% Mizar problem: t43_armstrng,armstrng,2279,72 
fof(t43_armstrng,conjecture,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( B = a_2_2_armstrng(A,C)
               => k2_xboole_0(k1_tarski(A),a_2_14_armstrng(A,C)) = k9_armstrng(A,B) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_altcat_1,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc2_armstrng,cc2_finset_1,cc2_funct_1,commutativity_k2_tarski,commutativity_k2_xboole_0,d11_armstrng,d17_armstrng,d18_armstrng,d1_tarski,d22_armstrng,d2_xboole_0,d4_subset_1,d5_tarski,d7_armstrng,dt_k1_armstrng,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_subset_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_armstrng,dt_k4_tarski,dt_k6_armstrng,dt_k7_armstrng,dt_k8_armstrng,dt_k9_armstrng,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc14_finset_1,fc1_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_altcat_1,fc2_armstrng,fc2_finseq_1,fc2_finset_1,fc2_subset_1,fc2_xboole_0,fc3_armstrng,fc3_subset_1,fc3_xboole_0,fc4_armstrng,fc4_subset_1,fc6_armstrng,fc9_finset_1,fraenkel_a_1_5_armstrng,fraenkel_a_2_14_armstrng,fraenkel_a_2_15_armstrng,fraenkel_a_2_2_armstrng,fraenkel_a_2_3_armstrng,fraenkel_a_2_4_armstrng,idempotence_k2_xboole_0,rc1_armstrng,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_margrel1,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_armstrng,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k6_armstrng,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r3_armstrng,t1_boole,t1_subset,t2_subset,t2_tarski,t32_armstrng,t33_armstrng,t33_zfmisc_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(armstrng,t43_armstrng)]).

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

fof(cc1_altcat_1,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    []).

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_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_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(cc2_armstrng,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(armstrng,cc2_armstrng),
    []).

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(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(d11_armstrng,axiom,(
    ! [A] : k7_armstrng(A) = a_1_5_armstrng(A) ),
    file(armstrng,d11_armstrng),
    []).

fof(d17_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => k8_armstrng(A,B) = k1_armstrng(B,k7_armstrng(A)) ) ),
    file(armstrng,d17_armstrng),
    []).

fof(d18_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ! [C,D] : 
          ( r4_armstrng(A,B,C,D)
        <=> r2_hidden(k4_tarski(C,D),k8_armstrng(A,B)) ) ) ),
    file(armstrng,d18_armstrng),
    []).

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

fof(d22_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => k9_armstrng(A,B) = a_2_4_armstrng(A,B) ) ),
    file(armstrng,d22_armstrng),
    []).

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(d4_subset_1,axiom,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_subset_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(d7_armstrng,axiom,(
    ! [A] : k4_armstrng(A) = k2_zfmisc_1(k1_zfmisc_1(A),k1_zfmisc_1(A)) ),
    file(armstrng,d7_armstrng),
    []).

fof(dt_k1_armstrng,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => m1_subset_1(k1_armstrng(A,B),k1_zfmisc_1(A)) ) ),
    file(armstrng,k1_armstrng),
    []).

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_k2_subset_1,axiom,(
    ! [A] : m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A)) ),
    file(subset_1,k2_subset_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_armstrng,axiom,(
    ! [A] : m2_relset_1(k4_armstrng(A),k1_zfmisc_1(A),k1_zfmisc_1(A)) ),
    file(armstrng,k4_armstrng),
    []).

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

fof(dt_k6_armstrng,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_armstrng(A,B,C),k4_armstrng(A)) ) ),
    file(armstrng,k6_armstrng),
    []).

fof(dt_k7_armstrng,axiom,(
    ! [A] : m2_relset_1(k7_armstrng(A),k4_armstrng(A),k4_armstrng(A)) ),
    file(armstrng,k7_armstrng),
    []).

fof(dt_k8_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => m2_relset_1(k8_armstrng(A,B),k1_zfmisc_1(A),k1_zfmisc_1(A)) ) ),
    file(armstrng,k8_armstrng),
    []).

fof(dt_k9_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => m1_subset_1(k9_armstrng(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(armstrng,k9_armstrng),
    []).

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_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(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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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_margrel1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    []).

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

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_altcat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    []).

fof(fc2_armstrng,axiom,(
    ! [A] : 
      ( v1_relat_1(k4_armstrng(A))
      & ~ v1_xboole_0(k4_armstrng(A)) ) ),
    file(armstrng,fc2_armstrng),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_armstrng,axiom,(
    ! [A] : 
      ( v1_relat_1(k7_armstrng(A))
      & ~ v1_xboole_0(k7_armstrng(A)) ) ),
    file(armstrng,fc3_armstrng),
    []).

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

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc4_armstrng,axiom,(
    ! [A] : 
      ( v1_relat_1(k7_armstrng(A))
      & v1_relat_2(k7_armstrng(A))
      & v4_relat_2(k7_armstrng(A))
      & v8_relat_2(k7_armstrng(A))
      & v1_partfun1(k7_armstrng(A),k4_armstrng(A),k4_armstrng(A)) ) ),
    file(armstrng,fc4_armstrng),
    []).

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(fc6_armstrng,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(B)
        & m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => v1_finset_1(k9_armstrng(A,B)) ) ),
    file(armstrng,fc6_armstrng),
    []).

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(fraenkel_a_1_5_armstrng,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_5_armstrng(B))
    <=> ? [C,D] : 
          ( m1_subset_1(C,k4_armstrng(B))
          & m1_subset_1(D,k4_armstrng(B))
          & A = k4_tarski(C,D)
          & r3_armstrng(B,D,C) ) ) ),
    file(armstrng,a_1_5_armstrng),
    []).

fof(fraenkel_a_2_14_armstrng,axiom,(
    ! [A,B,C] : 
      ( ( v1_finset_1(B)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_2_14_armstrng(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = D
            & ~ r1_tarski(C,D) ) ) ) ),
    file(armstrng,a_2_14_armstrng),
    []).
ERROR: Line 64 Char 204 Token "&" continuing with "  ~ (r1_tarski(C, E"