% Mizar problem: t15_petri,petri,623,12 
fof(t15_petri,conjecture,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => k6_petri(k10_petri(A),k11_petri(A,B)) = k5_petri(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_petri,antisymmetry_r2_hidden,cc1_relset_1,commutativity_k2_tarski,d10_petri,d10_xboole_0,d11_petri,d13_petri,d1_petri,d2_petri,d3_tarski,d5_tarski,d7_relat_1,d9_petri,dt_g1_petri,dt_k10_petri,dt_k11_petri,dt_k12_petri,dt_k14_petri,dt_k1_domain_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_relat_1,dt_k4_tarski,dt_k5_petri,dt_k6_petri,dt_k9_petri,dt_l1_petri,dt_m1_petri,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_petri,dt_u2_petri,dt_u3_petri,dt_u4_petri,existence_l1_petri,existence_m1_petri,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_subset_1,fc1_xboole_0,fc2_subset_1,fc3_subset_1,fc4_subset_1,fraenkel_a_2_0_petri,fraenkel_a_2_2_petri,free_g1_petri,involutiveness_k4_relat_1,involutiveness_k9_petri,rc1_petri,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc9_trees_2,redefinition_k1_domain_1,redefinition_k9_petri,redefinition_m1_petri,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_petri,t2_subset,t2_tarski,t3_subset,t4_petri,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(petri,t15_petri)]).

fof(abstractness_v1_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ( v1_petri(A)
       => A = g1_petri(u1_petri(A),u2_petri(A),u3_petri(A),u4_petri(A)) ) ) ),
    file(petri,v1_petri),
    []).

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

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d10_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => k11_petri(A,B) = B ) ) ),
    file(petri,d10_petri),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d11_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_petri(A))
         => k12_petri(A,B) = B ) ) ),
    file(petri,d11_petri),
    []).

fof(d13_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_petri(k10_petri(A)))
         => k14_petri(A,B) = B ) ) ),
    file(petri,d13_petri),
    []).

fof(d1_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => k5_petri(A,B) = a_2_0_petri(A,B) ) ) ),
    file(petri,d1_petri),
    []).

fof(d2_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => k6_petri(A,B) = a_2_2_petri(A,B) ) ) ),
    file(petri,d2_petri),
    []).

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_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ),
    file(relat_1,d7_relat_1),
    []).

fof(d9_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => k10_petri(A) = g1_petri(u1_petri(A),u2_petri(A),k9_petri(u2_petri(A),u1_petri(A),u4_petri(A)),k9_petri(u1_petri(A),u2_petri(A),u3_petri(A))) ) ),
    file(petri,d9_petri),
    []).

fof(dt_g1_petri,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B)
        & ~ v1_xboole_0(D)
        & m1_relset_1(D,B,A) )
     => ( v1_petri(g1_petri(A,B,C,D))
        & l1_petri(g1_petri(A,B,C,D)) ) ) ),
    file(petri,g1_petri),
    []).

fof(dt_k10_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ( v1_petri(k10_petri(A))
        & l1_petri(k10_petri(A)) ) ) ),
    file(petri,k10_petri),
    []).

fof(dt_k11_petri,axiom,(
    ! [A,B] : 
      ( ( l1_petri(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
     => m1_subset_1(k11_petri(A,B),k1_zfmisc_1(u1_petri(k10_petri(A)))) ) ),
    file(petri,k11_petri),
    []).

fof(dt_k12_petri,axiom,(
    ! [A,B] : 
      ( ( l1_petri(A)
        & m1_subset_1(B,u1_petri(A)) )
     => m1_subset_1(k12_petri(A,B),u1_petri(k10_petri(A))) ) ),
    file(petri,k12_petri),
    []).

fof(dt_k14_petri,axiom,(
    ! [A,B] : 
      ( ( l1_petri(A)
        & m1_subset_1(B,u1_petri(k10_petri(A))) )
     => m1_subset_1(k14_petri(A,B),u1_petri(A)) ) ),
    file(petri,k14_petri),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

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

fof(dt_k5_petri,axiom,(
    ! [A,B] : 
      ( ( l1_petri(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
     => m1_subset_1(k5_petri(A,B),k1_zfmisc_1(u2_petri(A))) ) ),
    file(petri,k5_petri),
    []).

fof(dt_k6_petri,axiom,(
    ! [A,B] : 
      ( ( l1_petri(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
     => m1_subset_1(k6_petri(A,B),k1_zfmisc_1(u2_petri(A))) ) ),
    file(petri,k6_petri),
    []).

fof(dt_k9_petri,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k9_petri(A,B,C))
        & m2_relset_1(k9_petri(A,B,C),B,A) ) ) ),
    file(petri,k9_petri),
    []).

fof(dt_l1_petri,axiom,(
    $true ),
    file(petri,l1_petri),
    []).

fof(dt_m1_petri,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B) )
     => ! [D] : 
          ( m1_petri(D,A,B,C)
         => m1_subset_1(D,k2_zfmisc_1(A,B)) ) ) ),
    file(petri,m1_petri),
    []).

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(dt_u1_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ~ v1_xboole_0(u1_petri(A)) ) ),
    file(petri,u1_petri),
    []).

fof(dt_u2_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ~ v1_xboole_0(u2_petri(A)) ) ),
    file(petri,u2_petri),
    []).

fof(dt_u3_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ( ~ v1_xboole_0(u3_petri(A))
        & m2_relset_1(u3_petri(A),u1_petri(A),u2_petri(A)) ) ) ),
    file(petri,u3_petri),
    []).

fof(dt_u4_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ( ~ v1_xboole_0(u4_petri(A))
        & m2_relset_1(u4_petri(A),u2_petri(A),u1_petri(A)) ) ) ),
    file(petri,u4_petri),
    []).

fof(existence_l1_petri,axiom,(
    ? [A] : l1_petri(A) ),
    file(petri,l1_petri),
    []).

fof(existence_m1_petri,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B) )
     => ? [D] : m1_petri(D,A,B,C) ) ),
    file(petri,m1_petri),
    []).

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

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_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_2_0_petri,axiom,(
    ! [A,B,C] : 
      ( ( l1_petri(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_petri(B))) )
     => ( r2_hidden(A,a_2_0_petri(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u2_petri(B))
            & A = D
            & ? [E] : 
                ( m1_petri(E,u2_petri(B),u1_petri(B),u4_petri(B))
                & ? [F] : 
                    ( m1_subset_1(F,u1_petri(B))
                    & r2_hidden(F,C)
                    & E = k1_domain_1(u2_petri(B),u1_petri(B),D,F) ) ) ) ) ) ),
    file(petri,a_2_0_petri),
    []).

fof(fraenkel_a_2_2_petri,axiom,(
    ! [A,B,C] : 
      ( ( l1_petri(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_petri(B))) )
     => ( r2_hidden(A,a_2_2_petri(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u2_petri(B))
            & A = D
            & ? [E] : 
                ( m1_petri(E,u1_petri(B),u2_petri(B),u3_petri(B))
                & ? [F] : 
                    ( m1_subset_1(F,u1_petri(B))
                    & r2_hidden(F,C)
                    & E = k1_domain_1(u1_petri(B),u2_petri(B),F,D) ) ) ) ) ) ),
    file(petri,a_2_2_petri),
    []).

fof(free_g1_petri,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B)
        & ~ v1_xboole_0(D)
        & m1_relset_1(D,B,A) )
     => ! [E,F,G,H] : 
          ( g1_petri(A,B,C,D) = g1_petri(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(petri,g1_petri),
    []).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

fof(involutiveness_k9_petri,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B) )
     => k9_petri(A,B,k9_petri(A,B,C)) = C ) ),
    file(petri,k9_petri),
    []).

fof(rc1_petri,axiom,(
    ? [A] : 
      ( l1_petri(A)
      & v1_petri(A) ) ),
    file(petri,rc1_petri),
    []).

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_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(rc9_trees_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & ~ v1_xboole_0(C) ) ) ),
    file(trees_2,rc9_trees_2),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k9_petri,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B) )
     => k9_petri(A,B,C) = k4_relat_1(C) ) ),
    file(petri,k9_petri),
    []).

fof(redefinition_m1_petri,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_relset_1(C,A,B) )
     => ! [D] : 
          ( m1_petri(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(petri,m1_petri),
    []).

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(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => ! [C] : 
              ( r2_hidden(C,k5_petri(A,B))
            <=> ? [D] : 
                  ( m1_petri(D,u2_petri(A),u1_petri(A),u4_petri(A))
                  & ? [E] : 
                      ( m1_subset_1(E,u1_petri(A))
                      & r2_hidden(E,B)
                      & D = k4_tarski(C,E) ) ) ) ) ) ),
    file(petri,t2_petri),
    []).

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

fof(t4_petri,axiom,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => ! [C] : 
              ( r2_hidden(C,k6_petri(A,B))
            <=> ? [D] : 
                  ( m1_petri(D,u1_petri(A),u2_petri(A),u3_petri(A))
                  & ? [E] : 
                      ( m1_subset_1(E,u1_petri(A))
                      & r2_hidden(E,B)
                      & D = k4_tarski(E,C) ) ) ) ) ) ),
    file(petri,t4_petri),
    []).

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),
    []).