition_k3_finseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k7_kurato_2,redefinition_k7_prob_3,redefinition_k8_funct_2,redefinition_k8_prob_3,redefinition_k9_prob_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,symmetry_r1_xboole_0,t1_numerals,t1_real,t1_subset,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t51_prob_3,t5_real,t5_subset,t60_prob_3,t61_prob_3,t65_xboole_1,t69_prob_3,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(prob_3,t70_prob_3)]).

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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

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

fof(cc1_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ( v2_finsub_1(B)
        & v1_prob_1(B,A) ) ) ),
    file(prob_1,cc1_prob_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_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_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

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

fof(cc2_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(d3_prob_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_prob_2(A)
      <=> ! [B,C] : 
            ( B != C
           => r1_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ),
    file(prob_2,d3_prob_2),
    []).

fof(d4_prob_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m2_prob_1(C,A,B)
             => ( v1_prob_2(C)
              <=> ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( D != E
                         => r1_xboole_0(k1_prob_2(A,B,C,D),k1_prob_2(A,B,C,E)) ) ) ) ) ) ) ) ),
    file(prob_2,d4_prob_2),
    []).

fof(dt_k11_prob_3,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_prob_1(B,A)
        & m1_prob_3(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => m3_prob_1(k11_prob_3(A,B,C,D),A,B) ) ),
    file(prob_3,k11_prob_3),
    []).

fof(dt_k13_prob_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m1_prob_3(C,A,B)
        & m4_prob_1(D,A,B) )
     => m2_finseq_1(k13_prob_3(A,B,C,D),k1_numbers) ) ),
    file(prob_3,k13_prob_3),
    []).

fof(dt_k15_rvsum_1,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k1_numbers)
     => m1_subset_1(k15_rvsum_1(A),k1_numbers) ) ),
    file(rvsum_1,k15_rvsum_1),
    []).

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

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

fof(dt_k1_kurato_2,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k1_kurato_2(A,B),k1_zfmisc_1(A)) ) ),
    file(kurato_2,k1_kurato_2),
    []).

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

fof(dt_k1_pcomps_1,axiom,(
    ! [A] : m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ),
    file(pcomps_1,k1_pcomps_1),
    []).

fof(dt_k1_prob_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k1_prob_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(prob_1,k1_prob_1),
    []).

fof(dt_k1_prob_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m2_prob_1(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => m3_prob_1(k1_prob_2(A,B,C,D),A,B) ) ),
    file(prob_2,k1_prob_2),
    []).

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

fof(dt_k1_series_1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k1_series_1(A))
        & v1_funct_2(k1_series_1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k1_series_1(A),k5_numbers,k1_numbers) ) ) ),
    file(series_1,k1_series_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_series_1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k2_series_1(A),k1_numbers) ) ),
    file(series_1,k2_series_1),
    []).

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

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

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k7_kurato_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k7_kurato_2(A,B,C),k1_zfmisc_1(A)) ) ),
    file(kurato_2,k7_kurato_2),
    []).

fof(dt_k7_prob_3,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,k1_pcomps_1(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k7_prob_3(A,B,C),k1_zfmisc_1(A)) ) ),
    file(prob_3,k7_prob_3),
    []).

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

fof(dt_k8_prob_3,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k1_pcomps_1(A))
     => m1_subset_1(k8_prob_3(A,B),k1_zfmisc_1(A)) ) ),
    file(prob_3,k8_prob_3),
    []).

fof(dt_k9_prob_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m2_prob_1(C,A,B)
        & v1_funct_1(D)
        & v1_funct_2(D,B,k1_numbers)
        & m1_relset_1(D,B,k1_numbers) )
     => ( v1_funct_1(k9_prob_1(A,B,C,D))
        & v1_funct_2(k9_prob_1(A,B,C,D),k5_numbers,k1_numbers)
        & m2_relset_1(k9_prob_1(A,B,C,D),k5_numbers,k1_numbers) ) ) ),
    file(prob_1,k9_prob_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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(prob_1,m1_prob_1),
    []).

fof(dt_m1_prob_3,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m1_prob_3(C,A,B)
         => m2_finseq_1(C,k1_pcomps_1(A)) ) ) ),
    file(prob_3,m1_prob_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_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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m2_prob_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) ) ) ) ),
    file(prob_1,m2_prob_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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m3_prob_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(A)) ) ) ),
    file(prob_1,m3_prob_1),
    []).

fof(dt_m4_prob_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A) )
     => ! [C] : 
          ( m4_prob_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,B,k1_numbers)
            & m2_relset_1(C,B,k1_numbers) ) ) ) ),
    file(prob_1,m4_prob_1),
    []).

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

fof(existence_m1_prob_1,axiom,(
    ! [A] : 
    ? [B] : m1_prob_1(B,A) ),
    file(prob_1,m1_prob_1),
    []).

fof(existence_m1_prob_3,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ? [C] : m1_prob_3(C,A,B) ) ),
    file(prob_3,m1_prob_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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ? [C] : m2_prob_1(C,A,B) ) ),
    file(prob_1,m2_prob_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_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ? [C] : m3_prob_1(C,A,B) ) ),
    file(prob_1,m3_prob_1),
    []).

fof(existence_m4_prob_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A) )
     => ? [C] : m4_prob_1(C,A,B) ) ),
    file(prob_1,m4_prob_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

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

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

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_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(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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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

fof(rc1_prob_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v2_finsub_1(B)
      & v1_prob_1(B,A) ) ),
    file(prob_1,rc1_prob_1),
    []).

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_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

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

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

fof(rc2_prob_1,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ? [C] : 
          ( m3_prob_1(C,A,B)
          & v1_xboole_0(C)
          & v1_funct_1(C)
          & v1_membered(C)
          & v2_membered(C)
          & v3_membered(C)
          & v4_membered(C)
          & v5_membered(C) ) ) ),
    file(prob_1,rc2_prob_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_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

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_k11_prob_3,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_prob_1(B,A)
        & m1_prob_3(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => k11_prob_3(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(prob_3,k11_prob_3),
    []).

fof(redefinition_k13_prob_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m1_prob_3(C,A,B)
        & m4_prob_1(D,A,B) )
     => k13_prob_3(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(prob_3,k13_prob_3),
    []).

fof(redefinition_k1_kurato_2,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => k1_kurato_2(A,B) = k3_card_3(B) ) ),
    file(kurato_2,k1_kurato_2),
    []).

fof(redefinition_k1_pcomps_1,axiom,(
    ! [A] : k1_pcomps_1(A) = k1_zfmisc_1(A) ),
    file(pcomps_1,k1_pcomps_1),
    []).

fof(redefinition_k1_prob_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => k1_prob_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(prob_1,k1_prob_1),
    []).

fof(redefinition_k1_prob_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m2_prob_1(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => k1_prob_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(prob_2,k1_prob_2),
    []).

fof(redefinition_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_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_k7_kurato_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => k7_kurato_2(A,B,C) = k1_funct_1(B,C) ) ),
    file(kurato_2,k7_kurato_2),
    []).

fof(redefinition_k7_prob_3,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,k1_pcomps_1(A))
        & m1_subset_1(C,k5_numbers) )
     => k7_prob_3(A,B,C) = k1_funct_1(B,C) ) ),
    file(prob_3,k7_prob_3),
    []).

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

fof(redefinition_k8_prob_3,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k1_pcomps_1(A))
     => k8_prob_3(A,B) = k3_card_3(B) ) ),
    file(prob_3,k8_prob_3),
    []).

fof(redefinition_k9_prob_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A)
        & m2_prob_1(C,A,B)
        & v1_funct_1(D)
        & v1_funct_2(D,B,k1_numbers)
        & m1_relset_1(D,B,k1_numbers) )
     => k9_prob_1(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(prob_1,k9_prob_1),
    []).

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

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

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

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(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(t51_prob_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m2_prob_1(C,A,B)
             => ! [D] : 
                  ( m4_prob_1(D,A,B)
                 => ( v1_prob_2(C)
                   => k1_funct_1(D,k1_kurato_2(A,C)) = k2_series_1(k9_prob_1(A,B,C,D)) ) ) ) ) ) ),
    file(prob_3,t51_prob_3),
    []).

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_prob_3,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,k1_pcomps_1(A))
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ( ( ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_hidden(D,k4_relset_1(k5_numbers,k1_pcomps_1(A),B))
                   => k1_prob_1(A,C,D) = k7_prob_3(A,B,D) ) )
              & ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ~ r2_hidden(D,k4_relset_1(k5_numbers,k1_pcomps_1(A),B))
                   => k1_prob_1(A,C,D) = k1_xboole_0 ) ) )
           => ( k1_prob_1(A,C,0) = k1_xboole_0
              & k1_kurato_2(A,C) = k8_prob_3(A,B) ) ) ) ) ),
    file(prob_3,t60_prob_3),
    []).

fof(t61_prob_3,axiom,(
    ! [A,B] : 
      ( m1_prob_1(B,A)
     => ! [C] : 
          ( m1_prob_3(C,A,B)
         => ? [D] : 
              ( m2_prob_1(D,A,B)
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => ( r2_hidden(E,k4_relset_1(k5_numbers,k1_pcomps_1(A),C))
                   => k1_prob_1(A,D,E) = k11_prob_3(A,B,C,E) ) )
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => ( ~ r2_hidden(E,k4_relset_1(k5_numbers,k1_pcomps_1(A),C))
                   => k1_prob_1(A,D,E) = k1_xboole_0 ) ) ) ) ) ),
    file(prob_3,t61_prob_3),
    []).

fof(t65_xboole_1,axiom,(
    ! [A] : r1_xboole_0(A,k1_xboole_0) ),
    file(xboole_1,t65_xboole_1),
    []).

fof(t69_prob_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_prob_1(B,A)
         => ! [C] : 
              ( m4_prob_1(C,A,B)
             => ! [D] : 
                  ( m1_prob_3(D,A,B)
                 => ! [E] : 
                      ( m2_prob_1(E,A,B)
                     => ( ( ! [F] : 
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(F,k4_relset_1(k5_numbers,k1_pcomps_1(A),D))
                               => k7_kurato_2(A,E,F) = k11_prob_3(A,B,D,F) ) )
                          & ! [F] : 
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( ~ r2_hidden(F,k4_relset_1(k5_numbers,k1_pcomps_1(A),D))
                               => k7_kurato_2(A,E,F) = k1_xboole_0 ) ) )
                       => ( v4_seq_2(k1_series_1(k9_prob_1(A,B,E,C)))
                          & k2_series_1(k9_prob_1(A,B,E,C)) = k8_funct_2(k5_numbers,k1_numbers,k1_series_1(k9_prob_1(A,B,E,C)),k3_finseq_1(D))
                          & r1_xreal_0(k1_funct_1(C,k1_kurato_2(A,E)),k2_series_1(k9_prob_1(A,B,E,C)))
                          & k15_rvsum_1(k13_prob_3(A,B,D,C)) = k2_series_1(k9_prob_1(A,B,E,C)) ) ) ) ) ) ) ) ),
    file(prob_3,t69_prob_3),
    []).

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),
    []).