% Mizar ND problem: t6_trees_2,trees_2,87,56 
fof(dh_c1_5__trees_2,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => k1_trees_1(k7_finseq_1(A,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(A),k1_tarski(A)) )
   => ! [B,C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finseq_1(C) )
       => k1_trees_1(k7_finseq_1(C,k9_finseq_1(B))) = k2_xboole_0(k1_trees_1(C),k1_tarski(C)) ) ),
    introduced(definition,[new_symbol(c1_5__trees_2),file(trees_2,c1_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c1_5__trees_2)]).

fof(dh_c2_5__trees_2,definition,
    ( ( ( v1_relat_1(c2_5__trees_2)
        & v1_funct_1(c2_5__trees_2)
        & v1_finseq_1(c2_5__trees_2) )
     => k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => k1_trees_1(k7_finseq_1(A,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(A),k1_tarski(A)) ) ),
    introduced(definition,[new_symbol(c2_5__trees_2),file(trees_2,c2_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c2_5__trees_2)]).

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]).

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(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_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(fc12_finseq_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]).

fof(fc13_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(A,B))
        & v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,fc13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]).

fof(fc14_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(B,A))
        & v1_relat_1(k7_finseq_1(B,A))
        & v1_funct_1(k7_finseq_1(B,A))
        & v1_finset_1(k7_finseq_1(B,A))
        & v1_finseq_1(k7_finseq_1(B,A)) ) ) ),
    file(finseq_1,fc14_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc14_finseq_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_finseq_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]).

fof(fc3_trees_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => v1_finset_1(k1_trees_1(A)) ) ),
    file(trees_1,fc3_trees_1),
    [interesting(0.9),axiom,file(trees_1,fc3_trees_1)]).

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_finseq_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]).

fof(fc9_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc9_finset_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_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_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_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_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(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(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(redefinition_k9_finseq_1,definition,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

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

fof(dt_k1_trees_1,axiom,(
    $true ),
    file(trees_1,k1_trees_1),
    [interesting(0.9),axiom,file(trees_1,k1_trees_1)]).

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_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k7_finseq_1)]).

fof(dt_k9_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k9_finseq_1(A))
      & v1_funct_1(k9_finseq_1(A)) ) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

fof(dt_c1_5__trees_2,assumption,(
    $true ),
    introduced(assumption,[file(trees_2,c1_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c1_5__trees_2)]).

fof(dt_c2_5__trees_2,assumption,
    ( v1_relat_1(c2_5__trees_2)
    & v1_funct_1(c2_5__trees_2)
    & v1_finseq_1(c2_5__trees_2) ),
    introduced(assumption,[file(trees_2,c2_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c2_5__trees_2)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_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(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

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_c1_5_1__trees_2,assumption,(
    $true ),
    introduced(assumption,[file(trees_2,c1_5_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_5_1__trees_2)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_5_1__trees_2,definition,
    ( ~ ( r2_hidden(c1_5_1__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))))
        & ~ r2_hidden(c1_5_1__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))))
          & ~ r2_hidden(A,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ) ),
    introduced(definition,[new_symbol(c1_5_1__trees_2),file(trees_2,c1_5_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_5_1__trees_2)]).

fof(e1_5_1__trees_2,assumption,(
    r2_hidden(c1_5_1__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    introduced(assumption,[file(trees_2,e1_5_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,e1_5_1__trees_2)]).

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

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(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(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(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(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(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(irreflexivity_r2_xboole_0,theorem,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r2_xboole_0)]).

fof(antisymmetry_r2_xboole_0,theorem,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r2_xboole_0)]).

fof(dh_c2_5_1__trees_2,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & c1_5_1__trees_2 = A
        & r2_xboole_0(A,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) )
   => ( v1_relat_1(c2_5_1__trees_2)
      & v1_funct_1(c2_5_1__trees_2)
      & v1_finseq_1(c2_5_1__trees_2)
      & c1_5_1__trees_2 = c2_5_1__trees_2
      & r2_xboole_0(c2_5_1__trees_2,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) ) ),
    introduced(definition,[new_symbol(c2_5_1__trees_2),file(trees_2,c2_5_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c2_5_1__trees_2)]).

fof(d4_trees_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( B = k1_trees_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & v1_finseq_1(D)
                  & C = D
                  & r2_xboole_0(D,A) ) ) ) ) ),
    file(trees_1,d4_trees_1),
    [interesting(0.9),axiom,file(trees_1,d4_trees_1)]).

fof(e2_5_1__trees_2,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A)
      & c1_5_1__trees_2 = A
      & r2_xboole_0(A,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k1_trees_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,cc1_finseq_1,fc3_trees_1,rc1_finseq_1,t1_subset,t7_boole,e1_5_1__trees_2,d4_trees_1]),
    [interesting(0.65),file(trees_2,e2_5_1__trees_2),[file(trees_2,e2_5_1__trees_2)]]).

fof(dt_c2_5_1__trees_2,plain,
    ( v1_relat_1(c2_5_1__trees_2)
    & v1_funct_1(c2_5_1__trees_2)
    & v1_finseq_1(c2_5_1__trees_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[dh_c2_5_1__trees_2,e2_5_1__trees_2]),
    [interesting(0.65),file(trees_2,c2_5_1__trees_2),[file(trees_2,c2_5_1__trees_2)]]).

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

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_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(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_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(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(e3_5_1__trees_2,plain,
    ( c1_5_1__trees_2 = c2_5_1__trees_2
    & r2_xboole_0(c2_5_1__trees_2,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[dh_c2_5_1__trees_2,e2_5_1__trees_2]),
    [interesting(0.65),file(trees_2,e3_5_1__trees_2),[file(trees_2,e3_5_1__trees_2)]]).

fof(t32_trees_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ( r2_xboole_0(B,k7_finseq_1(C,k9_finseq_1(A)))
           => r1_tarski(B,C) ) ) ) ),
    file(trees_1,t32_trees_1),
    [interesting(0.9),axiom,file(trees_1,t32_trees_1)]).

fof(e4_5_1__trees_2,plain,
    ( ( r1_tarski(c2_5_1__trees_2,c2_5__trees_2)
      & c2_5_1__trees_2 != c2_5__trees_2 )
    | c2_5_1__trees_2 = c2_5__trees_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_relat_1,fc13_finseq_1,fc14_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_m1_subset_1,cc2_finset_1,fc12_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,reflexivity_r1_tarski,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,dt_c2_5_1__trees_2,cc1_finseq_1,rc1_finseq_1,t3_subset,e3_5_1__trees_2,t32_trees_1]),
    [interesting(0.65),file(trees_2,e4_5_1__trees_2),[file(trees_2,e4_5_1__trees_2)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(d8_xboole_0,definition,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d8_xboole_0)]).

fof(e5_5_1__trees_2,plain,
    ( r2_xboole_0(c2_5_1__trees_2,c2_5__trees_2)
    | r2_hidden(c2_5_1__trees_2,k1_tarski(c2_5__trees_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,cc2_finset_1,fc1_subset_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,dt_k1_tarski,dt_c2_5__trees_2,dt_c2_5_1__trees_2,fc1_finset_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e4_5_1__trees_2,d1_tarski,d8_xboole_0]),
    [interesting(0.65),file(trees_2,e5_5_1__trees_2),[file(trees_2,e5_5_1__trees_2)]]).

fof(e6_5_1__trees_2,plain,
    ( r2_hidden(c1_5_1__trees_2,k1_trees_1(c2_5__trees_2))
    | r2_hidden(c1_5_1__trees_2,k1_tarski(c2_5__trees_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k1_tarski,dt_k1_trees_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,dt_c2_5_1__trees_2,cc1_finseq_1,fc1_finset_1,fc2_subset_1,fc3_trees_1,rc1_finseq_1,t1_subset,t7_boole,e5_5_1__trees_2,e3_5_1__trees_2,d4_trees_1]),
    [interesting(0.65),file(trees_2,e6_5_1__trees_2),[file(trees_2,e6_5_1__trees_2)]]).

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(e7_5_1__trees_2,plain,(
    r2_hidden(c1_5_1__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,fc2_relat_1,fc2_xboole_0,fc3_trees_1,fc3_xboole_0,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_trees_1,dt_k2_xboole_0,dt_c1_5_1__trees_2,dt_c2_5__trees_2,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e6_5_1__trees_2,d2_xboole_0]),
    [interesting(0.65),file(trees_2,e7_5_1__trees_2),[file(trees_2,e7_5_1__trees_2)]]).

fof(i3_5_1__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i3_5_1__trees_2)]),
    [interesting(0.65),trivial,file(trees_2,i3_5_1__trees_2)]).

fof(i2_5_1__trees_2,plain,(
    r2_hidden(c1_5_1__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2,e1_5_1__trees_2])],[e7_5_1__trees_2,i3_5_1__trees_2]),
    [interesting(0.65),file(trees_2,i2_5_1__trees_2),[file(trees_2,i2_5_1__trees_2)]]).

fof(i1_5_1__trees_2,plain,(
    ~ ( r2_hidden(c1_5_1__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))))
      & ~ r2_hidden(c1_5_1__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__trees_2,dt_c1_5_1__trees_2,dt_c2_5__trees_2]),discharge_asm(discharge,[e1_5_1__trees_2])],[e1_5_1__trees_2,i2_5_1__trees_2]),
    [interesting(0.65),file(trees_2,i1_5_1__trees_2),[file(trees_2,i1_5_1__trees_2)]]).

fof(i1_5_1_tmp__trees_2,plain,(
    ~ ( r2_hidden(c1_5_1__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))))
      & ~ r2_hidden(c1_5_1__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2]),discharge_asm(discharge,[dt_c1_5_1__trees_2])],[dt_c1_5_1__trees_2,i1_5_1__trees_2]),
    [interesting(0.8),e1_5__trees_2]).

fof(e1_5__trees_2,plain,(
    r1_tarski(k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))),k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ),
    inference(let,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[i1_5_1_tmp__trees_2,dt_k5_finseq_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_finseq_1,fc3_trees_1,fc3_xboole_0,fc4_finseq_1,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k9_finseq_1,dt_k1_tarski,dt_k1_trees_1,dt_k2_xboole_0,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,fc1_finset_1,fc2_subset_1,d3_tarski,dh_c1_5_1__trees_2]),
    [interesting(0.8),file(trees_2,e1_5__trees_2),[file(trees_2,e1_5__trees_2)]]).

fof(dt_c3_5__trees_2,assumption,(
    $true ),
    introduced(assumption,[file(trees_2,c3_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c3_5__trees_2)]).

fof(dh_c3_5__trees_2,definition,
    ( ~ ( r2_hidden(c3_5__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)))
        & ~ r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)))
          & ~ r2_hidden(A,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ) ),
    introduced(definition,[new_symbol(c3_5__trees_2),file(trees_2,c3_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c3_5__trees_2)]).

fof(e2_5__trees_2,assumption,(
    r2_hidden(c3_5__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2))) ),
    introduced(assumption,[file(trees_2,e2_5__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,e2_5__trees_2)]).

fof(t47_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    file(finseq_1,t47_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t47_finseq_1)]).

fof(e5_5__trees_2,plain,
    ( k1_xboole_0 != k9_finseq_1(c1_5__trees_2)
    & k7_finseq_1(c2_5__trees_2,k1_xboole_0) = c2_5__trees_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,dt_k5_finseq_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,redefinition_k9_finseq_1,dt_k1_xboole_0,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,cc1_finseq_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,t6_boole,t47_finseq_1]),
    [interesting(0.8),file(trees_2,e5_5__trees_2),[file(trees_2,e5_5__trees_2)]]).

fof(t46_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k7_finseq_1(A,B) = k7_finseq_1(C,B)
                  | k7_finseq_1(B,A) = k7_finseq_1(B,C) )
               => A = C ) ) ) ) ),
    file(finseq_1,t46_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t46_finseq_1)]).

fof(t8_trees_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & B = k7_finseq_1(A,C) ) ) ) ) ),
    file(trees_1,t8_trees_1),
    [interesting(0.9),axiom,file(trees_1,t8_trees_1)]).

fof(e6_5__trees_2,plain,
    ( r1_tarski(c2_5__trees_2,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))
    & c2_5__trees_2 != k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finset_1,cc1_relat_1,cc2_finset_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_relat_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k9_finseq_1,dt_k1_xboole_0,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,cc1_finseq_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,t3_subset,t6_boole,e5_5__trees_2,t46_finseq_1,t8_trees_1]),
    [interesting(0.8),file(trees_2,e6_5__trees_2),[file(trees_2,e6_5__trees_2)]]).

fof(e7_5__trees_2,plain,(
    r2_xboole_0(c2_5__trees_2,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_relat_1,cc2_finset_1,fc13_finseq_1,fc14_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finseq_1,fc12_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,reflexivity_r1_tarski,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,t3_subset,e6_5__trees_2,d8_xboole_0]),
    [interesting(0.8),file(trees_2,e7_5__trees_2),[file(trees_2,e7_5__trees_2)]]).

fof(e3_5__trees_2,plain,
    ( r2_hidden(c3_5__trees_2,k1_trees_1(c2_5__trees_2))
    | r2_hidden(c3_5__trees_2,k1_tarski(c2_5__trees_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__trees_2,dt_c3_5__trees_2,e2_5__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,fc2_relat_1,fc2_xboole_0,fc3_trees_1,fc3_xboole_0,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_trees_1,dt_k2_xboole_0,dt_c2_5__trees_2,dt_c3_5__trees_2,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e2_5__trees_2,d2_xboole_0]),
    [interesting(0.8),file(trees_2,e3_5__trees_2),[file(trees_2,e3_5__trees_2)]]).

fof(e8_5__trees_2,plain,
    ( r2_hidden(c3_5__trees_2,k1_trees_1(c2_5__trees_2))
    | ( c3_5__trees_2 = c2_5__trees_2
      & r2_hidden(c2_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,e2_5__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k1_tarski,dt_k1_trees_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,cc1_finseq_1,fc1_finset_1,fc2_subset_1,fc3_trees_1,rc1_finseq_1,t1_subset,t7_boole,e7_5__trees_2,e3_5__trees_2,d1_tarski,d4_trees_1]),
    [interesting(0.8),file(trees_2,e8_5__trees_2),[file(trees_2,e8_5__trees_2)]]).

fof(e1_5_2__trees_2,assumption,(
    r2_hidden(c3_5__trees_2,k1_trees_1(c2_5__trees_2)) ),
    introduced(assumption,[file(trees_2,e1_5_2__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,e1_5_2__trees_2)]).

fof(dh_c1_5_2__trees_2,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & c3_5__trees_2 = A
        & r2_xboole_0(A,c2_5__trees_2) )
   => ( v1_relat_1(c1_5_2__trees_2)
      & v1_funct_1(c1_5_2__trees_2)
      & v1_finseq_1(c1_5_2__trees_2)
      & c3_5__trees_2 = c1_5_2__trees_2
      & r2_xboole_0(c1_5_2__trees_2,c2_5__trees_2) ) ),
    introduced(definition,[new_symbol(c1_5_2__trees_2),file(trees_2,c1_5_2__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_5_2__trees_2)]).

fof(e2_5_2__trees_2,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A)
      & c3_5__trees_2 = A
      & r2_xboole_0(A,c2_5__trees_2) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__trees_2,dt_c3_5__trees_2,e1_5_2__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_relat_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,dt_k1_trees_1,dt_c2_5__trees_2,dt_c3_5__trees_2,cc1_finseq_1,fc3_trees_1,rc1_finseq_1,t1_subset,t7_boole,e1_5_2__trees_2,d4_trees_1]),
    [interesting(0.65),file(trees_2,e2_5_2__trees_2),[file(trees_2,e2_5_2__trees_2)]]).

fof(dt_c1_5_2__trees_2,plain,
    ( v1_relat_1(c1_5_2__trees_2)
    & v1_funct_1(c1_5_2__trees_2)
    & v1_finseq_1(c1_5_2__trees_2) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__trees_2,dt_c3_5__trees_2,e1_5_2__trees_2])],[dh_c1_5_2__trees_2,e2_5_2__trees_2]),
    [interesting(0.65),file(trees_2,c1_5_2__trees_2),[file(trees_2,c1_5_2__trees_2)]]).

fof(e4_5_2__trees_2,plain,(
    r1_tarski(c2_5__trees_2,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_relat_1,fc13_finseq_1,fc14_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_m1_subset_1,cc2_finset_1,fc12_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,reflexivity_r1_tarski,redefinition_k9_finseq_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,cc1_finseq_1,rc1_finseq_1,t3_subset,t8_trees_1]),
    [interesting(0.65),file(trees_2,e4_5_2__trees_2),[file(trees_2,e4_5_2__trees_2)]]).

fof(e3_5_2__trees_2,plain,
    ( c3_5__trees_2 = c1_5_2__trees_2
    & r2_xboole_0(c1_5_2__trees_2,c2_5__trees_2) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__trees_2,dt_c3_5__trees_2,e1_5_2__trees_2])],[dh_c1_5_2__trees_2,e2_5_2__trees_2]),
    [interesting(0.65),file(trees_2,e3_5_2__trees_2),[file(trees_2,e3_5_2__trees_2)]]).

fof(t27_trees_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ~ ( ~ ( r2_xboole_0(A,B)
                        & r2_xboole_0(B,C) )
                    & ~ ( r2_xboole_0(A,B)
                        & r1_tarski(B,C) )
                    & ~ ( r1_tarski(A,B)
                        & r2_xboole_0(B,C) ) )
               => r2_xboole_0(A,C) ) ) ) ) ),
    file(trees_1,t27_trees_1),
    [interesting(0.9),axiom,file(trees_1,t27_trees_1)]).

fof(e5_5_2__trees_2,plain,(
    r2_xboole_0(c1_5_2__trees_2,k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,e1_5_2__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_relat_1,fc13_finseq_1,fc14_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_m1_subset_1,cc2_finset_1,fc12_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,reflexivity_r1_tarski,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c1_5_2__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,cc1_finseq_1,rc1_finseq_1,t3_subset,e4_5_2__trees_2,e3_5_2__trees_2,t27_trees_1]),
    [interesting(0.65),file(trees_2,e5_5_2__trees_2),[file(trees_2,e5_5_2__trees_2)]]).

fof(e6_5_2__trees_2,plain,(
    r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,e1_5_2__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,existence_m1_subset_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,redefinition_k9_finseq_1,dt_k1_trees_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c1_5_2__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,cc1_finseq_1,fc3_trees_1,rc1_finseq_1,t1_subset,t7_boole,e5_5_2__trees_2,e3_5_2__trees_2,d4_trees_1]),
    [interesting(0.65),file(trees_2,e6_5_2__trees_2),[file(trees_2,e6_5_2__trees_2)]]).

fof(i2_5_2__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i2_5_2__trees_2)]),
    [interesting(0.65),trivial,file(trees_2,i2_5_2__trees_2)]).

fof(i1_5_2__trees_2,plain,(
    r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,e1_5_2__trees_2])],[e6_5_2__trees_2,i2_5_2__trees_2]),
    [interesting(0.65),file(trees_2,i1_5_2__trees_2),[file(trees_2,i1_5_2__trees_2)]]).

fof(e4_5__trees_2,plain,
    ( r2_hidden(c3_5__trees_2,k1_trees_1(c2_5__trees_2))
   => r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2]),discharge_asm(discharge,[e1_5_2__trees_2])],[e1_5_2__trees_2,i1_5_2__trees_2]),
    [interesting(0.8),file(trees_2,e4_5__trees_2),[file(trees_2,e4_5__trees_2)]]).

fof(e9_5__trees_2,plain,(
    r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    inference(mizar_by,[status(thm),assumptions([e2_5__trees_2,dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2])],[rc3_finseq_1,rc3_relat_1,rc6_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finset_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc3_trees_1,fc4_finseq_1,rc1_finseq_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k9_finseq_1,dt_k1_trees_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2,t1_subset,t7_boole,e8_5__trees_2,e4_5__trees_2]),
    [interesting(0.8),file(trees_2,e9_5__trees_2),[file(trees_2,e9_5__trees_2)]]).

fof(i6_5__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i6_5__trees_2)]),
    [interesting(0.8),trivial,file(trees_2,i6_5__trees_2)]).

fof(i5_5__trees_2,plain,(
    r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    inference(conclusion,[status(thm),assumptions([e2_5__trees_2,dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2])],[e9_5__trees_2,i6_5__trees_2]),
    [interesting(0.8),file(trees_2,i5_5__trees_2),[file(trees_2,i5_5__trees_2)]]).

fof(i4_5__trees_2,plain,(
    ~ ( r2_hidden(c3_5__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)))
      & ~ r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2,dt_c3_5__trees_2]),discharge_asm(discharge,[e2_5__trees_2])],[e2_5__trees_2,i5_5__trees_2]),
    [interesting(0.8),file(trees_2,i4_5__trees_2),[file(trees_2,i4_5__trees_2)]]).

fof(i4_5_tmp__trees_2,plain,(
    ~ ( r2_hidden(c3_5__trees_2,k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)))
      & ~ r2_hidden(c3_5__trees_2,k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2]),discharge_asm(discharge,[dt_c3_5__trees_2])],[dt_c3_5__trees_2,i4_5__trees_2]),
    [interesting(0.8),i3_5__trees_2]).

fof(i3_5__trees_2,plain,(
    r1_tarski(k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)),k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2)))) ),
    inference(let,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[i4_5_tmp__trees_2,dt_k5_finseq_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_finseq_1,fc3_trees_1,fc3_xboole_0,fc4_finseq_1,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k9_finseq_1,dt_k1_tarski,dt_k1_trees_1,dt_k2_xboole_0,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,fc1_finset_1,fc2_subset_1,d3_tarski,dh_c3_5__trees_2]),
    [interesting(0.8),file(trees_2,i3_5__trees_2),[file(trees_2,i3_5__trees_2)]]).

fof(i2_5__trees_2,plain,(
    k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__trees_2,dt_c2_5__trees_2])],[dt_k5_finseq_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_finseq_1,fc3_trees_1,fc3_xboole_0,fc4_finseq_1,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k9_finseq_1,dt_k1_tarski,dt_k1_trees_1,dt_k2_xboole_0,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_5__trees_2,dt_c2_5__trees_2,fc1_finset_1,fc2_subset_1,d10_xboole_0,e1_5__trees_2,i3_5__trees_2]),
    [interesting(0.8),file(trees_2,i2_5__trees_2),[file(trees_2,i2_5__trees_2)]]).

fof(i2_5_tmp__trees_2,plain,
    ( ( v1_relat_1(c2_5__trees_2)
      & v1_funct_1(c2_5__trees_2)
      & v1_finseq_1(c2_5__trees_2) )
   => k1_trees_1(k7_finseq_1(c2_5__trees_2,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(c2_5__trees_2),k1_tarski(c2_5__trees_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__trees_2]),discharge_asm(discharge,[dt_c2_5__trees_2])],[dt_c2_5__trees_2,i2_5__trees_2]),
    [interesting(0.8),i1_5__trees_2]).

fof(i1_5__trees_2,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k1_trees_1(k7_finseq_1(A,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(A),k1_tarski(A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__trees_2])],[i2_5_tmp__trees_2,dh_c2_5__trees_2]),
    [interesting(0.8),file(trees_2,i1_5__trees_2),[file(trees_2,i1_5__trees_2)]]).

fof(i1_5_tmp__trees_2,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k1_trees_1(k7_finseq_1(A,k9_finseq_1(c1_5__trees_2))) = k2_xboole_0(k1_trees_1(A),k1_tarski(A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__trees_2])],[dt_c1_5__trees_2,i1_5__trees_2]),
    [interesting(1),t6_trees_2]).

fof(t6_trees_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_trees_1(k7_finseq_1(B,k9_finseq_1(A))) = k2_xboole_0(k1_trees_1(B),k1_tarski(B)) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__trees_2,dh_c1_5__trees_2]),
    [interesting(1),file(trees_2,t6_trees_2),[file(trees_2,t6_trees_2)]]).