% Mizar problem: t19_zfmodel2,zfmodel2,1038,56 
fof(t19_zfmodel2,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_zfmodel1(B,A)
                  & r1_zfmodel1(C,A) )
               => r1_zfmodel1(k5_relat_1(C,B),A) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_funct_2,cc1_relset_1,cc1_xreal_0,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_xreal_0,cc3_arytm_3,cc3_xreal_0,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,connectedness_r1_xreal_0,d1_enumset1,d1_zf_lang1,d2_tarski,d2_xboole_0,d2_zfmodel1,d3_tarski,d3_zfmodel1,d4_xboole_0,d5_zf_model,dt_k12_zf_lang,dt_k13_zf_lang,dt_k16_zf_lang,dt_k1_enumset1,dt_k1_funct_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zf_lang,dt_k1_zf_lang1,dt_k1_zf_model,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zf_lang,dt_k2_zf_model,dt_k2_zfmisc_1,dt_k2_zfmodel1,dt_k3_zf_lang1,dt_k4_subset_1,dt_k4_xboole_0,dt_k4_zf_lang,dt_k4_zf_lang1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_zf_lang1,dt_k6_zf_lang1,dt_k7_funct_2,dt_k7_zf_lang,dt_k8_funct_2,dt_k8_zf_lang,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,fc12_finset_1,fc14_finset_1,fc1_finset_1,fc1_funct_1,fc1_zf_lang,fc2_finseq_1,fc2_finset_1,fc2_zf_lang,fc3_finset_1,fc5_zf_lang,fc6_zf_lang,fc9_finset_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc1_arytm_3,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xreal_0,rc1_zf_lang,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,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_k2_zf_model,redefinition_k4_subset_1,redefinition_k4_zf_lang1,redefinition_k5_numbers,redefinition_k6_zf_lang1,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,t10_zfmodel2,t12_zf_model,t13_zfmodel2,t154_zf_lang1,t15_zf_model,t162_zf_lang1,t19_zf_model,t1_boole,t1_numerals,t1_real,t1_subset,t1_xboole_1,t1_zfmodel2,t21_funct_2,t2_real,t2_subset,t36_xboole_1,t3_boole,t3_real,t3_subset,t4_boole,t4_real,t4_subset,t4_zfmodel2,t5_real,t5_subset,t66_zf_lang1,t6_boole,t6_real,t6_zfmodel2,t71_zf_lang1,t78_zf_lang1,t79_zf_lang1,t7_boole,t7_real,t7_zfmodel2,t80_zf_lang1,t82_zf_lang1,t86_zf_lang1,t8_boole,t8_real,t9_zfmodel2]),
    [file(zfmodel2,t19_zfmodel2)]).

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_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_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_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_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_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_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc5_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_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(cc6_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(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_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(d1_enumset1,axiom,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    []).

fof(d1_zf_lang1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,A)
                        & m2_relset_1(E,k1_zf_lang,A) )
                     => ( E = k1_zf_lang1(A,B,C,D)
                      <=> ( k8_funct_2(k1_zf_lang,A,E,C) = D
                          & ! [F] : 
                              ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                             => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F)
                               => C = F ) ) ) ) ) ) ) ) ) ),
    file(zf_lang1,d1_zf_lang1),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

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_zfmodel1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( ( r1_tarski(k2_zf_model(A),k2_tarski(k2_zf_lang(3),k2_zf_lang(4)))
              & r2_zf_model(B,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(0),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(0))))))) )
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,B,B)
                  & m2_relset_1(C,B,B) )
               => ( C = k2_zfmodel1(A,B)
                <=> ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k1_zf_lang,B)
                        & m2_relset_1(D,k1_zf_lang,B) )
                     => ( r1_zf_model(B,D,A)
                      <=> k8_funct_2(B,B,C,k8_funct_2(k1_zf_lang,B,D,k2_zf_lang(3))) = k8_funct_2(k1_zf_lang,B,D,k2_zf_lang(4)) ) ) ) ) ) ) ) ),
    file(zfmodel1,d2_zfmodel1),
    []).

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

fof(d3_zfmodel1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( r1_zfmodel1(A,B)
          <=> ? [C] : 
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & r1_tarski(k2_zf_model(C),k2_tarski(k2_zf_lang(3),k2_zf_lang(4)))
                & r2_zf_model(B,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(0),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(0)))))))
                & A = k2_zfmodel1(C,B) ) ) ) ) ),
    file(zfmodel1,d3_zfmodel1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_zf_model(A,B)
          <=> ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,A)
                  & m2_relset_1(C,k1_zf_lang,A) )
               => r1_zf_model(A,C,B) ) ) ) ) ),
    file(zf_model,d5_zf_model),
    []).

fof(dt_k12_zf_lang,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k12_zf_lang(A,B))
        & m2_finseq_1(k12_zf_lang(A,B),k5_numbers) ) ) ),
    file(zf_lang,k12_zf_lang),
    []).

fof(dt_k13_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k13_zf_lang(A,B))
        & m2_finseq_1(k13_zf_lang(A,B),k5_numbers) ) ) ),
    file(zf_lang,k13_zf_lang),
    []).

fof(dt_k16_zf_lang,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang)
        & v1_zf_lang(D)
        & m1_finseq_1(D,k5_numbers) )
     => ( v1_zf_lang(k16_zf_lang(A,B,C,D))
        & m2_finseq_1(k16_zf_lang(A,B,C,D),k5_numbers) ) ) ),
    file(zf_lang,k16_zf_lang),
    []).

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

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

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

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_zf_lang,axiom,(
    m1_subset_1(k1_zf_lang,k1_zfmisc_1(k5_numbers)) ),
    file(zf_lang,k1_zf_lang),
    []).

fof(dt_k1_zf_lang1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k1_zf_lang,A)
        & m1_relset_1(B,k1_zf_lang,A)
        & m1_subset_1(C,k1_zf_lang)
        & m1_subset_1(D,A) )
     => ( v1_funct_1(k1_zf_lang1(A,B,C,D))
        & v1_funct_2(k1_zf_lang1(A,B,C,D),k1_zf_lang,A)
        & m2_relset_1(k1_zf_lang1(A,B,C,D),k1_zf_lang,A) ) ) ),
    file(zf_lang1,k1_zf_lang1),
    []).

fof(dt_k1_zf_model,axiom,(
    $true ),
    file(zf_model,k1_zf_model),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_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_zf_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k2_zf_lang(A),k5_numbers,k1_zf_lang) ) ),
    file(zf_lang,k2_zf_lang),
    []).

fof(dt_k2_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m1_subset_1(k2_zf_model(A),k1_zfmisc_1(k1_zf_lang)) ) ),
    file(zf_model,k2_zf_model),
    []).

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

fof(dt_k2_zfmodel1,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => ( v1_funct_1(k2_zfmodel1(A,B))
        & v1_funct_2(k2_zfmodel1(A,B),B,B)
        & m2_relset_1(k2_zfmodel1(A,B),B,B) ) ) ),
    file(zfmodel1,k2_zfmodel1),
    []).

fof(dt_k3_zf_lang1,axiom,(
    $true ),
    file(zf_lang1,k3_zf_lang1),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k4_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => m2_finseq_1(k4_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k4_zf_lang),
    []).

fof(dt_k4_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( ~ v1_xboole_0(k4_zf_lang1(A))
        & m1_subset_1(k4_zf_lang1(A),k1_zfmisc_1(k1_zf_lang)) ) ) ),
    file(zf_lang1,k4_zf_lang1),
    []).

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

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

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_zf_lang1,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => ( v1_relat_1(k5_zf_lang1(A,B,C))
        & v1_funct_1(k5_zf_lang1(A,B,C)) ) ) ),
    file(zf_lang1,k5_zf_lang1),
    []).

fof(dt_k6_zf_lang1,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => ( v1_zf_lang(k6_zf_lang1(A,B,C))
        & m2_finseq_1(k6_zf_lang1(A,B,C),k5_numbers) ) ) ),
    file(zf_lang1,k6_zf_lang1),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(dt_k7_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k5_numbers)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k7_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k7_zf_lang),
    []).

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_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k8_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k8_zf_lang),
    []).

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(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_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(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_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_zf_lang,axiom,(
    ~ v1_xboole_0(k1_zf_lang) ),
    file(zf_lang,fc1_zf_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_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => ( v1_relat_1(k4_zf_lang(A,B))
        & v1_funct_1(k4_zf_lang(A,B))
        & v1_finset_1(k4_zf_lang(A,B))
        & v1_finseq_1(k4_zf_lang(A,B))
        & v1_zf_lang(k4_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc2_zf_lang),
    []).

fof(fc3_finset_1,axiom,(
    ! [A,B,C] : v1_finset_1(k1_enumset1(A,B,C)) ),
    file(finset_1,fc3_finset_1),
    []).

fof(fc5_zf_lang,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k7_zf_lang(A,B))
        & v1_funct_1(k7_zf_lang(A,B))
        & v1_finset_1(k7_zf_lang(A,B))
        & v1_finseq_1(k7_zf_lang(A,B))
        & v1_zf_lang(k7_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc5_zf_lang),
    []).

fof(fc6_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k8_zf_lang(A,B))
        & v1_funct_1(k8_zf_lang(A,B))
        & v1_finset_1(k8_zf_lang(A,B))
        & v1_finseq_1(k8_zf_lang(A,B))
        & v1_zf_lang(k8_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc6_zf_lang),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

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(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_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_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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

fof(rc1_zf_lang,axiom,(
    ? [A] : 
      ( m1_finseq_1(A,k5_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_zf_lang(A) ) ),
    file(zf_lang,rc1_zf_lang),
    []).

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_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_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_k2_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k2_zf_model(A) = k1_zf_model(A) ) ),
    file(zf_model,k2_zf_model),
    []).

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_k4_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k4_zf_lang1(A) = k3_zf_lang1(A) ) ),
    file(zf_lang1,k4_zf_lang1),
    []).

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

fof(redefinition_k6_zf_lang1,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => k6_zf_lang1(A,B,C) = k5_zf_lang1(A,B,C) ) ),
    file(zf_lang1,k6_zf_lang1),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

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_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(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(t10_zfmodel2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,B)
                        & m2_relset_1(E,k1_zf_lang,B) )
                     => ( ~ r2_hidden(A,k2_zf_model(D))
                       => ( r1_zf_model(B,E,D)
                        <=> r1_zf_model(B,k1_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) ),
    file(zfmodel2,t10_zfmodel2),
    []).

fof(t12_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k4_zf_lang(C,D))
                  <=> k8_funct_2(k1_zf_lang,A,B,C) = k8_funct_2(k1_zf_lang,A,B,D) ) ) ) ) ) ),
    file(zf_model,t12_zf_model),
    []).

fof(t13_zfmodel2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,C)
                        & m2_relset_1(E,k1_zf_lang,C) )
                     => ( ~ r2_hidden(A,k4_zf_lang1(D))
                       => ( r1_zf_model(C,E,k6_zf_lang1(D,B,A))
                        <=> r1_zf_model(C,k1_zf_lang1(C,E,B,k8_funct_2(k1_zf_lang,C,E,A)),D) ) ) ) ) ) ) ) ),
    file(zfmodel2,t13_zfmodel2),
    []).

fof(t154_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k3_zf_lang1(k7_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) ),
    file(zf_lang1,t154_zf_lang1),
    []).

fof(t15_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k7_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                      & r1_zf_model(A,B,D) ) ) ) ) ) ) ),
    file(zf_model,t15_zf_model),
    []).

fof(t162_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => k3_zf_lang1(k16_zf_lang(B,C,D,A)) = k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)) ) ) ) ) ),
    file(zf_lang1,t162_zf_lang1),
    []).

fof(t19_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k12_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                    <=> r1_zf_model(A,B,D) ) ) ) ) ) ) ),
    file(zf_model,t19_zf_model),
    []).

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

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_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t1_zfmodel2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B))) ) ) ) ),
    file(zfmodel2,t1_zfmodel2),
    []).

fof(t21_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    []).

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(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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_zfmodel2,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r2_hidden(k2_zf_lang(C),k4_zf_lang1(A))
                    & r1_xreal_0(B,C) ) ) )
        & ~ ! [B] : 
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => r2_hidden(B,k4_zf_lang1(A)) ) ) ) ),
    file(zfmodel2,t4_zfmodel2),
    []).

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(t66_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k2_zf_model(k7_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) ),
    file(zf_lang1,t66_zf_lang1),
    []).

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(t6_zfmodel2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,B)
                        & m2_relset_1(E,k1_zf_lang,B) )
                     => ( ~ r2_hidden(A,k4_zf_lang1(D))
                       => ( r1_zf_model(B,E,D)
                        <=> r1_zf_model(B,k1_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) ),
    file(zfmodel2,t6_zfmodel2),
    []).

fof(t71_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k13_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) ),
    file(zf_lang1,t71_zf_lang1),
    []).

fof(t78_zf_lang1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,B)
                        & m2_relset_1(E,k1_zf_lang,B) )
                     => ( k1_zf_lang1(B,k1_zf_lang1(B,E,A,C),A,D) = k1_zf_lang1(B,E,A,D)
                        & k1_zf_lang1(B,E,A,k8_funct_2(k1_zf_lang,B,E,A)) = E ) ) ) ) ) ) ),
    file(zf_lang1,t78_zf_lang1),
    []).

fof(t79_zf_lang1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,C)
                 => ! [E] : 
                      ( m1_subset_1(E,C)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k1_zf_lang,C)
                            & m2_relset_1(F,k1_zf_lang,C) )
                         => ( A != B
                           => k1_zf_lang1(C,k1_zf_lang1(C,F,A,D),B,E) = k1_zf_lang1(C,k1_zf_lang1(C,F,B,E),A,D) ) ) ) ) ) ) ) ),
    file(zf_lang1,t79_zf_lang1),
    []).

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

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

fof(t7_zfmodel2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( m1_subset_1(E,D)
                     => ! [F] : 
                          ( m1_subset_1(F,D)
                         => ! [G] : 
                              ( m1_subset_1(G,D)
                             => ! [H] : 
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k1_zf_lang,D)
                                    & m2_relset_1(H,k1_zf_lang,D) )
                                 => ~ ( A != B
                                      & B != C
                                      & C != A
                                      & ~ ( k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,A,E),B,F),C,G) = k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,C,G),B,F),A,E)
                                          & k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,A,E),B,F),C,G) = k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,B,F),C,G),A,E) ) ) ) ) ) ) ) ) ) ) ),
    file(zfmodel2,t7_zfmodel2),
    []).

fof(t80_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k8_zf_lang(B,A))
                  <=> ! [E] : 
                        ( m1_subset_1(E,C)
                       => r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) ),
    file(zf_lang1,t80_zf_lang1),
    []).

fof(t82_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k13_zf_lang(B,A))
                  <=> ? [E] : 
                        ( m1_subset_1(E,C)
                        & r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) ),
    file(zf_lang1,t82_zf_lang1),
    []).

fof(t86_zf_lang1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k2_zf_lang(A) = k2_zf_lang(B)
           => A = B ) ) ) ),
    file(zf_lang1,t86_zf_lang1),
    []).

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),
    []).

fof(t9_zfmodel2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] : 
                      ( ~ v1_xboole_0(E)
                     => ! [F] : 
                          ( m1_subset_1(F,E)
                         => ! [G] : 
                              ( m1_subset_1(G,E)
                             => ! [H] : 
                                  ( m1_subset_1(H,E)
                                 => ! [I] : 
                                      ( m1_subset_1(I,E)
                                     => ! [J] : 
                                          ( m1_subset_1(J,E)
                                         => ! [K] : 
                                              ( ( v1_funct_1(K)
                                                & v1_funct_2(K,k1_zf_lang,E)
                                                & m2_relset_1(K,k1_zf_lang,E) )
                                             => ( k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),A,H)
                                                & k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),C,I),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),C,I),A,H)
                                                & k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),C,I),D,J),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),C,I),D,J),A,H) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(zfmodel2,t9_zfmodel2),
    []).