% Mizar problem: t46_armstrng,armstrng,2435,31 
fof(t46_armstrng,conjecture,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ( v1_armstrng(B,A)
          & v2_finsub_1(B) )
       => r5_armstrng(A,k2_armstrng(B),B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,d10_setfam_1,d26_armstrng,d3_armstrng,d3_tarski,d4_armstrng,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_armstrng,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_m2_subset_1,existence_m1_subset_1,existence_m2_subset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fraenkel_a_2_16_armstrng,fraenkel_a_2_19_armstrng,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_armstrng,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k6_setfam_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t13_finset_1,t1_armstrng,t1_subset,t1_xboole_1,t2_subset,t2_tarski,t3_armstrng,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(armstrng,t46_armstrng)]).

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

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(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(d10_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    []).

fof(d26_armstrng,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r5_armstrng(A,B,C)
      <=> ( r1_tarski(B,C)
          & C = a_2_16_armstrng(A,B) ) ) ) ),
    file(armstrng,d26_armstrng),
    []).

fof(d3_armstrng,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( B = k2_armstrng(A)
          <=> ! [C] : 
                ( r2_hidden(C,B)
              <=> r1_armstrng(C,A) ) ) ) ) ),
    file(armstrng,d3_armstrng),
    []).

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

fof(d4_armstrng,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_armstrng(B,A)
      <=> r2_hidden(A,B) ) ) ),
    file(armstrng,d4_armstrng),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_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_k2_armstrng,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m1_subset_1(k2_armstrng(A),k1_zfmisc_1(A)) ) ),
    file(armstrng,k2_armstrng),
    []).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    []).

fof(dt_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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(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_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(fraenkel_a_2_16_armstrng,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,a_2_16_armstrng(B,C))
    <=> ? [D] : 
          ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
          & A = k8_setfam_1(B,D)
          & r1_tarski(D,C) ) ) ),
    file(armstrng,a_2_16_armstrng),
    []).

fof(fraenkel_a_2_19_armstrng,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & v1_finset_1(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) )
     => ( r2_hidden(A,a_2_19_armstrng(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
            & A = k8_setfam_1(B,D)
            & r1_tarski(D,k2_armstrng(C)) ) ) ) ),
    file(armstrng,a_2_19_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_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_armstrng,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & v2_finsub_1(B)
      & v1_armstrng(B,A) ) ),
    file(armstrng,rc2_armstrng),
    []).

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_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(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_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_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(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(t1_armstrng,axiom,(
    ! [A] : 
      ( v2_finsub_1(A)
     => ! [B,C] : 
          ( ( v1_finset_1(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) )
         => ( ( r2_hidden(B,A)
              & r1_tarski(C,A) )
           => r2_hidden(k8_setfam_1(B,C),A) ) ) ) ),
    file(armstrng,t1_armstrng),
    []).

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(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(t3_armstrng,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ? [C] : 
              ( ~ v1_xboole_0(C)
              & m1_subset_1(C,k1_zfmisc_1(A))
              & B = k1_setfam_1(C)
              & ! [D] : 
                  ( r2_hidden(D,C)
                 => r1_armstrng(D,A) ) ) ) ) ),
    file(armstrng,t3_armstrng),
    []).

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),
    []).