% Mizar ND problem: t3_boolmark,boolmark,75,52 
fof(dh_c1_3__boolmark,definition,
    ( ! [A,B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( r1_xboole_0(c1_3__boolmark,A)
           => k9_relat_1(k1_funct_4(B,k2_funcop_1(c1_3__boolmark,C)),A) = k9_relat_1(B,A) ) )
   => ! [D,E,F] : 
        ( ( v1_relat_1(F)
          & v1_funct_1(F) )
       => ! [G] : 
            ( r1_xboole_0(D,E)
           => k9_relat_1(k1_funct_4(F,k2_funcop_1(D,G)),E) = k9_relat_1(F,E) ) ) ),
    introduced(definition,[new_symbol(c1_3__boolmark),file(boolmark,c1_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c1_3__boolmark)]).

fof(dh_c2_3__boolmark,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
           => k9_relat_1(k1_funct_4(A,k2_funcop_1(c1_3__boolmark,B)),c2_3__boolmark) = k9_relat_1(A,c2_3__boolmark) ) )
   => ! [C,D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D) )
       => ! [E] : 
            ( r1_xboole_0(c1_3__boolmark,C)
           => k9_relat_1(k1_funct_4(D,k2_funcop_1(c1_3__boolmark,E)),C) = k9_relat_1(D,C) ) ) ),
    introduced(definition,[new_symbol(c2_3__boolmark),file(boolmark,c2_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c2_3__boolmark)]).

fof(dh_c3_3__boolmark,definition,
    ( ( ( v1_relat_1(c3_3__boolmark)
        & v1_funct_1(c3_3__boolmark) )
     => ! [A] : 
          ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
         => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,A)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
           => k9_relat_1(k1_funct_4(B,k2_funcop_1(c1_3__boolmark,C)),c2_3__boolmark) = k9_relat_1(B,c2_3__boolmark) ) ) ),
    introduced(definition,[new_symbol(c3_3__boolmark),file(boolmark,c3_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c3_3__boolmark)]).

fof(dh_c4_3__boolmark,definition,
    ( ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
     => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) )
   => ! [A] : 
        ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
       => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,A)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) ) ),
    introduced(definition,[new_symbol(c4_3__boolmark),file(boolmark,c4_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c4_3__boolmark)]).

fof(cc1_finseq_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(fc3_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc3_funcop_1)]).

fof(fc9_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc9_funcop_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

fof(rc3_finseq_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc6_finseq_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

fof(idempotence_k1_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

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

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_1)]).

fof(dt_c1_3__boolmark,assumption,(
    $true ),
    introduced(assumption,[file(boolmark,c1_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c1_3__boolmark)]).

fof(dt_c2_3__boolmark,assumption,(
    $true ),
    introduced(assumption,[file(boolmark,c2_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c2_3__boolmark)]).

fof(dt_c3_3__boolmark,assumption,
    ( v1_relat_1(c3_3__boolmark)
    & v1_funct_1(c3_3__boolmark) ),
    introduced(assumption,[file(boolmark,c3_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c3_3__boolmark)]).

fof(dt_c4_3__boolmark,assumption,(
    $true ),
    introduced(assumption,[file(boolmark,c4_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c4_3__boolmark)]).

fof(fc1_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc1_funcop_1)]).

fof(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

fof(fc2_finseq_1,theorem,
    ( 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),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(fc2_funcop_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc2_funcop_1)]).

fof(e1_3__boolmark,assumption,(
    k3_xboole_0(c1_3__boolmark,c2_3__boolmark) = k1_xboole_0 ),
    introduced(assumption,[file(boolmark,e1_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,e1_3__boolmark)]).

fof(e2_3__boolmark,assumption,(
    k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark) != k9_relat_1(c3_3__boolmark,c2_3__boolmark) ),
    introduced(assumption,[file(boolmark,e2_3__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,e2_3__boolmark)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d7_xboole_0)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(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(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(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(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(e1_3_1_1_1__boolmark,assumption,(
    ? [A] : 
      ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    introduced(assumption,[file(boolmark,e1_3_1_1_1__boolmark)]),
    [interesting(0.35),axiom,file(boolmark,e1_3_1_1_1__boolmark)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dh_c1_3_1_1_1__boolmark,definition,
    ( ? [A] : 
        ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
        & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
   => ( r2_hidden(c1_3_1_1_1__boolmark,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      & ~ r2_hidden(c1_3_1_1_1__boolmark,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    introduced(definition,[new_symbol(c1_3_1_1_1__boolmark),file(boolmark,c1_3_1_1_1__boolmark)]),
    [interesting(0.35),axiom,file(boolmark,c1_3_1_1_1__boolmark)]).

fof(e2_3_1_1_1__boolmark,plain,(
    ? [A] : 
      ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e1_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,e2_3_1_1_1__boolmark),[file(boolmark,e2_3_1_1_1__boolmark)]]).

fof(dt_c1_3_1_1_1__boolmark,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c1_3_1_1_1__boolmark,e2_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,c1_3_1_1_1__boolmark),[file(boolmark,c1_3_1_1_1__boolmark)]]).

fof(dh_c2_3_1_1_1__boolmark,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark))))
        & r2_hidden(A,c2_3__boolmark)
        & c1_3_1_1_1__boolmark = k1_funct_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),A) )
   => ( r2_hidden(c2_3_1_1_1__boolmark,k1_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark))))
      & r2_hidden(c2_3_1_1_1__boolmark,c2_3__boolmark)
      & c1_3_1_1_1__boolmark = k1_funct_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3_1_1_1__boolmark) ) ),
    introduced(definition,[new_symbol(c2_3_1_1_1__boolmark),file(boolmark,c2_3_1_1_1__boolmark)]),
    [interesting(0.35),axiom,file(boolmark,c2_3_1_1_1__boolmark)]).

fof(e3_3_1_1_1__boolmark,plain,(
    r2_hidden(c1_3_1_1_1__boolmark,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c1_3_1_1_1__boolmark,e2_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,e3_3_1_1_1__boolmark),[file(boolmark,e3_3_1_1_1__boolmark)]]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.9),axiom,file(funct_1,d12_funct_1)]).

fof(e5_3_1_1_1__boolmark,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark))))
      & r2_hidden(A,c2_3__boolmark)
      & c1_3_1_1_1__boolmark = k1_funct_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c1_3_1_1_1__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e3_3_1_1_1__boolmark,d12_funct_1]),
    [interesting(0.35),file(boolmark,e5_3_1_1_1__boolmark),[file(boolmark,e5_3_1_1_1__boolmark)]]).

fof(dt_c2_3_1_1_1__boolmark,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c2_3_1_1_1__boolmark,e5_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,c2_3_1_1_1__boolmark),[file(boolmark,c2_3_1_1_1__boolmark)]]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

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(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t19_funcop_1)]).

fof(e4_3__boolmark,plain,(
    k1_relat_1(k2_funcop_1(c1_3__boolmark,c4_3__boolmark)) = c1_3__boolmark ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c4_3__boolmark])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_c1_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,fc2_subset_1,t3_subset,t19_funcop_1]),
    [interesting(0.8),file(boolmark,e4_3__boolmark),[file(boolmark,e4_3__boolmark)]]).

fof(e8_3_1_1_1__boolmark,plain,(
    c1_3_1_1_1__boolmark = k1_funct_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3_1_1_1__boolmark) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c2_3_1_1_1__boolmark,e5_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,e8_3_1_1_1__boolmark),[file(boolmark,e8_3_1_1_1__boolmark)]]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

fof(e7_3_1_1_1__boolmark,plain,(
    r2_hidden(c2_3_1_1_1__boolmark,c2_3__boolmark) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c2_3_1_1_1__boolmark,e5_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,e7_3_1_1_1__boolmark),[file(boolmark,e7_3_1_1_1__boolmark)]]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]).

fof(e9_3_1_1_1__boolmark,plain,(
    ~ r2_hidden(c2_3_1_1_1__boolmark,c1_3__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_xboole_0,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c2_3_1_1_1__boolmark,fc1_margrel1,fc2_finseq_1,t1_subset,t2_boole,t6_boole,t7_boole,e1_3__boolmark,e7_3_1_1_1__boolmark,d3_xboole_0]),
    [interesting(0.35),file(boolmark,e9_3_1_1_1__boolmark),[file(boolmark,e9_3_1_1_1__boolmark)]]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.9),axiom,file(funct_4,t12_funct_4)]).

fof(e11_3_1_1_1__boolmark,plain,(
    c1_3_1_1_1__boolmark = k1_funct_1(c3_3__boolmark,c2_3_1_1_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_c1_3__boolmark,dt_c1_3_1_1_1__boolmark,dt_c2_3_1_1_1__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e4_3__boolmark,e8_3_1_1_1__boolmark,e9_3_1_1_1__boolmark,t12_funct_4]),
    [interesting(0.35),file(boolmark,e11_3_1_1_1__boolmark),[file(boolmark,e11_3_1_1_1__boolmark)]]).

fof(e4_3_1_1_1__boolmark,plain,(
    ~ r2_hidden(c1_3_1_1_1__boolmark,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c1_3_1_1_1__boolmark,e2_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,e4_3_1_1_1__boolmark),[file(boolmark,e4_3_1_1_1__boolmark)]]).

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

fof(d1_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.9),axiom,file(funct_4,d1_funct_4)]).

fof(e3_3__boolmark,plain,(
    k1_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark))) = k2_xboole_0(k1_relat_1(c3_3__boolmark),k1_relat_1(k2_funcop_1(c1_3__boolmark,c4_3__boolmark))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_k2_xboole_0,dt_c1_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,d1_funct_4]),
    [interesting(0.8),file(boolmark,e3_3__boolmark),[file(boolmark,e3_3__boolmark)]]).

fof(e6_3_1_1_1__boolmark,plain,(
    r2_hidden(c2_3_1_1_1__boolmark,k1_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)))) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[dh_c2_3_1_1_1__boolmark,e5_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,e6_3_1_1_1__boolmark),[file(boolmark,e6_3_1_1_1__boolmark)]]).

fof(d2_xboole_0,definition,(
    ! [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),
    [interesting(0.9),axiom,file(xboole_0,d2_xboole_0)]).

fof(e10_3_1_1_1__boolmark,plain,(
    r2_hidden(c2_3_1_1_1__boolmark,k1_relat_1(c3_3__boolmark)) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_k2_xboole_0,dt_c1_3__boolmark,dt_c2_3_1_1_1__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e9_3_1_1_1__boolmark,e3_3__boolmark,e4_3__boolmark,e6_3_1_1_1__boolmark,d2_xboole_0]),
    [interesting(0.35),file(boolmark,e10_3_1_1_1__boolmark),[file(boolmark,e10_3_1_1_1__boolmark)]]).

fof(e12_3_1_1_1__boolmark,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,existence_m1_subset_1,dt_m1_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_3_1_1_1__boolmark,dt_c2_3__boolmark,dt_c2_3_1_1_1__boolmark,dt_c3_3__boolmark,t1_subset,t7_boole,e11_3_1_1_1__boolmark,e4_3_1_1_1__boolmark,e7_3_1_1_1__boolmark,e10_3_1_1_1__boolmark,d12_funct_1]),
    [interesting(0.35),file(boolmark,e12_3_1_1_1__boolmark),[file(boolmark,e12_3_1_1_1__boolmark)]]).

fof(i2_3_1_1_1__boolmark,theorem,(
    $true ),
    introduced(tautology,[file(boolmark,i2_3_1_1_1__boolmark)]),
    [interesting(0.35),trivial,file(boolmark,i2_3_1_1_1__boolmark)]).

fof(i1_3_1_1_1__boolmark,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_1__boolmark])],[e12_3_1_1_1__boolmark,i2_3_1_1_1__boolmark]),
    [interesting(0.35),file(boolmark,i1_3_1_1_1__boolmark),[file(boolmark,i1_3_1_1_1__boolmark)]]).

fof(i1_3_1_1__boolmark,plain,
    ( ? [A] : 
        ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
        & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
   => ( ? [A] : 
          ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
          & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
      & ~ $true ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark]),discharge_asm(discharge,[e1_3_1_1_1__boolmark])],[e1_3_1_1_1__boolmark,i1_3_1_1_1__boolmark]),
    [interesting(0.5),file(boolmark,i1_3_1_1__boolmark),[file(boolmark,i1_3_1_1__boolmark)]]).

fof(e1_3_1_1_2__boolmark,assumption,(
    ? [A] : 
      ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    introduced(assumption,[file(boolmark,e1_3_1_1_2__boolmark)]),
    [interesting(0.35),axiom,file(boolmark,e1_3_1_1_2__boolmark)]).

fof(dh_c1_3_1_1_2__boolmark,definition,
    ( ? [A] : 
        ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
        & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
   => ( ~ r2_hidden(c1_3_1_1_2__boolmark,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      & r2_hidden(c1_3_1_1_2__boolmark,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    introduced(definition,[new_symbol(c1_3_1_1_2__boolmark),file(boolmark,c1_3_1_1_2__boolmark)]),
    [interesting(0.35),axiom,file(boolmark,c1_3_1_1_2__boolmark)]).

fof(e2_3_1_1_2__boolmark,plain,(
    ? [A] : 
      ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e1_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,e2_3_1_1_2__boolmark),[file(boolmark,e2_3_1_1_2__boolmark)]]).

fof(dt_c1_3_1_1_2__boolmark,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c1_3_1_1_2__boolmark,e2_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,c1_3_1_1_2__boolmark),[file(boolmark,c1_3_1_1_2__boolmark)]]).

fof(dh_c2_3_1_1_2__boolmark,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c3_3__boolmark))
        & r2_hidden(A,c2_3__boolmark)
        & c1_3_1_1_2__boolmark = k1_funct_1(c3_3__boolmark,A) )
   => ( r2_hidden(c2_3_1_1_2__boolmark,k1_relat_1(c3_3__boolmark))
      & r2_hidden(c2_3_1_1_2__boolmark,c2_3__boolmark)
      & c1_3_1_1_2__boolmark = k1_funct_1(c3_3__boolmark,c2_3_1_1_2__boolmark) ) ),
    introduced(definition,[new_symbol(c2_3_1_1_2__boolmark),file(boolmark,c2_3_1_1_2__boolmark)]),
    [interesting(0.35),axiom,file(boolmark,c2_3_1_1_2__boolmark)]).

fof(e4_3_1_1_2__boolmark,plain,(
    r2_hidden(c1_3_1_1_2__boolmark,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c1_3_1_1_2__boolmark,e2_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,e4_3_1_1_2__boolmark),[file(boolmark,e4_3_1_1_2__boolmark)]]).

fof(e5_3_1_1_2__boolmark,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c3_3__boolmark))
      & r2_hidden(A,c2_3__boolmark)
      & c1_3_1_1_2__boolmark = k1_funct_1(c3_3__boolmark,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,existence_m1_subset_1,dt_m1_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_3_1_1_2__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,t1_subset,t7_boole,e4_3_1_1_2__boolmark,d12_funct_1]),
    [interesting(0.35),file(boolmark,e5_3_1_1_2__boolmark),[file(boolmark,e5_3_1_1_2__boolmark)]]).

fof(dt_c2_3_1_1_2__boolmark,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c2_3_1_1_2__boolmark,e5_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,c2_3_1_1_2__boolmark),[file(boolmark,c2_3_1_1_2__boolmark)]]).

fof(e8_3_1_1_2__boolmark,plain,(
    c1_3_1_1_2__boolmark = k1_funct_1(c3_3__boolmark,c2_3_1_1_2__boolmark) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c2_3_1_1_2__boolmark,e5_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,e8_3_1_1_2__boolmark),[file(boolmark,e8_3_1_1_2__boolmark)]]).

fof(e7_3_1_1_2__boolmark,plain,(
    r2_hidden(c2_3_1_1_2__boolmark,c2_3__boolmark) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c2_3_1_1_2__boolmark,e5_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,e7_3_1_1_2__boolmark),[file(boolmark,e7_3_1_1_2__boolmark)]]).

fof(e9_3_1_1_2__boolmark,plain,(
    ~ r2_hidden(c2_3_1_1_2__boolmark,c1_3__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_xboole_0,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c2_3_1_1_2__boolmark,fc1_margrel1,fc2_finseq_1,t1_subset,t2_boole,t6_boole,t7_boole,e1_3__boolmark,e7_3_1_1_2__boolmark,d3_xboole_0]),
    [interesting(0.35),file(boolmark,e9_3_1_1_2__boolmark),[file(boolmark,e9_3_1_1_2__boolmark)]]).

fof(e11_3_1_1_2__boolmark,plain,(
    c1_3_1_1_2__boolmark = k1_funct_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3_1_1_2__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_c1_3__boolmark,dt_c1_3_1_1_2__boolmark,dt_c2_3_1_1_2__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e4_3__boolmark,e8_3_1_1_2__boolmark,e9_3_1_1_2__boolmark,t12_funct_4]),
    [interesting(0.35),file(boolmark,e11_3_1_1_2__boolmark),[file(boolmark,e11_3_1_1_2__boolmark)]]).

fof(e3_3_1_1_2__boolmark,plain,(
    ~ r2_hidden(c1_3_1_1_2__boolmark,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c1_3_1_1_2__boolmark,e2_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,e3_3_1_1_2__boolmark),[file(boolmark,e3_3_1_1_2__boolmark)]]).

fof(e6_3_1_1_2__boolmark,plain,(
    r2_hidden(c2_3_1_1_2__boolmark,k1_relat_1(c3_3__boolmark)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[dh_c2_3_1_1_2__boolmark,e5_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,e6_3_1_1_2__boolmark),[file(boolmark,e6_3_1_1_2__boolmark)]]).

fof(e10_3_1_1_2__boolmark,plain,(
    r2_hidden(c2_3_1_1_2__boolmark,k1_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_k2_xboole_0,dt_c1_3__boolmark,dt_c2_3_1_1_2__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e3_3__boolmark,e6_3_1_1_2__boolmark,d2_xboole_0]),
    [interesting(0.35),file(boolmark,e10_3_1_1_2__boolmark),[file(boolmark,e10_3_1_1_2__boolmark)]]).

fof(e12_3_1_1_2__boolmark,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c1_3_1_1_2__boolmark,dt_c2_3__boolmark,dt_c2_3_1_1_2__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e11_3_1_1_2__boolmark,e3_3_1_1_2__boolmark,e7_3_1_1_2__boolmark,e10_3_1_1_2__boolmark,d12_funct_1]),
    [interesting(0.35),file(boolmark,e12_3_1_1_2__boolmark),[file(boolmark,e12_3_1_1_2__boolmark)]]).

fof(i2_3_1_1_2__boolmark,theorem,(
    $true ),
    introduced(tautology,[file(boolmark,i2_3_1_1_2__boolmark)]),
    [interesting(0.35),trivial,file(boolmark,i2_3_1_1_2__boolmark)]).

fof(i1_3_1_1_2__boolmark,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e1_3_1_1_2__boolmark])],[e12_3_1_1_2__boolmark,i2_3_1_1_2__boolmark]),
    [interesting(0.35),file(boolmark,i1_3_1_1_2__boolmark),[file(boolmark,i1_3_1_1_2__boolmark)]]).

fof(i2_3_1_1__boolmark,plain,
    ( ? [A] : 
        ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
        & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
   => ( ? [A] : 
          ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
          & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
      & ~ $true ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark]),discharge_asm(discharge,[e1_3_1_1_2__boolmark])],[e1_3_1_1_2__boolmark,i1_3_1_1_2__boolmark]),
    [interesting(0.5),file(boolmark,i2_3_1_1__boolmark),[file(boolmark,i2_3_1_1__boolmark)]]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(e5_3__boolmark,plain,(
    ~ ! [A] : 
        ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
      <=> r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e2_3__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e2_3__boolmark,t2_tarski]),
    [interesting(0.8),file(boolmark,e5_3__boolmark),[file(boolmark,e5_3__boolmark)]]).

fof(e1_3_1_1__boolmark,plain,(
    ~ ( ! [A] : 
          ~ ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
            & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
      & ! [A] : 
          ~ ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
            & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e2_3__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e5_3__boolmark]),
    [interesting(0.5),file(boolmark,e1_3_1_1__boolmark),[file(boolmark,e1_3_1_1__boolmark)]]).

fof(e6_3__boolmark,plain,
    ( ( ? [A] : 
          ( r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
          & ~ r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
      & ~ $true )
    | ( ? [A] : 
          ( ~ r2_hidden(A,k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark))
          & r2_hidden(A,k9_relat_1(c3_3__boolmark,c2_3__boolmark)) )
      & ~ $true ) ),
    inference(percases,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e2_3__boolmark])],[i1_3_1_1__boolmark,i2_3_1_1__boolmark,e1_3_1_1__boolmark]),
    [interesting(0.8),file(boolmark,e6_3__boolmark),[file(boolmark,e6_3__boolmark)]]).

fof(e7_3__boolmark,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e2_3__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,existence_m1_subset_1,dt_m1_subset_1,fc3_funcop_1,fc9_funcop_1,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k2_funcop_1,dt_k9_relat_1,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,t1_subset,t7_boole,e6_3__boolmark]),
    [interesting(0.8),file(boolmark,e7_3__boolmark),[file(boolmark,e7_3__boolmark)]]).

fof(i5_3__boolmark,theorem,(
    $true ),
    introduced(tautology,[file(boolmark,i5_3__boolmark)]),
    [interesting(0.8),trivial,file(boolmark,i5_3__boolmark)]).

fof(i4_3__boolmark,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_3__boolmark,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,e2_3__boolmark])],[e7_3__boolmark,i5_3__boolmark]),
    [interesting(0.8),file(boolmark,i4_3__boolmark),[file(boolmark,i4_3__boolmark)]]).

fof(i4_3_tmp__boolmark,plain,
    ( ( k3_xboole_0(c1_3__boolmark,c2_3__boolmark) = k1_xboole_0
      & k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark) != k9_relat_1(c3_3__boolmark,c2_3__boolmark) )
   => ~ $true ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark]),discharge_asm(discharge,[e1_3__boolmark,e2_3__boolmark])],[e1_3__boolmark,e2_3__boolmark,i4_3__boolmark]),
    [interesting(0.8),i3_3__boolmark]).

fof(i3_3__boolmark,plain,
    ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
   => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark])],[i4_3_tmp__boolmark,d7_xboole_0,cc1_finseq_1,fc3_funcop_1,fc9_funcop_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,idempotence_k1_funct_4,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_xboole_0,dt_k1_funct_4,dt_k1_xboole_0,dt_k2_funcop_1,dt_k3_xboole_0,dt_k9_relat_1,dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark,dt_c4_3__boolmark,fc1_funcop_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1]),
    [interesting(0.8),file(boolmark,i3_3__boolmark),[file(boolmark,i3_3__boolmark)]]).

fof(i3_3_tmp__boolmark,plain,
    ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
   => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,c4_3__boolmark)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark]),discharge_asm(discharge,[dt_c4_3__boolmark])],[dt_c4_3__boolmark,i3_3__boolmark]),
    [interesting(0.8),i2_3__boolmark]).

fof(i2_3__boolmark,plain,(
    ! [A] : 
      ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
     => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,A)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark,dt_c3_3__boolmark])],[i3_3_tmp__boolmark,dh_c4_3__boolmark]),
    [interesting(0.8),file(boolmark,i2_3__boolmark),[file(boolmark,i2_3__boolmark)]]).

fof(i2_3_tmp__boolmark,plain,
    ( ( v1_relat_1(c3_3__boolmark)
      & v1_funct_1(c3_3__boolmark) )
   => ! [A] : 
        ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
       => k9_relat_1(k1_funct_4(c3_3__boolmark,k2_funcop_1(c1_3__boolmark,A)),c2_3__boolmark) = k9_relat_1(c3_3__boolmark,c2_3__boolmark) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark]),discharge_asm(discharge,[dt_c3_3__boolmark])],[dt_c3_3__boolmark,i2_3__boolmark]),
    [interesting(0.8),i1_3__boolmark]).

fof(i1_3__boolmark,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
         => k9_relat_1(k1_funct_4(A,k2_funcop_1(c1_3__boolmark,B)),c2_3__boolmark) = k9_relat_1(A,c2_3__boolmark) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__boolmark,dt_c2_3__boolmark])],[i2_3_tmp__boolmark,dh_c3_3__boolmark]),
    [interesting(0.8),file(boolmark,i1_3__boolmark),[file(boolmark,i1_3__boolmark)]]).

fof(i1_3_tmp__boolmark,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r1_xboole_0(c1_3__boolmark,c2_3__boolmark)
         => k9_relat_1(k1_funct_4(A,k2_funcop_1(c1_3__boolmark,B)),c2_3__boolmark) = k9_relat_1(A,c2_3__boolmark) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__boolmark,dt_c2_3__boolmark])],[dt_c1_3__boolmark,dt_c2_3__boolmark,i1_3__boolmark]),
    [interesting(1),t3_boolmark]).

fof(t3_boolmark,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( r1_xboole_0(A,B)
         => k9_relat_1(k1_funct_4(C,k2_funcop_1(A,D)),B) = k9_relat_1(C,B) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__boolmark,dh_c1_3__boolmark,dh_c2_3__boolmark]),
    [interesting(1),file(boolmark,t3_boolmark),[file(boolmark,t3_boolmark)]]).