TSTP Solution File: SEU387+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU387+1 : 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 08:08:31 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 20 unt; 0 def)
% Number of atoms : 336 ( 8 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 436 ( 158 ~; 176 |; 89 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 57 ( 8 sgn 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(46,axiom,
! [X1] :
( strict_rel_str(boole_POSet(X1))
& rel_str(boole_POSet(X1)) ),
file('/tmp/tmpf4Devn/sel_SEU387+1.p_1',dt_k3_yellow_1) ).
fof(57,axiom,
! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
file('/tmp/tmpf4Devn/sel_SEU387+1.p_1',t18_yellow_1) ).
fof(58,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/tmpf4Devn/sel_SEU387+1.p_1',t2_yellow19) ).
fof(61,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/tmp/tmpf4Devn/sel_SEU387+1.p_1',t7_boole) ).
fof(64,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))
& lower_bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1)) ),
file('/tmp/tmpf4Devn/sel_SEU387+1.p_1',fc8_yellow_1) ).
fof(66,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/tmpf4Devn/sel_SEU387+1.p_1',t8_waybel_7) ).
fof(71,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpf4Devn/sel_SEU387+1.p_1',t6_boole) ).
fof(86,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)],[58]) ).
fof(115,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)],[86,theory(equality)]) ).
fof(118,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))
& lower_bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1)) ),
inference(fof_simplification,[status(thm)],[64,theory(equality)]) ).
fof(119,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)],[66,theory(equality)]) ).
fof(384,plain,
! [X2] :
( strict_rel_str(boole_POSet(X2))
& rel_str(boole_POSet(X2)) ),
inference(variable_rename,[status(thm)],[46]) ).
cnf(385,plain,
rel_str(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[384]) ).
fof(436,plain,
! [X2] : bottom_of_relstr(boole_POSet(X2)) = empty_set,
inference(variable_rename,[status(thm)],[57]) ).
cnf(437,plain,
bottom_of_relstr(boole_POSet(X1)) = empty_set,
inference(split_conjunct,[status(thm)],[436]) ).
fof(438,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)],[115]) ).
fof(439,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)],[438]) ).
fof(440,negated_conjecture,
( ~ empty(esk20_0)
& ~ empty(esk21_0)
& filtered_subset(esk21_0,boole_POSet(esk20_0))
& upper_relstr_subset(esk21_0,boole_POSet(esk20_0))
& proper_element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0))))
& element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0))))
& in(esk22_0,esk21_0)
& empty(esk22_0) ),
inference(skolemize,[status(esa)],[439]) ).
cnf(441,negated_conjecture,
empty(esk22_0),
inference(split_conjunct,[status(thm)],[440]) ).
cnf(442,negated_conjecture,
in(esk22_0,esk21_0),
inference(split_conjunct,[status(thm)],[440]) ).
cnf(443,negated_conjecture,
element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))),
inference(split_conjunct,[status(thm)],[440]) ).
cnf(444,negated_conjecture,
proper_element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))),
inference(split_conjunct,[status(thm)],[440]) ).
cnf(445,negated_conjecture,
upper_relstr_subset(esk21_0,boole_POSet(esk20_0)),
inference(split_conjunct,[status(thm)],[440]) ).
cnf(446,negated_conjecture,
filtered_subset(esk21_0,boole_POSet(esk20_0)),
inference(split_conjunct,[status(thm)],[440]) ).
fof(455,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(fof_nnf,[status(thm)],[61]) ).
fof(456,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[455]) ).
cnf(457,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[456]) ).
fof(469,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))
& lower_bounded_relstr(boole_POSet(X2))
& upper_bounded_relstr(boole_POSet(X2))
& bounded_relstr(boole_POSet(X2))
& with_suprema_relstr(boole_POSet(X2))
& with_infima_relstr(boole_POSet(X2))
& complete_relstr(boole_POSet(X2)) ),
inference(variable_rename,[status(thm)],[118]) ).
cnf(475,plain,
lower_bounded_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[469]) ).
cnf(476,plain,
antisymmetric_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[469]) ).
cnf(477,plain,
transitive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[469]) ).
cnf(478,plain,
reflexive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[469]) ).
cnf(480,plain,
~ empty_carrier(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[469]) ).
fof(484,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)],[119]) ).
fof(485,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)],[484]) ).
fof(486,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)],[485]) ).
fof(487,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)],[486]) ).
cnf(489,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)],[487]) ).
fof(529,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[71]) ).
fof(530,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[529]) ).
cnf(531,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[530]) ).
cnf(601,negated_conjecture,
empty_set = esk22_0,
inference(spm,[status(thm)],[531,441,theory(equality)]) ).
cnf(945,plain,
( empty_carrier(X1)
| ~ lower_bounded_relstr(X1)
| ~ upper_relstr_subset(X2,X1)
| ~ filtered_subset(X2,X1)
| ~ proper_element(X2,powerset(the_carrier(X1)))
| ~ in(bottom_of_relstr(X1),X2)
| ~ antisymmetric_relstr(X1)
| ~ transitive_relstr(X1)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(csr,[status(thm)],[489,457]) ).
cnf(946,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| ~ lower_bounded_relstr(boole_POSet(esk20_0))
| ~ upper_relstr_subset(esk21_0,boole_POSet(esk20_0))
| ~ filtered_subset(esk21_0,boole_POSet(esk20_0))
| ~ in(bottom_of_relstr(boole_POSet(esk20_0)),esk21_0)
| ~ antisymmetric_relstr(boole_POSet(esk20_0))
| ~ transitive_relstr(boole_POSet(esk20_0))
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(spm,[status(thm)],[945,444,theory(equality)]) ).
cnf(949,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| ~ upper_relstr_subset(esk21_0,boole_POSet(esk20_0))
| ~ filtered_subset(esk21_0,boole_POSet(esk20_0))
| ~ in(bottom_of_relstr(boole_POSet(esk20_0)),esk21_0)
| ~ antisymmetric_relstr(boole_POSet(esk20_0))
| ~ transitive_relstr(boole_POSet(esk20_0))
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[946,475,theory(equality)]) ).
cnf(950,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| ~ filtered_subset(esk21_0,boole_POSet(esk20_0))
| ~ in(bottom_of_relstr(boole_POSet(esk20_0)),esk21_0)
| ~ antisymmetric_relstr(boole_POSet(esk20_0))
| ~ transitive_relstr(boole_POSet(esk20_0))
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[949,445,theory(equality)]) ).
cnf(951,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(bottom_of_relstr(boole_POSet(esk20_0)),esk21_0)
| ~ antisymmetric_relstr(boole_POSet(esk20_0))
| ~ transitive_relstr(boole_POSet(esk20_0))
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[950,446,theory(equality)]) ).
cnf(952,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(empty_set,esk21_0)
| ~ antisymmetric_relstr(boole_POSet(esk20_0))
| ~ transitive_relstr(boole_POSet(esk20_0))
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[951,437,theory(equality)]) ).
cnf(953,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(empty_set,esk21_0)
| $false
| ~ transitive_relstr(boole_POSet(esk20_0))
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[952,476,theory(equality)]) ).
cnf(954,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(empty_set,esk21_0)
| $false
| $false
| ~ reflexive_relstr(boole_POSet(esk20_0))
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[953,477,theory(equality)]) ).
cnf(955,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(empty_set,esk21_0)
| $false
| $false
| $false
| ~ rel_str(boole_POSet(esk20_0))
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[954,478,theory(equality)]) ).
cnf(956,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(empty_set,esk21_0)
| $false
| $false
| $false
| $false
| ~ element(esk21_0,powerset(the_carrier(boole_POSet(esk20_0)))) ),
inference(rw,[status(thm)],[955,385,theory(equality)]) ).
cnf(957,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| $false
| $false
| $false
| ~ in(empty_set,esk21_0)
| $false
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[956,443,theory(equality)]) ).
cnf(958,negated_conjecture,
( empty_carrier(boole_POSet(esk20_0))
| ~ in(empty_set,esk21_0) ),
inference(cn,[status(thm)],[957,theory(equality)]) ).
cnf(959,negated_conjecture,
~ in(empty_set,esk21_0),
inference(sr,[status(thm)],[958,480,theory(equality)]) ).
cnf(968,negated_conjecture,
in(empty_set,esk21_0),
inference(rw,[status(thm)],[442,601,theory(equality)]) ).
cnf(969,negated_conjecture,
$false,
inference(sr,[status(thm)],[968,959,theory(equality)]) ).
cnf(970,negated_conjecture,
$false,
969,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU387+1.p
% --creating new selector for []
% -running prover on /tmp/tmpf4Devn/sel_SEU387+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU387+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU387+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU387+1.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
%
%------------------------------------------------------------------------------