% Mizar problem: t34_goedelcp,goedelcp,1650,69 
fof(t34_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)) )
             => ! [C] : 
                  ( m1_henmodel(C,B)
                 => ~ r6_calcul_1(A,k2_henmodel,C,k4_henmodel) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,cc1_relset_1,d11_calcul_1,d8_goedelcp,dt_k1_qc_lang1,dt_k1_valuat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k24_qc_lang1,dt_k2_henmodel,dt_k2_qc_lang1,dt_k2_valuat_1,dt_k2_zfmisc_1,dt_k3_margrel1,dt_k3_tarski,dt_k4_henmodel,dt_k5_qc_lang1,dt_k6_goedelcp,dt_k7_cqc_lang,dt_k8_qc_lang1,dt_m1_fraenkel,dt_m1_henmodel,dt_m1_relset_1,dt_m1_subset_1,dt_m1_valuat_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,existence_m1_fraenkel,existence_m1_henmodel,existence_m1_relset_1,existence_m1_subset_1,existence_m1_valuat_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc12_relat_1,fc1_subset_1,fc2_cqc_lang,fc4_relat_1,fc4_subset_1,fraenkel_a_1_0_goedelcp,rc1_henmodel,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc3_relat_1,redefinition_k2_valuat_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t17_goedelcp,t1_subset,t1_xboole_1,t21_goedelcp,t2_subset,t2_tarski,t31_goedelcp,t33_goedelcp,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(goedelcp,t34_goedelcp)]).

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

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(d11_calcul_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_valuat_1(C,B)
             => ! [D] : 
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ( r6_calcul_1(A,B,C,D)
                  <=> ! [E] : 
                        ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                       => ( r2_hidden(E,A)
                         => r1_valuat_1(B,E,C,D) ) ) ) ) ) ) ) ),
    file(calcul_1,d11_calcul_1),
    []).

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_k1_qc_lang1,axiom,(
    $true ),
    file(qc_lang1,k1_qc_lang1),
    []).

fof(dt_k1_valuat_1,axiom,(
    $true ),
    file(valuat_1,k1_valuat_1),
    []).

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

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

fof(dt_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_henmodel,axiom,(
    ~ v1_xboole_0(k2_henmodel) ),
    file(henmodel,k2_henmodel),
    []).

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_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m1_fraenkel(k2_valuat_1(A),k2_qc_lang1,A) ) ),
    file(valuat_1,k2_valuat_1),
    []).

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

fof(dt_k3_margrel1,axiom,(
    $true ),
    file(margrel1,k3_margrel1),
    []).

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

fof(dt_k4_henmodel,axiom,(
    m2_fraenkel(k4_henmodel,k2_qc_lang1,k2_henmodel,k2_valuat_1(k2_henmodel)) ),
    file(henmodel,k4_henmodel),
    []).

fof(dt_k5_qc_lang1,axiom,(
    $true ),
    file(qc_lang1,k5_qc_lang1),
    []).

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_k7_cqc_lang,axiom,(
    m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) ),
    file(cqc_lang,k7_cqc_lang),
    []).

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

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_m1_henmodel,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] : 
          ( m1_henmodel(B,A)
         => m1_valuat_1(B,k2_henmodel) ) ) ),
    file(henmodel,m1_henmodel),
    []).

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_m1_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k5_qc_lang1,k3_margrel1(A))
            & m2_relset_1(B,k5_qc_lang1,k3_margrel1(A)) ) ) ) ),
    file(valuat_1,m1_valuat_1),
    []).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(existence_m1_henmodel,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ? [B] : m1_henmodel(B,A) ) ),
    file(henmodel,m1_henmodel),
    []).

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_m1_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_valuat_1(B,A) ) ),
    file(valuat_1,m1_valuat_1),
    []).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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

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

fof(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(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(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(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(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(redefinition_k2_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k2_valuat_1(A) = k1_valuat_1(A) ) ),
    file(valuat_1,k2_valuat_1),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(t17_goedelcp,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] : 
          ( m1_henmodel(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( v1_goedelcp(A)
                  & v2_goedelcp(A) )
               => ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
                <=> r1_henmodel(A,C) ) ) ) ) ) ),
    file(goedelcp,t17_goedelcp),
    []).

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(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(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(t31_goedelcp,axiom,(
    ! [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) ) ) ) ) ),
    file(goedelcp,t31_goedelcp),
    []).

fof(t33_goedelcp,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ~ ( v2_goedelcp(A)
          & ! [B] : 
              ( ( v1_henmodel(B)
                & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
             => ~ ( r1_tarski(A,B)
                  & v1_goedelcp(B)
                  & v2_goedelcp(B) ) ) ) ) ),
    file(goedelcp,t33_goedelcp),
    []).

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

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

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

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