TSTP Solution File: SEU387+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU387+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 08:08:54 EST 2010

% Result   : Theorem 22.90s
% Output   : CNFRefutation 22.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   79 (  39 unt;   0 def)
%            Number of atoms       :  391 (  15 equ)
%            Maximal formula atoms :   24 (   4 avg)
%            Number of connectives :  487 ( 175   ~; 198   |; 101   &)
%                                         (   2 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   24 (  22 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-1 aty)
%            Number of variables   :   74 (  15 sgn  41   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(118,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & reflexive_relstr(X1)
        & transitive_relstr(X1)
        & antisymmetric_relstr(X1)
        & lower_bounded_relstr(X1)
        & rel_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,X1)
            & upper_relstr_subset(X2,X1)
            & element(X2,powerset(the_carrier(X1))) )
         => ( proper_element(X2,powerset(the_carrier(X1)))
          <=> ~ in(bottom_of_relstr(X1),X2) ) ) ),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',t8_waybel_7) ).

fof(203,axiom,
    ! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',d2_yellow_1) ).

fof(231,axiom,
    ! [X1] :
      ( ~ empty_carrier(boole_POSet(X1))
      & strict_rel_str(boole_POSet(X1))
      & reflexive_relstr(boole_POSet(X1))
      & transitive_relstr(boole_POSet(X1))
      & antisymmetric_relstr(boole_POSet(X1))
      & with_suprema_relstr(boole_POSet(X1))
      & with_infima_relstr(boole_POSet(X1))
      & complete_relstr(boole_POSet(X1))
      & lower_bounded_relstr(boole_POSet(X1))
      & upper_bounded_relstr(boole_POSet(X1))
      & bounded_relstr(boole_POSet(X1))
      & up_complete_relstr(boole_POSet(X1))
      & join_complete_relstr(boole_POSet(X1))
      & distributive_relstr(boole_POSet(X1))
      & complemented_relstr(boole_POSet(X1)) ),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',fc9_waybel_1) ).

fof(233,axiom,
    ! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',t18_yellow_1) ).

fof(456,axiom,
    ! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',t4_waybel_7) ).

fof(493,axiom,
    ! [X1] :
      ( strict_rel_str(boole_POSet(X1))
      & rel_str(boole_POSet(X1)) ),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',dt_k3_yellow_1) ).

fof(754,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',t7_boole) ).

fof(759,conjecture,
    ! [X1] :
      ( ~ empty(X1)
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(X1))
            & upper_relstr_subset(X2,boole_POSet(X1))
            & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
            & element(X2,powerset(the_carrier(boole_POSet(X1)))) )
         => ! [X3] :
              ~ ( in(X3,X2)
                & empty(X3) ) ) ),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',t2_yellow19) ).

fof(810,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/tmp/tmpwIHhuV/sel_SEU387+2.p_1',t6_boole) ).

fof(861,negated_conjecture,
    ~ ! [X1] :
        ( ~ empty(X1)
       => ! [X2] :
            ( ( ~ empty(X2)
              & filtered_subset(X2,boole_POSet(X1))
              & upper_relstr_subset(X2,boole_POSet(X1))
              & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
              & element(X2,powerset(the_carrier(boole_POSet(X1)))) )
           => ! [X3] :
                ~ ( in(X3,X2)
                  & empty(X3) ) ) ),
    inference(assume_negation,[status(cth)],[759]) ).

fof(895,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & reflexive_relstr(X1)
        & transitive_relstr(X1)
        & antisymmetric_relstr(X1)
        & lower_bounded_relstr(X1)
        & rel_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,X1)
            & upper_relstr_subset(X2,X1)
            & element(X2,powerset(the_carrier(X1))) )
         => ( proper_element(X2,powerset(the_carrier(X1)))
          <=> ~ in(bottom_of_relstr(X1),X2) ) ) ),
    inference(fof_simplification,[status(thm)],[118,theory(equality)]) ).

fof(937,plain,
    ! [X1] :
      ( ~ empty_carrier(boole_POSet(X1))
      & strict_rel_str(boole_POSet(X1))
      & reflexive_relstr(boole_POSet(X1))
      & transitive_relstr(boole_POSet(X1))
      & antisymmetric_relstr(boole_POSet(X1))
      & with_suprema_relstr(boole_POSet(X1))
      & with_infima_relstr(boole_POSet(X1))
      & complete_relstr(boole_POSet(X1))
      & lower_bounded_relstr(boole_POSet(X1))
      & upper_bounded_relstr(boole_POSet(X1))
      & bounded_relstr(boole_POSet(X1))
      & up_complete_relstr(boole_POSet(X1))
      & join_complete_relstr(boole_POSet(X1))
      & distributive_relstr(boole_POSet(X1))
      & complemented_relstr(boole_POSet(X1)) ),
    inference(fof_simplification,[status(thm)],[231,theory(equality)]) ).

fof(1094,negated_conjecture,
    ~ ! [X1] :
        ( ~ empty(X1)
       => ! [X2] :
            ( ( ~ empty(X2)
              & filtered_subset(X2,boole_POSet(X1))
              & upper_relstr_subset(X2,boole_POSet(X1))
              & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
              & element(X2,powerset(the_carrier(boole_POSet(X1)))) )
           => ! [X3] :
                ~ ( in(X3,X2)
                  & empty(X3) ) ) ),
    inference(fof_simplification,[status(thm)],[861,theory(equality)]) ).

fof(2190,plain,
    ! [X1] :
      ( empty_carrier(X1)
      | ~ reflexive_relstr(X1)
      | ~ transitive_relstr(X1)
      | ~ antisymmetric_relstr(X1)
      | ~ lower_bounded_relstr(X1)
      | ~ rel_str(X1)
      | ! [X2] :
          ( empty(X2)
          | ~ filtered_subset(X2,X1)
          | ~ upper_relstr_subset(X2,X1)
          | ~ element(X2,powerset(the_carrier(X1)))
          | ( ( ~ proper_element(X2,powerset(the_carrier(X1)))
              | ~ in(bottom_of_relstr(X1),X2) )
            & ( in(bottom_of_relstr(X1),X2)
              | proper_element(X2,powerset(the_carrier(X1))) ) ) ) ),
    inference(fof_nnf,[status(thm)],[895]) ).

fof(2191,plain,
    ! [X3] :
      ( empty_carrier(X3)
      | ~ reflexive_relstr(X3)
      | ~ transitive_relstr(X3)
      | ~ antisymmetric_relstr(X3)
      | ~ lower_bounded_relstr(X3)
      | ~ rel_str(X3)
      | ! [X4] :
          ( empty(X4)
          | ~ filtered_subset(X4,X3)
          | ~ upper_relstr_subset(X4,X3)
          | ~ element(X4,powerset(the_carrier(X3)))
          | ( ( ~ proper_element(X4,powerset(the_carrier(X3)))
              | ~ in(bottom_of_relstr(X3),X4) )
            & ( in(bottom_of_relstr(X3),X4)
              | proper_element(X4,powerset(the_carrier(X3))) ) ) ) ),
    inference(variable_rename,[status(thm)],[2190]) ).

fof(2192,plain,
    ! [X3,X4] :
      ( empty(X4)
      | ~ filtered_subset(X4,X3)
      | ~ upper_relstr_subset(X4,X3)
      | ~ element(X4,powerset(the_carrier(X3)))
      | ( ( ~ proper_element(X4,powerset(the_carrier(X3)))
          | ~ in(bottom_of_relstr(X3),X4) )
        & ( in(bottom_of_relstr(X3),X4)
          | proper_element(X4,powerset(the_carrier(X3))) ) )
      | empty_carrier(X3)
      | ~ reflexive_relstr(X3)
      | ~ transitive_relstr(X3)
      | ~ antisymmetric_relstr(X3)
      | ~ lower_bounded_relstr(X3)
      | ~ rel_str(X3) ),
    inference(shift_quantors,[status(thm)],[2191]) ).

fof(2193,plain,
    ! [X3,X4] :
      ( ( ~ proper_element(X4,powerset(the_carrier(X3)))
        | ~ in(bottom_of_relstr(X3),X4)
        | empty(X4)
        | ~ filtered_subset(X4,X3)
        | ~ upper_relstr_subset(X4,X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | empty_carrier(X3)
        | ~ reflexive_relstr(X3)
        | ~ transitive_relstr(X3)
        | ~ antisymmetric_relstr(X3)
        | ~ lower_bounded_relstr(X3)
        | ~ rel_str(X3) )
      & ( in(bottom_of_relstr(X3),X4)
        | proper_element(X4,powerset(the_carrier(X3)))
        | empty(X4)
        | ~ filtered_subset(X4,X3)
        | ~ upper_relstr_subset(X4,X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | empty_carrier(X3)
        | ~ reflexive_relstr(X3)
        | ~ transitive_relstr(X3)
        | ~ antisymmetric_relstr(X3)
        | ~ lower_bounded_relstr(X3)
        | ~ rel_str(X3) ) ),
    inference(distribute,[status(thm)],[2192]) ).

cnf(2195,plain,
    ( empty_carrier(X1)
    | empty(X2)
    | ~ rel_str(X1)
    | ~ lower_bounded_relstr(X1)
    | ~ antisymmetric_relstr(X1)
    | ~ transitive_relstr(X1)
    | ~ reflexive_relstr(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ upper_relstr_subset(X2,X1)
    | ~ filtered_subset(X2,X1)
    | ~ in(bottom_of_relstr(X1),X2)
    | ~ proper_element(X2,powerset(the_carrier(X1))) ),
    inference(split_conjunct,[status(thm)],[2193]) ).

fof(2843,plain,
    ! [X2] : boole_POSet(X2) = poset_of_lattice(boole_lattice(X2)),
    inference(variable_rename,[status(thm)],[203]) ).

cnf(2844,plain,
    boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[2843]) ).

fof(3114,plain,
    ! [X2] :
      ( ~ empty_carrier(boole_POSet(X2))
      & strict_rel_str(boole_POSet(X2))
      & reflexive_relstr(boole_POSet(X2))
      & transitive_relstr(boole_POSet(X2))
      & antisymmetric_relstr(boole_POSet(X2))
      & with_suprema_relstr(boole_POSet(X2))
      & with_infima_relstr(boole_POSet(X2))
      & complete_relstr(boole_POSet(X2))
      & lower_bounded_relstr(boole_POSet(X2))
      & upper_bounded_relstr(boole_POSet(X2))
      & bounded_relstr(boole_POSet(X2))
      & up_complete_relstr(boole_POSet(X2))
      & join_complete_relstr(boole_POSet(X2))
      & distributive_relstr(boole_POSet(X2))
      & complemented_relstr(boole_POSet(X2)) ),
    inference(variable_rename,[status(thm)],[937]) ).

cnf(3121,plain,
    lower_bounded_relstr(boole_POSet(X1)),
    inference(split_conjunct,[status(thm)],[3114]) ).

cnf(3125,plain,
    antisymmetric_relstr(boole_POSet(X1)),
    inference(split_conjunct,[status(thm)],[3114]) ).

cnf(3126,plain,
    transitive_relstr(boole_POSet(X1)),
    inference(split_conjunct,[status(thm)],[3114]) ).

cnf(3127,plain,
    reflexive_relstr(boole_POSet(X1)),
    inference(split_conjunct,[status(thm)],[3114]) ).

cnf(3129,plain,
    ~ empty_carrier(boole_POSet(X1)),
    inference(split_conjunct,[status(thm)],[3114]) ).

fof(3133,plain,
    ! [X2] : bottom_of_relstr(boole_POSet(X2)) = empty_set,
    inference(variable_rename,[status(thm)],[233]) ).

cnf(3134,plain,
    bottom_of_relstr(boole_POSet(X1)) = empty_set,
    inference(split_conjunct,[status(thm)],[3133]) ).

fof(4557,plain,
    ! [X2] : the_carrier(boole_POSet(X2)) = powerset(X2),
    inference(variable_rename,[status(thm)],[456]) ).

cnf(4558,plain,
    the_carrier(boole_POSet(X1)) = powerset(X1),
    inference(split_conjunct,[status(thm)],[4557]) ).

fof(4790,plain,
    ! [X2] :
      ( strict_rel_str(boole_POSet(X2))
      & rel_str(boole_POSet(X2)) ),
    inference(variable_rename,[status(thm)],[493]) ).

cnf(4791,plain,
    rel_str(boole_POSet(X1)),
    inference(split_conjunct,[status(thm)],[4790]) ).

fof(6677,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | ~ empty(X2) ),
    inference(fof_nnf,[status(thm)],[754]) ).

fof(6678,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ empty(X4) ),
    inference(variable_rename,[status(thm)],[6677]) ).

cnf(6679,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[6678]) ).

fof(6693,negated_conjecture,
    ? [X1] :
      ( ~ empty(X1)
      & ? [X2] :
          ( ~ empty(X2)
          & filtered_subset(X2,boole_POSet(X1))
          & upper_relstr_subset(X2,boole_POSet(X1))
          & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
          & element(X2,powerset(the_carrier(boole_POSet(X1))))
          & ? [X3] :
              ( in(X3,X2)
              & empty(X3) ) ) ),
    inference(fof_nnf,[status(thm)],[1094]) ).

fof(6694,negated_conjecture,
    ? [X4] :
      ( ~ empty(X4)
      & ? [X5] :
          ( ~ empty(X5)
          & filtered_subset(X5,boole_POSet(X4))
          & upper_relstr_subset(X5,boole_POSet(X4))
          & proper_element(X5,powerset(the_carrier(boole_POSet(X4))))
          & element(X5,powerset(the_carrier(boole_POSet(X4))))
          & ? [X6] :
              ( in(X6,X5)
              & empty(X6) ) ) ),
    inference(variable_rename,[status(thm)],[6693]) ).

fof(6695,negated_conjecture,
    ( ~ empty(esk507_0)
    & ~ empty(esk508_0)
    & filtered_subset(esk508_0,boole_POSet(esk507_0))
    & upper_relstr_subset(esk508_0,boole_POSet(esk507_0))
    & proper_element(esk508_0,powerset(the_carrier(boole_POSet(esk507_0))))
    & element(esk508_0,powerset(the_carrier(boole_POSet(esk507_0))))
    & in(esk509_0,esk508_0)
    & empty(esk509_0) ),
    inference(skolemize,[status(esa)],[6694]) ).

cnf(6696,negated_conjecture,
    empty(esk509_0),
    inference(split_conjunct,[status(thm)],[6695]) ).

cnf(6697,negated_conjecture,
    in(esk509_0,esk508_0),
    inference(split_conjunct,[status(thm)],[6695]) ).

cnf(6698,negated_conjecture,
    element(esk508_0,powerset(the_carrier(boole_POSet(esk507_0)))),
    inference(split_conjunct,[status(thm)],[6695]) ).

cnf(6699,negated_conjecture,
    proper_element(esk508_0,powerset(the_carrier(boole_POSet(esk507_0)))),
    inference(split_conjunct,[status(thm)],[6695]) ).

cnf(6700,negated_conjecture,
    upper_relstr_subset(esk508_0,boole_POSet(esk507_0)),
    inference(split_conjunct,[status(thm)],[6695]) ).

cnf(6701,negated_conjecture,
    filtered_subset(esk508_0,boole_POSet(esk507_0)),
    inference(split_conjunct,[status(thm)],[6695]) ).

fof(6991,plain,
    ! [X1] :
      ( ~ empty(X1)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[810]) ).

fof(6992,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[6991]) ).

cnf(6993,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[6992]) ).

cnf(7577,negated_conjecture,
    element(esk508_0,the_carrier(boole_POSet(the_carrier(boole_POSet(esk507_0))))),
    inference(rw,[status(thm)],[6698,4558,theory(equality)]),
    [unfolding] ).

cnf(7578,negated_conjecture,
    proper_element(esk508_0,the_carrier(boole_POSet(the_carrier(boole_POSet(esk507_0))))),
    inference(rw,[status(thm)],[6699,4558,theory(equality)]),
    [unfolding] ).

cnf(8546,plain,
    ( empty_carrier(X1)
    | empty(X2)
    | ~ rel_str(X1)
    | ~ antisymmetric_relstr(X1)
    | ~ transitive_relstr(X1)
    | ~ lower_bounded_relstr(X1)
    | ~ reflexive_relstr(X1)
    | ~ filtered_subset(X2,X1)
    | ~ upper_relstr_subset(X2,X1)
    | ~ in(bottom_of_relstr(X1),X2)
    | ~ element(X2,the_carrier(boole_POSet(the_carrier(X1))))
    | ~ proper_element(X2,the_carrier(boole_POSet(the_carrier(X1)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2195,4558,theory(equality)]),4558,theory(equality)]),
    [unfolding] ).

cnf(8595,plain,
    bottom_of_relstr(poset_of_lattice(boole_lattice(X1))) = empty_set,
    inference(rw,[status(thm)],[3134,2844,theory(equality)]),
    [unfolding] ).

cnf(8596,plain,
    rel_str(poset_of_lattice(boole_lattice(X1))),
    inference(rw,[status(thm)],[4791,2844,theory(equality)]),
    [unfolding] ).

cnf(8597,plain,
    antisymmetric_relstr(poset_of_lattice(boole_lattice(X1))),
    inference(rw,[status(thm)],[3125,2844,theory(equality)]),
    [unfolding] ).

cnf(8603,plain,
    transitive_relstr(poset_of_lattice(boole_lattice(X1))),
    inference(rw,[status(thm)],[3126,2844,theory(equality)]),
    [unfolding] ).

cnf(8610,plain,
    lower_bounded_relstr(poset_of_lattice(boole_lattice(X1))),
    inference(rw,[status(thm)],[3121,2844,theory(equality)]),
    [unfolding] ).

cnf(8632,plain,
    reflexive_relstr(poset_of_lattice(boole_lattice(X1))),
    inference(rw,[status(thm)],[3127,2844,theory(equality)]),
    [unfolding] ).

cnf(8673,negated_conjecture,
    filtered_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0))),
    inference(rw,[status(thm)],[6701,2844,theory(equality)]),
    [unfolding] ).

cnf(8674,negated_conjecture,
    upper_relstr_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0))),
    inference(rw,[status(thm)],[6700,2844,theory(equality)]),
    [unfolding] ).

cnf(8681,negated_conjecture,
    element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[7577,2844,theory(equality)]),2844,theory(equality)]),
    [unfolding] ).

cnf(8682,negated_conjecture,
    proper_element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[7578,2844,theory(equality)]),2844,theory(equality)]),
    [unfolding] ).

cnf(9671,plain,
    ( empty_carrier(X1)
    | empty(X2)
    | ~ rel_str(X1)
    | ~ antisymmetric_relstr(X1)
    | ~ transitive_relstr(X1)
    | ~ lower_bounded_relstr(X1)
    | ~ reflexive_relstr(X1)
    | ~ filtered_subset(X2,X1)
    | ~ upper_relstr_subset(X2,X1)
    | ~ in(bottom_of_relstr(X1),X2)
    | ~ element(X2,the_carrier(poset_of_lattice(boole_lattice(the_carrier(X1)))))
    | ~ proper_element(X2,the_carrier(poset_of_lattice(boole_lattice(the_carrier(X1))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[8546,2844,theory(equality)]),2844,theory(equality)]),
    [unfolding] ).

cnf(9692,plain,
    ~ empty_carrier(poset_of_lattice(boole_lattice(X1))),
    inference(rw,[status(thm)],[3129,2844,theory(equality)]),
    [unfolding] ).

cnf(10519,negated_conjecture,
    empty_set = esk509_0,
    inference(spm,[status(thm)],[6993,6696,theory(equality)]) ).

cnf(77306,plain,
    ( empty_carrier(X1)
    | ~ proper_element(X2,the_carrier(poset_of_lattice(boole_lattice(the_carrier(X1)))))
    | ~ upper_relstr_subset(X2,X1)
    | ~ reflexive_relstr(X1)
    | ~ lower_bounded_relstr(X1)
    | ~ filtered_subset(X2,X1)
    | ~ transitive_relstr(X1)
    | ~ antisymmetric_relstr(X1)
    | ~ rel_str(X1)
    | ~ in(bottom_of_relstr(X1),X2)
    | ~ element(X2,the_carrier(poset_of_lattice(boole_lattice(the_carrier(X1))))) ),
    inference(csr,[status(thm)],[9671,6679]) ).

cnf(77307,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ upper_relstr_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0)))
    | ~ reflexive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ filtered_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0)))
    | ~ transitive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(spm,[status(thm)],[77306,8682,theory(equality)]) ).

cnf(77321,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | ~ reflexive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ filtered_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0)))
    | ~ transitive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77307,8674,theory(equality)]) ).

cnf(77322,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ filtered_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0)))
    | ~ transitive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77321,8632,theory(equality)]) ).

cnf(77323,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | ~ filtered_subset(esk508_0,poset_of_lattice(boole_lattice(esk507_0)))
    | ~ transitive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77322,8610,theory(equality)]) ).

cnf(77324,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | $false
    | ~ transitive_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77323,8673,theory(equality)]) ).

cnf(77325,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | $false
    | $false
    | ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77324,8603,theory(equality)]) ).

cnf(77326,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | ~ rel_str(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77325,8597,theory(equality)]) ).

cnf(77327,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(esk507_0))),esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77326,8596,theory(equality)]) ).

cnf(77328,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | ~ in(empty_set,esk508_0)
    | ~ element(esk508_0,the_carrier(poset_of_lattice(boole_lattice(the_carrier(poset_of_lattice(boole_lattice(esk507_0))))))) ),
    inference(rw,[status(thm)],[77327,8595,theory(equality)]) ).

cnf(77329,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | $false
    | ~ in(empty_set,esk508_0)
    | $false ),
    inference(rw,[status(thm)],[77328,8681,theory(equality)]) ).

cnf(77330,negated_conjecture,
    ( empty_carrier(poset_of_lattice(boole_lattice(esk507_0)))
    | ~ in(empty_set,esk508_0) ),
    inference(cn,[status(thm)],[77329,theory(equality)]) ).

cnf(77331,negated_conjecture,
    ~ in(empty_set,esk508_0),
    inference(sr,[status(thm)],[77330,9692,theory(equality)]) ).

cnf(238011,negated_conjecture,
    in(empty_set,esk508_0),
    inference(rw,[status(thm)],[6697,10519,theory(equality)]) ).

cnf(238062,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[238011,77331,theory(equality)]) ).

cnf(238063,negated_conjecture,
    $false,
    238062,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU387+2.p
% --creating new selector for []
% -running prover on /tmp/tmpwIHhuV/sel_SEU387+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU387+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU387+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU387+2.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------