% Mizar problem: t31_goedelcp,goedelcp,920,71 
fof(t31_goedelcp,conjecture,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ~ ( v1_finset_1(k6_goedelcp(A))
          & ! [B] : 
              ( ( v1_henmodel(B)
                & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
             => ~ ( r1_tarski(A,B)
                  & v2_goedelcp(B) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_arytm_3,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k4_subset_1,connectedness_r1_xreal_0,d10_xboole_0,d1_henmodel,d1_tarski,d1_xboole_0,d2_goedelcp,d2_henmodel,d2_xboole_0,d2_zfmisc_1,d3_goedelcp,d3_tarski,d4_tarski,d5_funct_1,d5_tarski,d6_goedelcp,d7_goedelcp,d8_goedelcp,dt_k10_cqc_lang,dt_k11_qc_lang1,dt_k12_finseq_1,dt_k12_qc_lang1,dt_k13_cqc_lang,dt_k16_cqc_lang,dt_k1_calcul_1,dt_k1_card_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_goedelcp,dt_k1_henmodel,dt_k1_mcart_1,dt_k1_nat_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_goedelcp,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_qc_lang3,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_calcul_1,dt_k3_finseq_1,dt_k3_goedelcp,dt_k3_qc_lang2,dt_k3_tarski,dt_k4_goedelcp,dt_k4_relset_1,dt_k4_subset_1,dt_k4_substut2,dt_k4_tarski,dt_k5_finseq_1,dt_k5_goedelcp,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang2,dt_k5_real_1,dt_k5_relset_1,dt_k5_setfam_1,dt_k6_domain_1,dt_k6_goedelcp,dt_k6_xcmplx_0,dt_k7_cqc_lang,dt_k7_finseq_1,dt_k8_finseq_1,dt_k8_funct_2,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,fc10_xreal_0,fc11_xreal_0,fc12_relat_1,fc12_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_ordinal2,fc1_subset_1,fc20_xreal_0,fc2_cqc_lang,fc2_relat_1,fc2_subset_1,fc3_subset_1,fc3_xreal_0,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc5_xreal_0,fc6_relat_1,fc7_relat_1,fc7_xreal_0,fc8_relat_1,fc8_xreal_0,fc9_xreal_0,fraenkel_a_1_0_goedelcp,fraenkel_a_1_3_goedelcp,fraenkel_a_1_4_goedelcp,fraenkel_a_1_5_goedelcp,fraenkel_a_2_1_goedelcp,fraenkel_a_2_2_goedelcp,fraenkel_a_2_3_goedelcp,fraenkel_a_2_4_goedelcp,fraenkel_a_2_5_goedelcp,fraenkel_a_2_6_goedelcp,fraenkel_a_2_7_goedelcp,fraenkel_a_3_0_goedelcp,fraenkel_a_3_1_goedelcp,fraenkel_a_3_2_goedelcp,fraenkel_a_3_3_goedelcp,fraenkel_a_3_4_goedelcp,idempotence_k2_xboole_0,idempotence_k4_subset_1,l24_goedelcp,rc1_arytm_3,rc1_henmodel,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_relat_1,rc3_xreal_0,rc4_xreal_0,redefinition_k10_cqc_lang,redefinition_k12_finseq_1,redefinition_k13_cqc_lang,redefinition_k16_cqc_lang,redefinition_k1_domain_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_relset_1,redefinition_k5_setfam_1,redefinition_k6_domain_1,redefinition_k8_finseq_1,redefinition_k8_funct_2,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,s1_nat_1__e24_36__goedelcp,s1_nat_1__e3_36_8__goedelcp,s1_nat_1__e3_36_9__goedelcp,s2_recdef_1__e7_36__goedelcp,s3_funct_1__e13_36__goedelcp,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t10_calcul_1,t10_mcart_1,t11_henmodel,t11_qc_lang3,t12_funct_1,t14_finset_1,t1_arithm,t1_boole,t1_euler_1,t1_numerals,t1_real,t1_subset,t20_cqc_sim1,t20_goedelcp,t21_calcul_2,t21_goedelcp,t22_goedelcp,t22_nat_1,t24_calcul_2,t24_goedelcp,t25_goedelcp,t26_calcul_2,t26_goedelcp,t26_nat_1,t27_goedelcp,t28_goedelcp,t29_goedelcp,t29_nat_1,t2_real,t2_subset,t2_tarski,t2_xreal_1,t30_goedelcp,t36_qc_lang3,t38_nat_1,t3_real,t3_subset,t4_arithm,t4_funct_2,t4_real,t4_subset,t4_xboole_1,t51_calcul_1,t52_calcul_1,t59_calcul_1,t5_calcul_1,t5_real,t5_subset,t60_calcul_1,t61_calcul_1,t6_boole,t6_henmodel,t6_real,t7_boole,t7_mcart_1,t7_qc_lang3,t7_real,t7_xboole_1,t8_boole,t8_henmodel,t8_real,t8_xboole_1,t9_xboole_1]),
    [file(goedelcp,t31_goedelcp)]).

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

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_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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

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

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_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_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_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_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

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

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

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

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

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(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_henmodel,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( ( ( ~ v1_xboole_0(A)
            & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
         => ( B = k1_henmodel(A)
          <=> ( r2_hidden(B,A)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,A)
                   => r1_xreal_0(B,C) ) ) ) ) )
        & ( ~ ( ~ v1_xboole_0(A)
              & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
         => ( B = k1_henmodel(A)
          <=> B = 0 ) ) ) ) ),
    file(henmodel,d1_henmodel),
    []).

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

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( v2_goedelcp(A)
      <=> ! [B] : 
            ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
           => ! [C] : 
                ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
               => ? [D] : 
                    ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                    & r1_henmodel(A,k13_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,C)),k4_substut2(C,B,D))) ) ) ) ) ) ),
    file(goedelcp,d2_goedelcp),
    []).

fof(d2_henmodel,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r1_henmodel(A,B)
          <=> ? [C] : 
                ( m2_finseq_1(C,k7_cqc_lang)
                & r1_tarski(k5_relset_1(k5_numbers,k7_cqc_lang,C),A)
                & r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    file(henmodel,d2_henmodel),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d2_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    []).

fof(d3_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( A = k1_goedelcp
      <=> ! [B] : 
            ( r2_hidden(B,A)
          <=> ? [C] : 
                ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
                & ? [D] : 
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                    & B = k16_cqc_lang(C,D) ) ) ) ) ) ),
    file(goedelcp,d3_goedelcp),
    []).

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_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_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_goedelcp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m2_relset_1(A,k5_numbers,k7_cqc_lang) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( C = k4_goedelcp(A,B)
              <=> ! [D] : 
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ( D = k8_funct_2(k5_numbers,k7_cqc_lang,A,B)
                     => C = k2_goedelcp(D) ) ) ) ) ) ) ),
    file(goedelcp,d6_goedelcp),
    []).

fof(d7_goedelcp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m2_relset_1(A,k5_numbers,k7_cqc_lang) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( C = k5_goedelcp(A,B)
              <=> ! [D] : 
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ( D = k8_funct_2(k5_numbers,k7_cqc_lang,A,B)
                     => C = k3_goedelcp(D) ) ) ) ) ) ) ),
    file(goedelcp,d7_goedelcp),
    []).

fof(d8_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => k6_goedelcp(A) = k3_tarski(a_1_0_goedelcp(A)) ) ),
    file(goedelcp,d8_goedelcp),
    []).

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_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_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k13_cqc_lang),
    []).

fof(dt_k16_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k16_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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_goedelcp,axiom,(
    m1_subset_1(k1_goedelcp,k1_zfmisc_1(k7_cqc_lang)) ),
    file(goedelcp,k1_goedelcp),
    []).

fof(dt_k1_henmodel,axiom,(
    ! [A] : m2_subset_1(k1_henmodel(A),k1_numbers,k5_numbers) ),
    file(henmodel,k1_henmodel),
    []).

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

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

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

fof(dt_k1_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_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m2_subset_1(k2_goedelcp(A),k1_qc_lang1,k2_qc_lang1) ) ),
    file(goedelcp,k2_goedelcp),
    []).

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_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k2_qc_lang3(A),k1_qc_lang1,k2_qc_lang1) ) ),
    file(qc_lang3,k2_qc_lang3),
    []).

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

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_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_k3_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k7_cqc_lang)
     => m2_subset_1(k3_goedelcp(A),k8_qc_lang1,k7_cqc_lang) ) ),
    file(goedelcp,k3_goedelcp),
    []).

fof(dt_k3_qc_lang2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k3_qc_lang2(A,B),k8_qc_lang1) ) ),
    file(qc_lang2,k3_qc_lang2),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k4_goedelcp,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m1_relset_1(A,k5_numbers,k7_cqc_lang)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k4_goedelcp(A,B),k1_qc_lang1,k2_qc_lang1) ) ),
    file(goedelcp,k4_goedelcp),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_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_goedelcp,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m1_relset_1(A,k5_numbers,k7_cqc_lang)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k5_goedelcp(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(goedelcp,k5_goedelcp),
    []).

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_qc_lang2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1) ) ),
    file(qc_lang2,k5_qc_lang2),
    []).

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

fof(dt_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_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_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_k6_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => m1_subset_1(k6_goedelcp(A),k1_zfmisc_1(k2_qc_lang1)) ) ),
    file(goedelcp,k6_goedelcp),
    []).

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

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_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_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(fc10_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    []).

fof(fc11_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    []).

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

fof(fc12_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    []).

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_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

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

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

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

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

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

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    []).

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

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

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

fof(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_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

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

fof(fc7_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    []).

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

fof(fc8_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    []).

fof(fc9_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    []).

fof(fraenkel_a_1_0_goedelcp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
     => ( r2_hidden(A,a_1_0_goedelcp(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
            & A = k24_qc_lang1(C)
            & r2_hidden(C,B) ) ) ) ),
    file(goedelcp,a_1_0_goedelcp),
    []).

fof(fraenkel_a_1_3_goedelcp,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1))
     => ( r2_hidden(A,a_1_3_goedelcp(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & ~ r2_hidden(k2_qc_lang3(C),B) ) ) ) ),
    file(goedelcp,a_1_3_goedelcp),
    []).

fof(fraenkel_a_1_4_goedelcp,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ( r2_hidden(A,a_1_4_goedelcp(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,C)) ) ) ) ),
    file(goedelcp,a_1_4_goedelcp),
    []).

fof(fraenkel_a_1_5_goedelcp,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ( r2_hidden(A,a_1_5_goedelcp(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,C))
            & r2_hidden(C,0) ) ) ) ),
    file(goedelcp,a_1_5_goedelcp),
    []).

fof(fraenkel_a_2_1_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_henmodel(B)
        & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k7_cqc_lang)
        & m2_relset_1(C,k5_numbers,k7_cqc_lang) )
     => ( r2_hidden(A,a_2_1_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & ~ r2_hidden(k2_qc_lang3(D),k6_goedelcp(k4_subset_1(k7_cqc_lang,B,k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,C,0))))) ) ) ) ),
    file(goedelcp,a_2_1_goedelcp),
    []).

fof(fraenkel_a_2_2_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_henmodel(B)
        & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
        & m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) )
     => ( r2_hidden(A,a_2_2_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & ~ r2_hidden(k2_qc_lang3(D),k6_goedelcp(k4_subset_1(k7_cqc_lang,B,k6_domain_1(k7_cqc_lang,C)))) ) ) ) ),
    file(goedelcp,a_2_2_goedelcp),
    []).

fof(fraenkel_a_2_3_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ( r2_hidden(A,a_2_3_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,D))
            & r2_hidden(D,C) ) ) ) ),
    file(goedelcp,a_2_3_goedelcp),
    []).

fof(fraenkel_a_2_4_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_4_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,D))
            & r2_hidden(D,k1_nat_1(C,1)) ) ) ) ),
    file(goedelcp,a_2_4_goedelcp),
    []).

fof(fraenkel_a_2_5_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_5_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,D))
            & r2_hidden(D,C) ) ) ) ),
    file(goedelcp,a_2_5_goedelcp),
    []).

fof(fraenkel_a_2_6_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k7_cqc_lang)
        & m2_relset_1(B,k5_numbers,k7_cqc_lang)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ( r2_hidden(A,a_2_6_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & ~ r2_hidden(k2_qc_lang3(D),k2_xboole_0(k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,B,k1_nat_1(0,1)))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,0)))) ) ) ) ),
    file(goedelcp,a_2_6_goedelcp),
    []).

fof(fraenkel_a_2_7_goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
        & m1_subset_1(C,k1_zfmisc_1(k2_qc_lang1)) )
     => ( r2_hidden(A,a_2_7_goedelcp(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & ~ r2_hidden(k2_qc_lang3(D),k4_subset_1(k2_qc_lang1,k6_goedelcp(k6_domain_1(k7_cqc_lang,B)),C)) ) ) ) ),
    file(goedelcp,a_2_7_goedelcp),
    []).

fof(fraenkel_a_3_0_goedelcp,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k7_cqc_lang)
        & m2_relset_1(B,k5_numbers,k7_cqc_lang)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & m1_subset_1(D,k1_zfmisc_1(k2_qc_lang1)) )
     => ( r2_hidden(A,a_3_0_goedelcp(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = E
            & ~ r2_hidden(k2_qc_lang3(E),k4_subset_1(k2_qc_lang1,D,k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,B,k1_nat_1(C,1)))))) ) ) ) ),
    file(goedelcp,a_3_0_goedelcp),
    []).

fof(fraenkel_a_3_1_goedelcp,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
        & m2_subset_1(D,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_3_1_goedelcp(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = E
            & ~ r2_hidden(k2_qc_lang3(E),k2_xboole_0(k6_goedelcp(k6_domain_1(k7_cqc_lang,C)),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,D)))) ) ) ) ),
    file(goedelcp,a_3_1_goedelcp),
    []).

fof(fraenkel_a_3_2_goedelcp,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k7_cqc_lang)
        & m2_relset_1(B,k5_numbers,k7_cqc_lang)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_subset_1(D,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_3_2_goedelcp(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = E
            & ~ r2_hidden(k2_qc_lang3(E),k2_xboole_0(k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,B,k1_nat_1(D,1)))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,D)))) ) ) ) ),
    file(goedelcp,a_3_2_goedelcp),
    []).

fof(fraenkel_a_3_3_goedelcp,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k7_cqc_lang)
        & m2_relset_1(B,k5_numbers,k7_cqc_lang)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_subset_1(D,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_3_3_goedelcp(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = E
            & ~ r2_hidden(k2_qc_lang3(E),k2_xboole_0(k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,B,k1_nat_1(k1_nat_1(D,1),1)))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,k1_nat_1(D,1))))) ) ) ) ),
    file(goedelcp,a_3_3_goedelcp),
    []).

fof(fraenkel_a_3_4_goedelcp,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k7_cqc_lang)
        & m2_relset_1(B,k5_numbers,k7_cqc_lang)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_subset_1(D,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_3_4_goedelcp(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = E
            & ~ r2_hidden(k2_qc_lang3(E),k2_xboole_0(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,D)),k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,B,k1_nat_1(D,1)))))) ) ) ) ),
    file(goedelcp,a_3_4_goedelcp),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(l24_goedelcp,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ ( v1_card_4(A)
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ~ ( k1_relat_1(B) = k5_numbers
                  & A = k2_relat_1(B) ) ) ) ) ),
    file(goedelcp,l24_goedelcp),
    []).

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_henmodel,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
      & v1_henmodel(A) ) ),
    file(henmodel,rc1_henmodel),
    []).

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

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

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

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

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

fof(rc2_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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_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_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_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_k13_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k13_cqc_lang(A,B) = k3_qc_lang2(A,B) ) ),
    file(cqc_lang,k13_cqc_lang),
    []).

fof(redefinition_k16_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => k16_cqc_lang(A,B) = k5_qc_lang2(A,B) ) ),
    file(cqc_lang,k16_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_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

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

fof(redefinition_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(real_1,k5_real_1),
    []).

fof(redefinition_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_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_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_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_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(s1_nat_1__e24_36__goedelcp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k7_cqc_lang))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k7_cqc_lang)) )
     => ( ( v1_henmodel(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,0))
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( v1_henmodel(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,B))
               => v1_henmodel(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,k1_nat_1(B,1))) ) ) )
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => v1_henmodel(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,B)) ) ) ) ),
    file(goedelcp,s1_nat_1__e24_36__goedelcp),
    []).

fof(s1_nat_1__e3_36_8__goedelcp,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(A,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ( ( v1_finset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,0)))
          & m1_subset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,0)),k1_zfmisc_1(k2_qc_lang1))
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ( v1_finset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,B)))
                  & m1_subset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,B)),k1_zfmisc_1(k2_qc_lang1)) )
               => ( v1_finset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,k1_nat_1(B,1))))
                  & m1_subset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,k1_nat_1(B,1))),k1_zfmisc_1(k2_qc_lang1)) ) ) ) )
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( v1_finset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,B)))
              & m1_subset_1(k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),A,B)),k1_zfmisc_1(k2_qc_lang1)) ) ) ) ) ),
    file(goedelcp,s1_nat_1__e3_36_8__goedelcp),
    []).

fof(s1_nat_1__e3_36_9__goedelcp,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m2_relset_1(A,k5_numbers,k7_cqc_lang)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k1_zfmisc_1(k7_cqc_lang))
        & m2_relset_1(C,k5_numbers,k1_zfmisc_1(k7_cqc_lang)) )
     => ( ( r1_tarski(k6_goedelcp(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(0,1))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,0)))
          & ~ r2_hidden(k2_qc_lang3(k1_henmodel(a_2_6_goedelcp(A,B))),k6_goedelcp(k4_subset_1(k7_cqc_lang,k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(0,1)),k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(0,1))))))
          & ! [D] : 
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( ( r1_tarski(k6_goedelcp(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(D,1))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,D)))
                  & ~ r2_hidden(k2_qc_lang3(k1_henmodel(a_3_2_goedelcp(A,B,D))),k6_goedelcp(k4_subset_1(k7_cqc_lang,k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(D,1)),k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(D,1)))))) )
               => ( r1_tarski(k6_goedelcp(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(k1_nat_1(D,1),1))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,k1_nat_1(D,1))))
                  & ~ r2_hidden(k2_qc_lang3(k1_henmodel(a_3_3_goedelcp(A,B,D))),k6_goedelcp(k4_subset_1(k7_cqc_lang,k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(k1_nat_1(D,1),1)),k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(k1_nat_1(D,1),1)))))) ) ) ) )
       => ! [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
           => ( r1_tarski(k6_goedelcp(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(D,1))),k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),B,D)))
              & ~ r2_hidden(k2_qc_lang3(k1_henmodel(a_3_2_goedelcp(A,B,D))),k6_goedelcp(k4_subset_1(k7_cqc_lang,k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),C,k1_nat_1(D,1)),k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(D,1)))))) ) ) ) ) ),
    file(goedelcp,s1_nat_1__e3_36_9__goedelcp),
    []).

fof(s2_recdef_1__e7_36__goedelcp,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m2_relset_1(A,k5_numbers,k7_cqc_lang)
        & m1_subset_1(B,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ( ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ! [D] : 
                ( m1_subset_1(D,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
               => ? [E] : 
                    ( m1_subset_1(E,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
                    & ? [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(k2_qc_lang1))
                        & ? [G] : 
                            ( m1_subset_1(G,k1_zfmisc_1(k2_qc_lang1))
                            & F = k2_mcart_1(D)
                            & G = k4_subset_1(k2_qc_lang1,F,k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(C,1)))))
                            & E = k1_domain_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1),k13_cqc_lang(k10_cqc_lang(k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(C,1))),k4_substut2(k5_goedelcp(A,k1_nat_1(C,1)),k4_goedelcp(A,k1_nat_1(C,1)),k2_qc_lang3(k1_henmodel(a_1_3_goedelcp(G))))),k4_subset_1(k2_qc_lang1,F,k24_qc_lang1(k13_cqc_lang(k10_cqc_lang(k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(C,1))),k4_substut2(k5_goedelcp(A,k1_nat_1(C,1)),k4_goedelcp(A,k1_nat_1(C,1)),k2_qc_lang3(k1_henmodel(a_1_3_goedelcp(G)))))))) ) ) ) ) )
       => ? [C] : 
            ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
            & m2_relset_1(C,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
            & k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,0) = B
            & ! [D] : 
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ? [H] : 
                    ( m1_subset_1(H,k1_zfmisc_1(k2_qc_lang1))
                    & ? [I] : 
                        ( m1_subset_1(I,k1_zfmisc_1(k2_qc_lang1))
                        & H = k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,D))
                        & I = k4_subset_1(k2_qc_lang1,H,k6_goedelcp(k6_domain_1(k7_cqc_lang,k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(D,1)))))
                        & k8_funct_2(k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)),C,k1_nat_1(D,1)) = k1_domain_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1),k13_cqc_lang(k10_cqc_lang(k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(D,1))),k4_substut2(k5_goedelcp(A,k1_nat_1(D,1)),k4_goedelcp(A,k1_nat_1(D,1)),k2_qc_lang3(k1_henmodel(a_1_3_goedelcp(I))))),k4_subset_1(k2_qc_lang1,H,k24_qc_lang1(k13_cqc_lang(k10_cqc_lang(k8_funct_2(k5_numbers,k7_cqc_lang,A,k1_nat_1(D,1))),k4_substut2(k5_goedelcp(A,k1_nat_1(D,1)),k4_goedelcp(A,k1_nat_1(D,1)),k2_qc_lang3(k1_henmodel(a_1_3_goedelcp(I)))))))) ) ) ) ) ) ) ),
    file(goedelcp,s2_recdef_1__e7_36__goedelcp),
    []).

fof(s3_funct_1__e13_36__goedelcp,axiom,(
    ! [A,B] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1)))
        & m2_relset_1(B,k5_numbers,k2_zfmisc_1(k7_cqc_lang,k1_zfmisc_1(k2_qc_lang1))) )
     => ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = k5_numbers
          & ! [D] : 
              ( r2_hidden(D,k5_numbers)
             => k1_funct_1(C,D) = k2_xboole_0(A,a_2_3_goedelcp(B,D)) ) ) ) ),
    file(goedelcp,s3_funct_1__e13_36__goedelcp),
    []).

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(t10_calcul_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( r1_xreal_0(1,k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))))
        & r2_hidden(k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))),k1_relat_1(k7_finseq_1(B,k9_finseq_1(A)))) ) ) ),
    file(calcul_1,t10_calcul_1),
    []).

fof(t10_mcart_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => ( r2_hidden(k1_mcart_1(A),B)
        & r2_hidden(k2_mcart_1(A),C) ) ) ),
    file(mcart_1,t10_mcart_1),
    []).

fof(t11_henmodel,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k7_cqc_lang))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k7_cqc_lang)) )
     => ( ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r2_hidden(C,k4_relset_1(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A))
                    & r2_hidden(B,k4_relset_1(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A)) )
                 => ( r1_xreal_0(C,B)
                    | ( v1_henmodel(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,B))
                      & r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,B),k8_funct_2(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A,C)) ) ) ) ) )
       => v1_henmodel(k5_setfam_1(k7_cqc_lang,k5_relset_1(k5_numbers,k1_zfmisc_1(k7_cqc_lang),A))) ) ) ),
    file(henmodel,t11_henmodel),
    []).

fof(t11_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => k24_qc_lang1(k12_qc_lang1(A)) = k24_qc_lang1(A) ) ),
    file(qc_lang3,t11_qc_lang3),
    []).

fof(t12_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ),
    file(funct_1,t12_funct_1),
    []).

fof(t14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,t14_finset_1),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_euler_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,B)
          <=> ~ r1_xreal_0(B,A) ) ) ) ),
    file(euler_1,t1_euler_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(t20_cqc_sim1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => v1_finset_1(k24_qc_lang1(A)) ) ),
    file(cqc_sim1,t20_cqc_sim1),
    []).

fof(t20_goedelcp,axiom,
    ( ~ v1_xboole_0(k1_goedelcp)
    & v1_card_4(k1_goedelcp) ),
    file(goedelcp,t20_goedelcp),
    []).

fof(t21_calcul_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,A))) ) ) ),
    file(calcul_2,t21_calcul_2),
    []).

fof(t21_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(B,A)
           => r1_henmodel(A,B) ) ) ) ),
    file(goedelcp,t21_goedelcp),
    []).

fof(t22_goedelcp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( k2_goedelcp(k16_cqc_lang(B,A)) = B
            & k3_goedelcp(k16_cqc_lang(B,A)) = A ) ) ) ),
    file(goedelcp,t22_goedelcp),
    []).

fof(t22_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( A != 0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => A != k1_nat_1(B,1) ) ) ) ),
    file(nat_1,t22_nat_1),
    []).

fof(t24_calcul_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    file(calcul_2,t24_calcul_2),
    []).

fof(t24_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( r1_henmodel(A,k10_cqc_lang(k9_cqc_lang))
      <=> ~ v1_henmodel(A) ) ) ),
    file(goedelcp,t24_goedelcp),
    []).

fof(t25_goedelcp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))
               => ( r1_xreal_0(k3_finseq_1(B),0)
                  | r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),C),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,B))),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ) ),
    file(goedelcp,t25_goedelcp),
    []).

fof(t26_calcul_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B)))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A))),k12_finseq_1(k7_cqc_lang,B))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    file(calcul_2,t26_calcul_2),
    []).

fof(t26_goedelcp,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => k6_goedelcp(k6_domain_1(k7_cqc_lang,A)) = k24_qc_lang1(A) ) ),
    file(goedelcp,t26_goedelcp),
    []).

fof(t26_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,k2_xcmplx_0(B,1))
              & ~ r1_xreal_0(A,B)
              & A != k2_xcmplx_0(B,1) ) ) ) ),
    file(nat_1,t26_nat_1),
    []).

fof(t27_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => k6_goedelcp(k4_subset_1(k7_cqc_lang,A,B)) = k4_subset_1(k2_qc_lang1,k6_goedelcp(A),k6_goedelcp(B)) ) ) ),
    file(goedelcp,t27_goedelcp),
    []).

fof(t28_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k2_qc_lang1))
     => ~ ( v1_finset_1(A)
          & ! [B] : 
              ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
             => r2_hidden(B,A) ) ) ) ),
    file(goedelcp,t28_goedelcp),
    []).

fof(t29_goedelcp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( r1_tarski(A,B)
           => r1_tarski(k6_goedelcp(A),k6_goedelcp(B)) ) ) ) ),
    file(goedelcp,t29_goedelcp),
    []).

fof(t29_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t2_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    []).

fof(t30_goedelcp,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => k6_goedelcp(k5_relset_1(k5_numbers,k7_cqc_lang,A)) = k3_calcul_1(A) ) ),
    file(goedelcp,t30_goedelcp),
    []).

fof(t36_qc_lang3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & k2_qc_lang3(B) = A ) ) ),
    file(qc_lang3,t36_qc_lang3),
    []).

fof(t38_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    []).

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_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    []).

fof(t4_funct_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_2),
    []).

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(t4_xboole_1,axiom,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    []).

fof(t51_calcul_1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(A,B)))) ) ) ) ) ),
    file(calcul_1,t51_calcul_1),
    []).

fof(t52_calcul_1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(B,A)))) ) ) ) ) ),
    file(calcul_1,t52_calcul_1),
    []).

fof(t59_calcul_1,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k3_calcul_1(k8_finseq_1(k7_cqc_lang,A,B)) = k4_subset_1(k2_qc_lang1,k3_calcul_1(A),k3_calcul_1(B)) ) ) ),
    file(calcul_1,t59_calcul_1),
    []).

fof(t5_calcul_1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( k2_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) = A
            & k1_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) = B ) ) ) ),
    file(calcul_1,t5_calcul_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(t60_calcul_1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => k3_calcul_1(k12_finseq_1(k7_cqc_lang,A)) = k24_qc_lang1(A) ) ),
    file(calcul_1,t60_calcul_1),
    []).

fof(t61_calcul_1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] : 
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] : 
                      ( m2_finseq_1(E,k7_cqc_lang)
                     => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,E,k12_finseq_1(k7_cqc_lang,k4_substut2(A,C,D))),k12_finseq_1(k7_cqc_lang,B)))
                       => ( r2_hidden(D,k3_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,E,k12_finseq_1(k7_cqc_lang,k16_cqc_lang(C,A))),k12_finseq_1(k7_cqc_lang,B))))
                          | r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,E,k12_finseq_1(k7_cqc_lang,k16_cqc_lang(C,A))),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ) ) ) ),
    file(calcul_1,t61_calcul_1),
    []).

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

fof(t6_henmodel,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( ~ v1_henmodel(A)
      <=> ! [B] : 
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => r1_henmodel(A,B) ) ) ) ),
    file(henmodel,t6_henmodel),
    []).

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_qc_lang3,axiom,(
    k24_qc_lang1(k11_qc_lang1) = k1_xboole_0 ),
    file(qc_lang3,t7_qc_lang3),
    []).

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(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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

fof(t8_henmodel,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ~ ( r1_henmodel(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,B)),C)
                  & ! [D] : 
                      ( m2_finseq_1(D,k7_cqc_lang)
                     => ~ ( r1_tarski(k5_relset_1(k5_numbers,k7_cqc_lang,D),A)
                          & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,B)),k12_finseq_1(k7_cqc_lang,C))) ) ) ) ) ) ) ),
    file(henmodel,t8_henmodel),
    []).

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),
    []).

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

fof(t9_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)) ) ),
    file(xboole_1,t9_xboole_1),
    []).