TSTP Solution File: SET707+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET707+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:14:26 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 74 ( 23 unt; 0 def)
% Number of atoms : 188 ( 67 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 65 ~; 77 |; 30 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 4 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpKYHSqf/sel_SET707+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpKYHSqf/sel_SET707+4.p_1',equal_set) ).
fof(3,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/tmp/tmpKYHSqf/sel_SET707+4.p_1',singleton) ).
fof(4,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/tmp/tmpKYHSqf/sel_SET707+4.p_1',unordered_pair) ).
fof(5,conjecture,
! [X1,X2,X4,X5] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X4),unordered_pair(X4,X5)))
=> ( X1 = X4
& X2 = X5 ) ),
file('/tmp/tmpKYHSqf/sel_SET707+4.p_1',thI50) ).
fof(6,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X4),unordered_pair(X4,X5)))
=> ( X1 = X4
& X2 = X5 ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(8,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[8]) ).
fof(10,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[9]) ).
fof(11,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[10]) ).
cnf(14,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( subset(X2,X1)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X3,X1] :
( ( ~ member(X3,singleton(X1))
| X3 = X1 )
& ( X3 != X1
| member(X3,singleton(X1)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(22,plain,
! [X4,X5] :
( ( ~ member(X4,singleton(X5))
| X4 = X5 )
& ( X4 != X5
| member(X4,singleton(X5)) ) ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(25,plain,
! [X3,X1,X2] :
( ( ~ member(X3,unordered_pair(X1,X2))
| X3 = X1
| X3 = X2 )
& ( ( X3 != X1
& X3 != X2 )
| member(X3,unordered_pair(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ member(X4,unordered_pair(X5,X6))
| X4 = X5
| X4 = X6 )
& ( ( X4 != X5
& X4 != X6 )
| member(X4,unordered_pair(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] :
( ( ~ member(X4,unordered_pair(X5,X6))
| X4 = X5
| X4 = X6 )
& ( X4 != X5
| member(X4,unordered_pair(X5,X6)) )
& ( X4 != X6
| member(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(31,negated_conjecture,
? [X1,X2,X4,X5] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X4),unordered_pair(X4,X5)))
& ( X1 != X4
| X2 != X5 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(32,negated_conjecture,
? [X6,X7,X8,X9] :
( equal_set(unordered_pair(singleton(X6),unordered_pair(X6,X7)),unordered_pair(singleton(X8),unordered_pair(X8,X9)))
& ( X6 != X8
| X7 != X9 ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( equal_set(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)))
& ( esk2_0 != esk4_0
| esk3_0 != esk5_0 ) ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
( esk3_0 != esk5_0
| esk2_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
equal_set(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[23,theory(equality)]) ).
cnf(37,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[28,theory(equality)]) ).
cnf(38,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[29,theory(equality)]) ).
cnf(39,negated_conjecture,
subset(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))),
inference(spm,[status(thm)],[19,35,theory(equality)]) ).
cnf(40,negated_conjecture,
subset(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(spm,[status(thm)],[20,35,theory(equality)]) ).
cnf(65,negated_conjecture,
( member(X1,unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)))
| ~ member(X1,unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))) ),
inference(spm,[status(thm)],[14,39,theory(equality)]) ).
cnf(67,negated_conjecture,
( equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)))
| ~ subset(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))) ),
inference(spm,[status(thm)],[18,40,theory(equality)]) ).
cnf(69,negated_conjecture,
( equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)))
| $false ),
inference(rw,[status(thm)],[67,39,theory(equality)]) ).
cnf(70,negated_conjecture,
equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))),
inference(cn,[status(thm)],[69,theory(equality)]) ).
cnf(178,negated_conjecture,
member(singleton(esk4_0),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))),
inference(spm,[status(thm)],[65,38,theory(equality)]) ).
cnf(180,negated_conjecture,
( singleton(esk4_0) = unordered_pair(esk2_0,esk3_0)
| singleton(esk4_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[30,178,theory(equality)]) ).
cnf(185,negated_conjecture,
( member(esk2_0,singleton(esk4_0))
| singleton(esk4_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[38,180,theory(equality)]) ).
cnf(240,negated_conjecture,
( esk2_0 = esk4_0
| singleton(esk4_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[24,185,theory(equality)]) ).
cnf(247,negated_conjecture,
( member(esk4_0,singleton(esk2_0))
| esk4_0 = esk2_0 ),
inference(spm,[status(thm)],[36,240,theory(equality)]) ).
cnf(266,negated_conjecture,
esk4_0 = esk2_0,
inference(csr,[status(thm)],[247,24]) ).
cnf(269,negated_conjecture,
equal_set(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk5_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[70,266,theory(equality)]),266,theory(equality)]) ).
cnf(288,negated_conjecture,
( member(X1,unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)))
| ~ member(X1,unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk5_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[65,266,theory(equality)]),266,theory(equality)]) ).
cnf(289,negated_conjecture,
( $false
| esk5_0 != esk3_0 ),
inference(rw,[status(thm)],[34,266,theory(equality)]) ).
cnf(290,negated_conjecture,
esk5_0 != esk3_0,
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(311,negated_conjecture,
member(unordered_pair(esk2_0,esk5_0),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))),
inference(spm,[status(thm)],[288,37,theory(equality)]) ).
cnf(331,negated_conjecture,
( unordered_pair(esk2_0,esk5_0) = unordered_pair(esk2_0,esk3_0)
| unordered_pair(esk2_0,esk5_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[30,311,theory(equality)]) ).
cnf(337,negated_conjecture,
( member(esk5_0,unordered_pair(esk2_0,esk3_0))
| unordered_pair(esk2_0,esk5_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[37,331,theory(equality)]) ).
cnf(355,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk2_0
| unordered_pair(esk2_0,esk5_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[30,337,theory(equality)]) ).
cnf(360,negated_conjecture,
( esk5_0 = esk2_0
| unordered_pair(esk2_0,esk5_0) = singleton(esk2_0) ),
inference(sr,[status(thm)],[355,290,theory(equality)]) ).
cnf(376,negated_conjecture,
( member(esk5_0,singleton(esk2_0))
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[37,360,theory(equality)]) ).
cnf(401,negated_conjecture,
esk5_0 = esk2_0,
inference(csr,[status(thm)],[376,24]) ).
cnf(403,negated_conjecture,
esk2_0 != esk3_0,
inference(rw,[status(thm)],[290,401,theory(equality)]) ).
cnf(410,negated_conjecture,
( unordered_pair(esk2_0,esk2_0) = unordered_pair(esk2_0,esk3_0)
| unordered_pair(esk2_0,esk5_0) = singleton(esk2_0) ),
inference(rw,[status(thm)],[331,401,theory(equality)]) ).
cnf(411,negated_conjecture,
( unordered_pair(esk2_0,esk2_0) = unordered_pair(esk2_0,esk3_0)
| unordered_pair(esk2_0,esk2_0) = singleton(esk2_0) ),
inference(rw,[status(thm)],[410,401,theory(equality)]) ).
cnf(413,negated_conjecture,
( member(esk3_0,unordered_pair(esk2_0,esk2_0))
| unordered_pair(esk2_0,esk2_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[37,411,theory(equality)]) ).
cnf(435,negated_conjecture,
( esk3_0 = esk2_0
| unordered_pair(esk2_0,esk2_0) = singleton(esk2_0) ),
inference(spm,[status(thm)],[30,413,theory(equality)]) ).
cnf(443,negated_conjecture,
unordered_pair(esk2_0,esk2_0) = singleton(esk2_0),
inference(sr,[status(thm)],[435,403,theory(equality)]) ).
cnf(526,negated_conjecture,
equal_set(unordered_pair(singleton(esk2_0),singleton(esk2_0)),unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[269,401,theory(equality)]),443,theory(equality)]) ).
cnf(527,negated_conjecture,
subset(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),unordered_pair(singleton(esk2_0),singleton(esk2_0))),
inference(spm,[status(thm)],[19,526,theory(equality)]) ).
cnf(531,negated_conjecture,
( member(X1,unordered_pair(singleton(esk2_0),singleton(esk2_0)))
| ~ member(X1,unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0))) ),
inference(spm,[status(thm)],[14,527,theory(equality)]) ).
cnf(596,negated_conjecture,
member(unordered_pair(esk2_0,esk3_0),unordered_pair(singleton(esk2_0),singleton(esk2_0))),
inference(spm,[status(thm)],[531,37,theory(equality)]) ).
cnf(604,negated_conjecture,
unordered_pair(esk2_0,esk3_0) = singleton(esk2_0),
inference(spm,[status(thm)],[30,596,theory(equality)]) ).
cnf(612,negated_conjecture,
member(esk3_0,singleton(esk2_0)),
inference(spm,[status(thm)],[37,604,theory(equality)]) ).
cnf(645,negated_conjecture,
esk3_0 = esk2_0,
inference(spm,[status(thm)],[24,612,theory(equality)]) ).
cnf(654,negated_conjecture,
$false,
inference(sr,[status(thm)],[645,403,theory(equality)]) ).
cnf(655,negated_conjecture,
$false,
654,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET707+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpKYHSqf/sel_SET707+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET707+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET707+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET707+4.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
%
%------------------------------------------------------------------------------