% Mizar ND problem: t1_partfun1,partfun1,29,69 
fof(dh_c1_1__partfun1,definition,
    ( ! [A,B,C,D,E] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(A,B))
          & r1_tarski(C,k2_zfmisc_1(D,E)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,C),k2_zfmisc_1(k2_xboole_0(A,D),k2_xboole_0(B,E))) )
   => ! [F,G,H,I,J,K] : 
        ( ( r1_tarski(F,k2_zfmisc_1(G,H))
          & r1_tarski(I,k2_zfmisc_1(J,K)) )
       => r1_tarski(k2_xboole_0(F,I),k2_zfmisc_1(k2_xboole_0(G,J),k2_xboole_0(H,K))) ) ),
    introduced(definition,[new_symbol(c1_1__partfun1),file(partfun1,c1_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c1_1__partfun1)]).

fof(dh_c2_1__partfun1,definition,
    ( ! [A,B,C,D] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,A))
          & r1_tarski(B,k2_zfmisc_1(C,D)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,B),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,C),k2_xboole_0(A,D))) )
   => ! [E,F,G,H,I] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(E,F))
          & r1_tarski(G,k2_zfmisc_1(H,I)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,G),k2_zfmisc_1(k2_xboole_0(E,H),k2_xboole_0(F,I))) ) ),
    introduced(definition,[new_symbol(c2_1__partfun1),file(partfun1,c2_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c2_1__partfun1)]).

fof(dh_c3_1__partfun1,definition,
    ( ! [A,B,C] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
          & r1_tarski(A,k2_zfmisc_1(B,C)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,A),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,B),k2_xboole_0(c3_1__partfun1,C))) )
   => ! [D,E,F,G] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,D))
          & r1_tarski(E,k2_zfmisc_1(F,G)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,E),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,F),k2_xboole_0(D,G))) ) ),
    introduced(definition,[new_symbol(c3_1__partfun1),file(partfun1,c3_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c3_1__partfun1)]).

fof(dh_c4_1__partfun1,definition,
    ( ! [A,B] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
          & r1_tarski(c4_1__partfun1,k2_zfmisc_1(A,B)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,A),k2_xboole_0(c3_1__partfun1,B))) )
   => ! [C,D,E] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
          & r1_tarski(C,k2_zfmisc_1(D,E)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,C),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,D),k2_xboole_0(c3_1__partfun1,E))) ) ),
    introduced(definition,[new_symbol(c4_1__partfun1),file(partfun1,c4_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c4_1__partfun1)]).

fof(dh_c5_1__partfun1,definition,
    ( ! [A] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
          & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,A)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,A))) )
   => ! [B,C] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
          & r1_tarski(c4_1__partfun1,k2_zfmisc_1(B,C)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,B),k2_xboole_0(c3_1__partfun1,C))) ) ),
    introduced(definition,[new_symbol(c5_1__partfun1),file(partfun1,c5_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c5_1__partfun1)]).

fof(dh_c6_1__partfun1,definition,
    ( ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) )
   => ! [A] : 
        ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
          & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,A)) )
       => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,A))) ) ),
    introduced(definition,[new_symbol(c6_1__partfun1),file(partfun1,c6_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c6_1__partfun1)]).

fof(e4_1__partfun1,assumption,
    ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
    & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1)) ),
    introduced(assumption,[file(partfun1,e4_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,e4_1__partfun1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(cc2_funct_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(fc2_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc2_relat_1)]).

fof(fc2_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]).

fof(fc3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc1_relset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_c1_1__partfun1,assumption,(
    $true ),
    introduced(assumption,[file(partfun1,c1_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c1_1__partfun1)]).

fof(dt_c2_1__partfun1,assumption,(
    $true ),
    introduced(assumption,[file(partfun1,c2_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c2_1__partfun1)]).

fof(dt_c3_1__partfun1,assumption,(
    $true ),
    introduced(assumption,[file(partfun1,c3_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c3_1__partfun1)]).

fof(dt_c4_1__partfun1,assumption,(
    $true ),
    introduced(assumption,[file(partfun1,c4_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c4_1__partfun1)]).

fof(dt_c5_1__partfun1,assumption,(
    $true ),
    introduced(assumption,[file(partfun1,c5_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c5_1__partfun1)]).

fof(dt_c6_1__partfun1,assumption,(
    $true ),
    introduced(assumption,[file(partfun1,c6_1__partfun1)]),
    [interesting(0.8),axiom,file(partfun1,c6_1__partfun1)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t13_xboole_1)]).

fof(e5_1__partfun1,plain,(
    r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_xboole_0(k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1),k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c4_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1,e4_1__partfun1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc2_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,fc2_relat_1,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c1_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c4_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1,t3_subset,e4_1__partfun1,t13_xboole_1]),
    [interesting(0.8),file(partfun1,e5_1__partfun1),[file(partfun1,e5_1__partfun1)]]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t7_xboole_1)]).

fof(e1_1__partfun1,plain,
    ( r1_tarski(c2_1__partfun1,k2_xboole_0(c2_1__partfun1,c5_1__partfun1))
    & r1_tarski(c6_1__partfun1,k2_xboole_0(c3_1__partfun1,c6_1__partfun1))
    & r1_tarski(c5_1__partfun1,k2_xboole_0(c2_1__partfun1,c5_1__partfun1))
    & r1_tarski(c3_1__partfun1,k2_xboole_0(c3_1__partfun1,c6_1__partfun1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc2_relat_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,fc2_xboole_0,fc3_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1,t3_subset,t7_xboole_1]),
    [interesting(0.8),file(partfun1,e1_1__partfun1),[file(partfun1,e1_1__partfun1)]]).

fof(t119_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t119_zfmisc_1)]).

fof(e2_1__partfun1,plain,
    ( r1_tarski(k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1)))
    & r1_tarski(k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1)))
    & k2_xboole_0(k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1)),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) = k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc2_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,fc2_relat_1,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1,t3_subset,e1_1__partfun1,t119_zfmisc_1]),
    [interesting(0.8),file(partfun1,e2_1__partfun1),[file(partfun1,e2_1__partfun1)]]).

fof(e3_1__partfun1,plain,(
    r1_tarski(k2_xboole_0(k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1),k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1)),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc2_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,fc2_relat_1,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1,t3_subset,e2_1__partfun1,t13_xboole_1]),
    [interesting(0.8),file(partfun1,e3_1__partfun1),[file(partfun1,e3_1__partfun1)]]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e6_1__partfun1,plain,(
    r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,e4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc2_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,fc2_relat_1,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c1_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c4_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1,t3_subset,e5_1__partfun1,e3_1__partfun1,t1_xboole_1]),
    [interesting(0.8),file(partfun1,e6_1__partfun1),[file(partfun1,e6_1__partfun1)]]).

fof(i8_1__partfun1,theorem,(
    $true ),
    introduced(tautology,[file(partfun1,i8_1__partfun1)]),
    [interesting(0.8),trivial,file(partfun1,i8_1__partfun1)]).

fof(i7_1__partfun1,plain,(
    r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,e4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1])],[e6_1__partfun1,i8_1__partfun1]),
    [interesting(0.8),file(partfun1,i7_1__partfun1),[file(partfun1,i7_1__partfun1)]]).

fof(i6_1__partfun1,plain,
    ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
      & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1)) )
   => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1,dt_c6_1__partfun1]),discharge_asm(discharge,[e4_1__partfun1])],[e4_1__partfun1,i7_1__partfun1]),
    [interesting(0.8),file(partfun1,i6_1__partfun1),[file(partfun1,i6_1__partfun1)]]).

fof(i6_1_tmp__partfun1,plain,
    ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
      & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,c6_1__partfun1)) )
   => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,c6_1__partfun1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1]),discharge_asm(discharge,[dt_c6_1__partfun1])],[dt_c6_1__partfun1,i6_1__partfun1]),
    [interesting(0.8),i5_1__partfun1]).

fof(i5_1__partfun1,plain,(
    ! [A] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,A)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,A))) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1,dt_c5_1__partfun1])],[i6_1_tmp__partfun1,dh_c6_1__partfun1]),
    [interesting(0.8),file(partfun1,i5_1__partfun1),[file(partfun1,i5_1__partfun1)]]).

fof(i5_1_tmp__partfun1,plain,(
    ! [A] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(c4_1__partfun1,k2_zfmisc_1(c5_1__partfun1,A)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,c5_1__partfun1),k2_xboole_0(c3_1__partfun1,A))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1]),discharge_asm(discharge,[dt_c5_1__partfun1])],[dt_c5_1__partfun1,i5_1__partfun1]),
    [interesting(0.8),i4_1__partfun1]).

fof(i4_1__partfun1,plain,(
    ! [A,B] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(c4_1__partfun1,k2_zfmisc_1(A,B)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,A),k2_xboole_0(c3_1__partfun1,B))) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__partfun1,dt_c4_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1])],[i5_1_tmp__partfun1,dh_c5_1__partfun1]),
    [interesting(0.8),file(partfun1,i4_1__partfun1),[file(partfun1,i4_1__partfun1)]]).

fof(i4_1_tmp__partfun1,plain,(
    ! [A,B] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(c4_1__partfun1,k2_zfmisc_1(A,B)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,c4_1__partfun1),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,A),k2_xboole_0(c3_1__partfun1,B))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1]),discharge_asm(discharge,[dt_c4_1__partfun1])],[dt_c4_1__partfun1,i4_1__partfun1]),
    [interesting(0.8),i3_1__partfun1]).

fof(i3_1__partfun1,plain,(
    ! [A,B,C] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(A,k2_zfmisc_1(B,C)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,A),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,B),k2_xboole_0(c3_1__partfun1,C))) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__partfun1,dt_c2_1__partfun1,dt_c3_1__partfun1])],[i4_1_tmp__partfun1,dh_c4_1__partfun1]),
    [interesting(0.8),file(partfun1,i3_1__partfun1),[file(partfun1,i3_1__partfun1)]]).

fof(i3_1_tmp__partfun1,plain,(
    ! [A,B,C] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,c3_1__partfun1))
        & r1_tarski(A,k2_zfmisc_1(B,C)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,A),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,B),k2_xboole_0(c3_1__partfun1,C))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__partfun1,dt_c2_1__partfun1]),discharge_asm(discharge,[dt_c3_1__partfun1])],[dt_c3_1__partfun1,i3_1__partfun1]),
    [interesting(0.8),i2_1__partfun1]).

fof(i2_1__partfun1,plain,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,A))
        & r1_tarski(B,k2_zfmisc_1(C,D)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,B),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,C),k2_xboole_0(A,D))) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__partfun1,dt_c2_1__partfun1])],[i3_1_tmp__partfun1,dh_c3_1__partfun1]),
    [interesting(0.8),file(partfun1,i2_1__partfun1),[file(partfun1,i2_1__partfun1)]]).

fof(i2_1_tmp__partfun1,plain,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(c2_1__partfun1,A))
        & r1_tarski(B,k2_zfmisc_1(C,D)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,B),k2_zfmisc_1(k2_xboole_0(c2_1__partfun1,C),k2_xboole_0(A,D))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__partfun1]),discharge_asm(discharge,[dt_c2_1__partfun1])],[dt_c2_1__partfun1,i2_1__partfun1]),
    [interesting(0.8),i1_1__partfun1]).

fof(i1_1__partfun1,plain,(
    ! [A,B,C,D,E] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(A,B))
        & r1_tarski(C,k2_zfmisc_1(D,E)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,C),k2_zfmisc_1(k2_xboole_0(A,D),k2_xboole_0(B,E))) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__partfun1])],[i2_1_tmp__partfun1,dh_c2_1__partfun1]),
    [interesting(0.8),file(partfun1,i1_1__partfun1),[file(partfun1,i1_1__partfun1)]]).

fof(i1_1_tmp__partfun1,plain,(
    ! [A,B,C,D,E] : 
      ( ( r1_tarski(c1_1__partfun1,k2_zfmisc_1(A,B))
        & r1_tarski(C,k2_zfmisc_1(D,E)) )
     => r1_tarski(k2_xboole_0(c1_1__partfun1,C),k2_zfmisc_1(k2_xboole_0(A,D),k2_xboole_0(B,E))) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__partfun1])],[dt_c1_1__partfun1,i1_1__partfun1]),
    [interesting(1),t1_partfun1]).

fof(t1_partfun1,theorem,(
    ! [A,B,C,D,E,F] : 
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r1_tarski(D,k2_zfmisc_1(E,F)) )
     => r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__partfun1,dh_c1_1__partfun1]),
    [interesting(1),file(partfun1,t1_partfun1),[file(partfun1,t1_partfun1)]]).