% Mizar problem: t15_henmodel,henmodel,1529,14 
fof(t15_henmodel,conjecture,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => r4_calcul_1(k8_finseq_1(k7_cqc_lang,A,k12_finseq_1(k7_cqc_lang,k9_cqc_lang))) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relset_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_ordinal1,cc2_xreal_0,cc3_int_1,cc3_ordinal1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_tarski,connectedness_r1_xreal_0,d1_tarski,d3_tarski,d4_finseq_1,d5_tarski,d6_calcul_1,d7_calcul_1,d8_calcul_1,d9_calcul_1,dt_k10_cqc_lang,dt_k11_cqc_lang,dt_k11_qc_lang1,dt_k12_finseq_1,dt_k12_qc_lang1,dt_k13_qc_lang1,dt_k14_qc_lang1,dt_k15_cqc_lang,dt_k1_calcul_1,dt_k1_card_1,dt_k1_domain_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k24_qc_lang1,dt_k2_calcul_1,dt_k2_cqc_the1,dt_k2_finseq_1,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_calcul_1,dt_k3_finseq_1,dt_k4_calcul_1,dt_k4_finseq_1,dt_k4_substut2,dt_k4_tarski,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relset_1,dt_k6_domain_1,dt_k7_cqc_lang,dt_k7_finseq_1,dt_k8_finseq_1,dt_k8_qc_lang1,dt_k9_cqc_lang,dt_k9_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc11_finseq_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_finset_1,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc2_cqc_lang,fc2_finseq_1,fc2_finset_1,fc2_ordinal1,fc2_qc_lang1,fc2_subset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_int_1,rc1_ordinal1,rc1_subset_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_ordinal1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k10_cqc_lang,redefinition_k11_cqc_lang,redefinition_k12_finseq_1,redefinition_k15_cqc_lang,redefinition_k1_domain_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k6_domain_1,redefinition_k8_finseq_1,redefinition_k9_cqc_lang,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,spc5_boole,spc5_numerals,spc6_boole,spc6_numerals,spc7_boole,spc7_numerals,spc8_boole,spc8_numerals,spc9_boole,spc9_numerals,t106_zfmisc_1,t1_numerals,t1_real,t1_subset,t1_xreal_1,t2_real,t2_subset,t3_real,t3_subset,t43_cqc_the1,t4_real,t4_subset,t55_finseq_1,t56_finseq_1,t57_finseq_1,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_mcart_1,t7_real,t8_boole,t8_real]),
    [file(henmodel,t15_henmodel)]).

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

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

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

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

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

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

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

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

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_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_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

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

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

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

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

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

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

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

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

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

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

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

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(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

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

fof(d4_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    []).

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

fof(d6_calcul_1,axiom,(
    ! [A] : 
      ( A = k4_calcul_1
    <=> ! [B] : 
          ( r2_hidden(B,A)
        <=> m2_finseq_1(B,k7_cqc_lang) ) ) ),
    file(calcul_1,d6_calcul_1),
    []).

fof(d7_calcul_1,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( k2_mcart_1(k1_funct_1(A,B)) = 0
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_finseq_1(C,k7_cqc_lang)
                    & r1_calcul_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,C),k1_calcul_1(k7_cqc_lang,C))
                    & k1_mcart_1(k1_funct_1(A,B)) = C ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 1
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_finseq_1(C,k7_cqc_lang)
                    & k1_mcart_1(k1_funct_1(A,B)) = k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k9_cqc_lang)) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 2
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_finseq_1(D,k7_cqc_lang)
                        & ? [E] : 
                            ( m2_finseq_1(E,k7_cqc_lang)
                            & r1_xreal_0(1,C)
                            & ~ r1_xreal_0(B,C)
                            & r2_calcul_1(k1_calcul_1(k7_cqc_lang,D),k1_calcul_1(k7_cqc_lang,E))
                            & k2_calcul_1(k7_cqc_lang,D) = k2_calcul_1(k7_cqc_lang,E)
                            & k1_mcart_1(k1_funct_1(A,C)) = D
                            & k1_mcart_1(k1_funct_1(A,B)) = E ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 3
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] : 
                            ( m2_finseq_1(E,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_finseq_1(F,k7_cqc_lang)
                                & r1_xreal_0(1,C)
                                & ~ r1_xreal_0(B,C)
                                & r1_xreal_0(1,D)
                                & ~ r1_xreal_0(C,D)
                                & ~ r1_xreal_0(k3_finseq_1(E),1)
                                & ~ r1_xreal_0(k3_finseq_1(F),1)
                                & k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)) = k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,F))
                                & k10_cqc_lang(k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E))) = k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,F))
                                & k2_calcul_1(k7_cqc_lang,E) = k2_calcul_1(k7_cqc_lang,F)
                                & E = k1_mcart_1(k1_funct_1(A,D))
                                & F = k1_mcart_1(k1_funct_1(A,C))
                                & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,E))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 4
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] : 
                            ( m2_finseq_1(E,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_finseq_1(F,k7_cqc_lang)
                                & ? [G] : 
                                    ( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
                                    & r1_xreal_0(1,C)
                                    & ~ r1_xreal_0(B,C)
                                    & r1_xreal_0(1,D)
                                    & ~ r1_xreal_0(C,D)
                                    & ~ r1_xreal_0(k3_finseq_1(E),1)
                                    & k1_calcul_1(k7_cqc_lang,E) = k1_calcul_1(k7_cqc_lang,F)
                                    & k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)) = k10_cqc_lang(G)
                                    & k10_cqc_lang(k2_calcul_1(k7_cqc_lang,E)) = k2_calcul_1(k7_cqc_lang,F)
                                    & E = k1_mcart_1(k1_funct_1(A,D))
                                    & F = k1_mcart_1(k1_funct_1(A,C))
                                    & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)),k12_finseq_1(k7_cqc_lang,G)) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 5
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] : 
                            ( m2_finseq_1(E,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_finseq_1(F,k7_cqc_lang)
                                & r1_xreal_0(1,C)
                                & ~ r1_xreal_0(B,C)
                                & r1_xreal_0(1,D)
                                & ~ r1_xreal_0(C,D)
                                & k1_calcul_1(k7_cqc_lang,E) = k1_calcul_1(k7_cqc_lang,F)
                                & E = k1_mcart_1(k1_funct_1(A,D))
                                & F = k1_mcart_1(k1_funct_1(A,C))
                                & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E),k12_finseq_1(k7_cqc_lang,k11_cqc_lang(k2_calcul_1(k7_cqc_lang,E),k2_calcul_1(k7_cqc_lang,F)))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 6
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_finseq_1(D,k7_cqc_lang)
                        & ? [E] : 
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
                                & r1_xreal_0(1,C)
                                & ~ r1_xreal_0(B,C)
                                & k11_cqc_lang(E,F) = k2_calcul_1(k7_cqc_lang,D)
                                & D = k1_mcart_1(k1_funct_1(A,C))
                                & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,E)) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 7
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_finseq_1(D,k7_cqc_lang)
                        & ? [E] : 
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
                                & r1_xreal_0(1,C)
                                & ~ r1_xreal_0(B,C)
                                & k11_cqc_lang(E,F) = k2_calcul_1(k7_cqc_lang,D)
                                & D = k1_mcart_1(k1_funct_1(A,C))
                                & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,F)) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 8
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_finseq_1(D,k7_cqc_lang)
                        & ? [E] : 
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                                & ? [G] : 
                                    ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                    & r1_xreal_0(1,C)
                                    & ~ r1_xreal_0(B,C)
                                    & k2_calcul_1(k7_cqc_lang,D) = k15_cqc_lang(F,E)
                                    & D = k1_mcart_1(k1_funct_1(A,C))
                                    & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,k4_substut2(E,F,G))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) )
            & ( k2_mcart_1(k1_funct_1(A,B)) = 9
             => ( r3_calcul_1(A,B)
              <=> ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & ? [D] : 
                        ( m2_finseq_1(D,k7_cqc_lang)
                        & ? [E] : 
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & ? [F] : 
                                ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                                & ? [G] : 
                                    ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                    & r1_xreal_0(1,C)
                                    & ~ r1_xreal_0(B,C)
                                    & k2_calcul_1(k7_cqc_lang,D) = k4_substut2(E,F,G)
                                    & ~ r2_hidden(G,k3_calcul_1(k1_calcul_1(k7_cqc_lang,D)))
                                    & ~ r2_hidden(G,k24_qc_lang1(k15_cqc_lang(F,E)))
                                    & D = k1_mcart_1(k1_funct_1(A,C))
                                    & k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,k15_cqc_lang(F,E))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) ) ) ) ) ),
    file(calcul_1,d7_calcul_1),
    []).

fof(d8_calcul_1,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
     => ( v1_calcul_1(A)
      <=> ( A != k1_xboole_0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(1,B)
                  & r1_xreal_0(B,k3_finseq_1(A)) )
               => r3_calcul_1(A,B) ) ) ) ) ) ),
    file(calcul_1,d8_calcul_1),
    []).

fof(d9_calcul_1,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ( r4_calcul_1(A)
      <=> ? [B] : 
            ( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
            & v1_calcul_1(B)
            & A = k1_mcart_1(k1_funct_1(B,k3_finseq_1(B))) ) ) ) ),
    file(calcul_1,d9_calcul_1),
    []).

fof(dt_k10_cqc_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k7_cqc_lang)
     => m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k10_cqc_lang),
    []).

fof(dt_k11_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k11_cqc_lang),
    []).

fof(dt_k11_qc_lang1,axiom,(
    m1_subset_1(k11_qc_lang1,k8_qc_lang1) ),
    file(qc_lang1,k11_qc_lang1),
    []).

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_k12_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k12_qc_lang1(A),k8_qc_lang1) ) ),
    file(qc_lang1,k12_qc_lang1),
    []).

fof(dt_k13_qc_lang1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1) ) ),
    file(qc_lang1,k13_qc_lang1),
    []).

fof(dt_k14_qc_lang1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1) ) ),
    file(qc_lang1,k14_qc_lang1),
    []).

fof(dt_k15_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k15_cqc_lang),
    []).

fof(dt_k1_calcul_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => m2_finseq_1(k1_calcul_1(A,B),A) ) ),
    file(calcul_1,k1_calcul_1),
    []).

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

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    []).

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

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

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

fof(dt_k1_qc_lang1,axiom,(
    $true ),
    file(qc_lang1,k1_qc_lang1),
    []).

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

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

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

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

fof(dt_k24_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k24_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ),
    file(qc_lang1,k24_qc_lang1),
    []).

fof(dt_k2_calcul_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => m1_subset_1(k2_calcul_1(A,B),A) ) ),
    file(calcul_1,k2_calcul_1),
    []).

fof(dt_k2_cqc_the1,axiom,(
    $true ),
    file(cqc_the1,k2_cqc_the1),
    []).

fof(dt_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    []).

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

fof(dt_k2_qc_lang1,axiom,(
    m1_subset_1(k2_qc_lang1,k1_zfmisc_1(k1_qc_lang1)) ),
    file(qc_lang1,k2_qc_lang1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k3_calcul_1,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k7_cqc_lang)
     => m1_subset_1(k3_calcul_1(A),k1_zfmisc_1(k2_qc_lang1)) ) ),
    file(calcul_1,k3_calcul_1),
    []).

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_calcul_1,axiom,(
    $true ),
    file(calcul_1,k4_calcul_1),
    []).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    []).

fof(dt_k4_substut2,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k2_qc_lang1) )
     => m2_subset_1(k4_substut2(A,B,C),k8_qc_lang1,k7_cqc_lang) ) ),
    file(substut2,k4_substut2),
    []).

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

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_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_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(dt_k7_cqc_lang,axiom,(
    m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) ),
    file(cqc_lang,k7_cqc_lang),
    []).

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_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ),
    file(finseq_1,k8_finseq_1),
    []).

fof(dt_k8_qc_lang1,axiom,(
    ~ v1_xboole_0(k8_qc_lang1) ),
    file(qc_lang1,k8_qc_lang1),
    []).

fof(dt_k9_cqc_lang,axiom,(
    m2_subset_1(k9_cqc_lang,k8_qc_lang1,k7_cqc_lang) ),
    file(cqc_lang,k9_cqc_lang),
    []).

fof(dt_k9_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k9_finseq_1(A))
      & v1_funct_1(k9_finseq_1(A)) ) ),
    file(finseq_1,k9_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_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(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

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(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc12_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    []).

fof(fc13_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(A,B))
        & v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,fc13_finseq_1),
    []).

fof(fc14_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(B,A))
        & v1_relat_1(k7_finseq_1(B,A))
        & v1_funct_1(k7_finseq_1(B,A))
        & v1_finset_1(k7_finseq_1(B,A))
        & v1_finseq_1(k7_finseq_1(B,A)) ) ) ),
    file(finseq_1,fc14_finseq_1),
    []).

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

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

fof(fc1_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    []).

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

fof(fc1_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_qc_lang1,axiom,(
    ~ v1_xboole_0(k1_qc_lang1) ),
    file(qc_lang1,fc1_qc_lang1),
    []).

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

fof(fc2_cqc_lang,axiom,(
    ~ v1_xboole_0(k7_cqc_lang) ),
    file(cqc_lang,fc2_cqc_lang),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc2_qc_lang1,axiom,(
    ~ v1_xboole_0(k2_qc_lang1) ),
    file(qc_lang1,fc2_qc_lang1),
    []).

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

fof(fc3_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    []).

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

fof(fc4_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_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(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

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

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

fof(rc1_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_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    []).

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

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

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

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

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

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

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

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

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

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

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

fof(rc4_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    []).

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

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

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

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k10_cqc_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k7_cqc_lang)
     => k10_cqc_lang(A) = k12_qc_lang1(A) ) ),
    file(cqc_lang,k10_cqc_lang),
    []).

fof(redefinition_k11_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k11_cqc_lang(A,B) = k13_qc_lang1(A,B) ) ),
    file(cqc_lang,k11_cqc_lang),
    []).

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_k15_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => k15_cqc_lang(A,B) = k14_qc_lang1(A,B) ) ),
    file(cqc_lang,k15_cqc_lang),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    []).

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_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_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_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(redefinition_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ),
    file(finseq_1,k8_finseq_1),
    []).

fof(redefinition_k9_cqc_lang,axiom,(
    k9_cqc_lang = k11_qc_lang1 ),
    file(cqc_lang,k9_cqc_lang),
    []).

fof(redefinition_k9_finseq_1,axiom,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_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(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(spc3_boole,axiom,(
    ~ v1_xboole_0(3) ),
    file(boole,spc3_boole),
    []).

fof(spc3_numerals,axiom,
    ( v2_xreal_0(3)
    & m1_subset_1(3,k5_numbers) ),
    file(numerals,spc3_numerals),
    []).

fof(spc4_boole,axiom,(
    ~ v1_xboole_0(4) ),
    file(boole,spc4_boole),
    []).

fof(spc4_numerals,axiom,
    ( v2_xreal_0(4)
    & m1_subset_1(4,k5_numbers) ),
    file(numerals,spc4_numerals),
    []).

fof(spc5_boole,axiom,(
    ~ v1_xboole_0(5) ),
    file(boole,spc5_boole),
    []).

fof(spc5_numerals,axiom,
    ( v2_xreal_0(5)
    & m1_subset_1(5,k5_numbers) ),
    file(numerals,spc5_numerals),
    []).

fof(spc6_boole,axiom,(
    ~ v1_xboole_0(6) ),
    file(boole,spc6_boole),
    []).

fof(spc6_numerals,axiom,
    ( v2_xreal_0(6)
    & m1_subset_1(6,k5_numbers) ),
    file(numerals,spc6_numerals),
    []).

fof(spc7_boole,axiom,(
    ~ v1_xboole_0(7) ),
    file(boole,spc7_boole),
    []).

fof(spc7_numerals,axiom,
    ( v2_xreal_0(7)
    & m1_subset_1(7,k5_numbers) ),
    file(numerals,spc7_numerals),
    []).

fof(spc8_boole,axiom,(
    ~ v1_xboole_0(8) ),
    file(boole,spc8_boole),
    []).

fof(spc8_numerals,axiom,
    ( v2_xreal_0(8)
    & m1_subset_1(8,k5_numbers) ),
    file(numerals,spc8_numerals),
    []).

fof(spc9_boole,axiom,(
    ~ v1_xboole_0(9) ),
    file(boole,spc9_boole),
    []).

fof(spc9_numerals,axiom,
    ( v2_xreal_0(9)
    & m1_subset_1(9,k5_numbers) ),
    file(numerals,spc9_numerals),
    []).

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

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(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(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(t43_cqc_the1,axiom,
    ( r2_hidden(0,k2_cqc_the1)
    & r2_hidden(1,k2_cqc_the1)
    & r2_hidden(2,k2_cqc_the1)
    & r2_hidden(3,k2_cqc_the1)
    & r2_hidden(4,k2_cqc_the1)
    & r2_hidden(5,k2_cqc_the1)
    & r2_hidden(6,k2_cqc_the1)
    & r2_hidden(7,k2_cqc_the1)
    & r2_hidden(8,k2_cqc_the1)
    & r2_hidden(9,k2_cqc_the1) ),
    file(cqc_the1,t43_cqc_the1),
    []).

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(t55_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t55_finseq_1),
    []).

fof(t56_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t56_finseq_1),
    []).

fof(t57_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,t57_finseq_1),
    []).

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(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_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

fof(t7_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),
    []).