TSTP Solution File: SEU171+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU171+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 05:04:50 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 206 ( 33 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 254 ( 93 ~; 85 |; 50 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn 56 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,conjecture,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/tmp/tmpWvFQ5H/sel_SEU171+1.p_1',t50_subset_1) ).
fof(12,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/tmp/tmpWvFQ5H/sel_SEU171+1.p_1',d2_subset_1) ).
fof(13,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpWvFQ5H/sel_SEU171+1.p_1',d4_xboole_0) ).
fof(15,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/tmp/tmpWvFQ5H/sel_SEU171+1.p_1',d5_subset_1) ).
fof(18,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpWvFQ5H/sel_SEU171+1.p_1',t6_boole) ).
fof(24,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(27,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(30,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(31,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).
fof(47,negated_conjecture,
? [X1] :
( X1 != empty_set
& ? [X2] :
( element(X2,powerset(X1))
& ? [X3] :
( element(X3,X1)
& ~ in(X3,X2)
& ~ in(X3,subset_complement(X1,X2)) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(48,negated_conjecture,
? [X4] :
( X4 != empty_set
& ? [X5] :
( element(X5,powerset(X4))
& ? [X6] :
( element(X6,X4)
& ~ in(X6,X5)
& ~ in(X6,subset_complement(X4,X5)) ) ) ),
inference(variable_rename,[status(thm)],[47]) ).
fof(49,negated_conjecture,
( esk3_0 != empty_set
& element(esk4_0,powerset(esk3_0))
& element(esk5_0,esk3_0)
& ~ in(esk5_0,esk4_0)
& ~ in(esk5_0,subset_complement(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[48]) ).
cnf(50,negated_conjecture,
~ in(esk5_0,subset_complement(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(51,negated_conjecture,
~ in(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(52,negated_conjecture,
element(esk5_0,esk3_0),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(53,negated_conjecture,
element(esk4_0,powerset(esk3_0)),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(54,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[49]) ).
fof(68,plain,
! [X1,X2] :
( ( empty(X1)
| ( ( ~ element(X2,X1)
| in(X2,X1) )
& ( ~ in(X2,X1)
| element(X2,X1) ) ) )
& ( ~ empty(X1)
| ( ( ~ element(X2,X1)
| empty(X2) )
& ( ~ empty(X2)
| element(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(69,plain,
! [X3,X4] :
( ( empty(X3)
| ( ( ~ element(X4,X3)
| in(X4,X3) )
& ( ~ in(X4,X3)
| element(X4,X3) ) ) )
& ( ~ empty(X3)
| ( ( ~ element(X4,X3)
| empty(X4) )
& ( ~ empty(X4)
| element(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[68]) ).
fof(70,plain,
! [X3,X4] :
( ( ~ element(X4,X3)
| in(X4,X3)
| empty(X3) )
& ( ~ in(X4,X3)
| element(X4,X3)
| empty(X3) )
& ( ~ element(X4,X3)
| empty(X4)
| ~ empty(X3) )
& ( ~ empty(X4)
| element(X4,X3)
| ~ empty(X3) ) ),
inference(distribute,[status(thm)],[69]) ).
cnf(74,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(75,plain,
! [X1,X2,X3] :
( ( X3 != set_difference(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) )
& ( ~ in(X4,X1)
| in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) ) )
| X3 = set_difference(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(76,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& ~ in(X9,X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(variable_rename,[status(thm)],[75]) ).
fof(77,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& ~ in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[76]) ).
fof(78,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) )
| X7 != set_difference(X5,X6) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& ~ in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[77]) ).
fof(79,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk6_3(X5,X6,X7),X6)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[78]) ).
cnf(83,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(87,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(88,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[87]) ).
cnf(89,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(94,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(95,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[94]) ).
cnf(96,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(115,negated_conjecture,
( in(esk5_0,esk3_0)
| empty(esk3_0) ),
inference(spm,[status(thm)],[74,52,theory(equality)]) ).
cnf(137,negated_conjecture,
( ~ in(esk5_0,set_difference(esk3_0,esk4_0))
| ~ element(esk4_0,powerset(esk3_0)) ),
inference(spm,[status(thm)],[50,89,theory(equality)]) ).
cnf(141,negated_conjecture,
( ~ in(esk5_0,set_difference(esk3_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[137,53,theory(equality)]) ).
cnf(142,negated_conjecture,
~ in(esk5_0,set_difference(esk3_0,esk4_0)),
inference(cn,[status(thm)],[141,theory(equality)]) ).
cnf(151,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[83,theory(equality)]) ).
cnf(177,negated_conjecture,
( empty_set = esk3_0
| in(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[96,115,theory(equality)]) ).
cnf(179,negated_conjecture,
in(esk5_0,esk3_0),
inference(sr,[status(thm)],[177,54,theory(equality)]) ).
cnf(451,negated_conjecture,
( in(esk5_0,esk4_0)
| ~ in(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[142,151,theory(equality)]) ).
cnf(463,negated_conjecture,
( in(esk5_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[451,179,theory(equality)]) ).
cnf(464,negated_conjecture,
in(esk5_0,esk4_0),
inference(cn,[status(thm)],[463,theory(equality)]) ).
cnf(465,negated_conjecture,
$false,
inference(sr,[status(thm)],[464,51,theory(equality)]) ).
cnf(466,negated_conjecture,
$false,
465,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU171+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWvFQ5H/sel_SEU171+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU171+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU171+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU171+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
%
%------------------------------------------------------------------------------