% Mizar problem: t30_armstrng,armstrng,1347,38 
fof(t30_armstrng,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] : 
          ( ( v6_armstrng(B,A)
            & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
         => ( v8_armstrng(k8_armstrng(A,B),A)
            & v9_armstrng(k8_armstrng(A,B),A)
            & v10_armstrng(k8_armstrng(A,B),A) ) ) ) ),
    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,cc3_armstrng,cc4_armstrng,cc5_armstrng,cc6_armstrng,cc7_armstrng,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,d11_armstrng,d13_armstrng,d14_armstrng,d16_armstrng,d17_armstrng,d18_armstrng,d19_armstrng,d1_armstrng,d20_armstrng,d21_armstrng,d24_waybel_4,d2_zfmisc_1,d3_tarski,d5_tarski,d7_armstrng,dt_k1_armstrng,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_armstrng,dt_k4_subset_1,dt_k4_tarski,dt_k6_armstrng,dt_k7_armstrng,dt_k8_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,fc9_finset_1,fraenkel_a_1_5_armstrng,idempotence_k2_xboole_0,idempotence_k4_subset_1,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,rc5_armstrng,rc6_armstrng,rc6_finseq_1,rc7_armstrng,rc7_finseq_1,rc8_armstrng,rc8_finseq_1,redefinition_k4_subset_1,redefinition_k6_armstrng,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r3_armstrng,s1_xboole_0__e2_72_1__armstrng,t11_xboole_1,t13_finset_1,t14_armstrng,t15_armstrng,t19_armstrng,t1_boole,t1_subset,t1_xboole_1,t20_armstrng,t29_armstrng,t2_armstrng,t2_subset,t2_tarski,t33_zfmisc_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_xboole_1,t8_boole]),
    [file(armstrng,t30_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(cc3_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v6_armstrng(B,A)
       => ( v8_relat_2(B)
          & v3_armstrng(B,A)
          & v4_armstrng(B,A)
          & v5_armstrng(B,A) ) ) ) ),
    file(armstrng,cc3_armstrng),
    []).

fof(cc4_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( ( v8_relat_2(B)
          & v3_armstrng(B,A)
          & v4_armstrng(B,A)
          & v5_armstrng(B,A) )
       => v6_armstrng(B,A) ) ) ),
    file(armstrng,cc4_armstrng),
    []).

fof(cc5_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( ( v3_armstrng(B,A)
          & v4_armstrng(B,A) )
       => v7_armstrng(B,A) ) ) ),
    file(armstrng,cc5_armstrng),
    []).

fof(cc6_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( ( v8_relat_2(B)
          & v7_armstrng(B,A) )
       => ( v3_armstrng(B,A)
          & v4_armstrng(B,A) ) ) ) ),
    file(armstrng,cc6_armstrng),
    []).

fof(cc7_armstrng,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v3_armstrng(B,A)
       => ~ v1_xboole_0(B) ) ) ),
    file(armstrng,cc7_armstrng),
    []).

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

fof(d13_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v4_armstrng(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                   => ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(A))
                       => ( ( r2_hidden(k6_armstrng(A,C,D),B)
                            & r3_armstrng(A,k6_armstrng(A,C,D),k6_armstrng(A,E,F)) )
                         => r2_hidden(k6_armstrng(A,E,F),B) ) ) ) ) ) ) ) ),
    file(armstrng,d13_armstrng),
    []).

fof(d14_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v5_armstrng(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                   => ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(A))
                       => ( ( r2_hidden(k6_armstrng(A,C,D),B)
                            & r2_hidden(k6_armstrng(A,E,F),B) )
                         => r2_hidden(k6_armstrng(A,k4_subset_1(A,C,E),k4_subset_1(A,D,F)),B) ) ) ) ) ) ) ) ),
    file(armstrng,d14_armstrng),
    []).

fof(d16_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v7_armstrng(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r1_tarski(D,C)
                 => r2_hidden(k6_armstrng(A,C,D),B) ) ) ) ) ) ),
    file(armstrng,d16_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(d19_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v8_armstrng(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ? [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
                & ? [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                    & r3_armstrng(A,k6_armstrng(A,D,E),k6_armstrng(A,C,C))
                    & r2_hidden(k6_armstrng(A,D,E),B) ) ) ) ) ) ),
    file(armstrng,d19_armstrng),
    []).

fof(d1_armstrng,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( C = k1_armstrng(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,C)
              <=> r2_waybel_4(A,D,B) ) ) ) ) ),
    file(armstrng,d1_armstrng),
    []).

fof(d20_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v9_armstrng(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                   => ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(A))
                       => ( ( r2_hidden(k6_armstrng(A,C,D),B)
                            & r2_hidden(k6_armstrng(A,E,F),B)
                            & r3_armstrng(A,k6_armstrng(A,C,D),k6_armstrng(A,E,F)) )
                         => ( C = E
                            & D = F ) ) ) ) ) ) ) ) ),
    file(armstrng,d20_armstrng),
    []).

fof(d21_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v10_armstrng(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                   => ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(A))
                       => ( ( r2_hidden(k6_armstrng(A,C,D),B)
                            & r2_hidden(k6_armstrng(A,E,F),B)
                            & r1_tarski(E,D) )
                         => r1_tarski(F,D) ) ) ) ) ) ) ) ),
    file(armstrng,d21_armstrng),
    []).

fof(d24_waybel_4,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_waybel_4(A,B,C)
      <=> ( r2_hidden(B,A)
          & ! [D] : ~ ( r2_hidden(D,A)
              & D != B
              & r2_hidden(k4_tarski(B,D),C) ) ) ) ) ),
    file(waybel_4,d24_waybel_4),
    []).

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

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_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_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_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_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_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_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(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(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_armstrng,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & ~ v1_xboole_0(A)
      & v1_relat_2(A)
      & v4_relat_2(A)
      & v8_relat_2(A) ) ),
    file(armstrng,rc1_armstrng),
    []).

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_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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

fof(rc1_margrel1,axiom,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

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_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

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_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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_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(rc4_armstrng,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
      & v1_relat_1(B)
      & ~ v1_xboole_0(B)
      & v1_finset_1(B) ) ),
    file(armstrng,rc4_armstrng),
    []).

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(rc5_armstrng,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
      & v1_relat_1(B)
      & ~ v1_xboole_0(B)
      & v8_relat_2(B)
      & v3_armstrng(B,A)
      & v4_armstrng(B,A)
      & v5_armstrng(B,A) ) ),
    file(armstrng,rc5_armstrng),
    []).

fof(rc6_armstrng,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
      & v1_relat_1(B)
      & v6_armstrng(B,A) ) ),
    file(armstrng,rc6_armstrng),
    []).

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_armstrng,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ? [B] : 
          ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
          & v1_relat_1(B)
          & v1_finset_1(B)
          & v6_armstrng(B,A) ) ) ),
    file(armstrng,rc7_armstrng),
    []).

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_armstrng,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
      & v1_relat_1(B)
      & ~ v1_xboole_0(B)
      & v8_relat_2(B)
      & v3_armstrng(B,A)
      & v4_armstrng(B,A)
      & v5_armstrng(B,A)
      & v6_armstrng(B,A)
      & v7_armstrng(B,A) ) ),
    file(armstrng,rc8_armstrng),
    []).

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_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_k6_armstrng,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_armstrng(A,B,C) = k4_tarski(B,C) ) ),
    file(armstrng,k6_armstrng),
    []).

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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r3_armstrng,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k4_armstrng(A))
        & m1_subset_1(C,k4_armstrng(A)) )
     => r3_armstrng(A,B,B) ) ),
    file(armstrng,r3_armstrng),
    []).

fof(s1_xboole_0__e2_72_1__armstrng,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v6_armstrng(B,A)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => ? [D] : 
        ! [E] : 
          ( r2_hidden(E,D)
        <=> ( r2_hidden(E,B)
            & ? [F] : 
                ( m1_subset_1(F,k4_armstrng(A))
                & E = F
                & r3_armstrng(A,F,k6_armstrng(A,C,C)) ) ) ) ) ),
    file(armstrng,s1_xboole_0__e2_72_1__armstrng),
    []).

fof(t11_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(k2_xboole_0(A,B),C)
     => r1_tarski(A,C) ) ),
    file(xboole_1,t11_xboole_1),
    []).

fof(t13_finset_1,axiom,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    []).

fof(t14_armstrng,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k4_armstrng(A))
     => ! [C] : 
          ( m1_subset_1(C,k4_armstrng(A))
         => ! [D] : 
              ( m1_subset_1(D,k4_armstrng(A))
             => ( ( r3_armstrng(A,C,B)
                  & r3_armstrng(A,D,C) )
               => r3_armstrng(A,D,B) ) ) ) ) ),
    file(armstrng,t14_armstrng),
    []).

fof(t15_armstrng,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ! [E] : 
                  ( m1_subset_1(E,k1_zfmisc_1(A))
                 => ( r3_armstrng(A,k6_armstrng(A,B,C),k6_armstrng(A,D,E))
                  <=> ( r1_tarski(B,D)
                      & r1_tarski(E,C) ) ) ) ) ) ) ),
    file(armstrng,t15_armstrng),
    []).

fof(t19_armstrng,axiom,(
    ! [A] : k3_relat_1(k7_armstrng(A)) = k2_zfmisc_1(k1_zfmisc_1(A),k1_zfmisc_1(A)) ),
    file(armstrng,t19_armstrng),
    []).

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

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(t20_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ( v8_relat_2(B)
      <=> ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( m1_subset_1(E,k1_zfmisc_1(A))
                   => ( ( r2_hidden(k6_armstrng(A,C,D),B)
                        & r2_hidden(k6_armstrng(A,D,E),B) )
                     => r2_hidden(k6_armstrng(A,C,E),B) ) ) ) ) ) ) ),
    file(armstrng,t20_armstrng),
    []).

fof(t29_armstrng,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( r4_armstrng(A,B,C,D)
              <=> ( r2_hidden(k6_armstrng(A,C,D),B)
                  & ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(k6_armstrng(A,E,F),B)
                              & ~ ( C = E
                                  & D = F )
                              & r3_armstrng(A,k6_armstrng(A,E,F),k6_armstrng(A,C,D)) ) ) ) ) ) ) ) ) ),
    file(armstrng,t29_armstrng),
    []).

fof(t2_armstrng,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & ~ v1_xboole_0(A)
        & v4_relat_2(A)
        & v8_relat_2(A) )
     => ! [B] : 
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_relat_1(A))) )
         => ~ ( B != k1_xboole_0
              & ! [C] : 
                  ( m1_subset_1(C,B)
                 => ~ r2_waybel_4(B,C,A) ) ) ) ) ),
    file(armstrng,t2_armstrng),
    []).

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(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    []).

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(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),
    []).