TSTP Solution File: SEU177+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU177+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 05:07:04 EST 2010
% Result : Theorem 2.09s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 19 unt; 0 def)
% Number of atoms : 211 ( 48 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 266 ( 105 ~; 113 |; 38 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 129 ( 4 sgn 72 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',d5_relat_1) ).
fof(36,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',t20_relat_1) ).
fof(39,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',t69_enumset1) ).
fof(80,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',commutativity_k2_tarski) ).
fof(88,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',d4_relat_1) ).
fof(98,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',d5_tarski) ).
fof(143,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
inference(assume_negation,[status(cth)],[36]) ).
fof(165,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_rng(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) )
& ( ! [X4] : ~ in(ordered_pair(X4,X3),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X4,X3),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) ) )
| X2 = relation_rng(X1) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(166,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X8,X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X11,X10),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X12,X10),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk2_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(skolemize,[status(esa)],[166]) ).
fof(168,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) )
& ( ( ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) ) )
| X6 != relation_rng(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[167]) ).
fof(169,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[168]) ).
cnf(171,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[169]) ).
fof(284,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& in(ordered_pair(X1,X2),X3)
& ( ~ in(X1,relation_dom(X3))
| ~ in(X2,relation_rng(X3)) ) ),
inference(fof_nnf,[status(thm)],[143]) ).
fof(285,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& in(ordered_pair(X4,X5),X6)
& ( ~ in(X4,relation_dom(X6))
| ~ in(X5,relation_rng(X6)) ) ),
inference(variable_rename,[status(thm)],[284]) ).
fof(286,negated_conjecture,
( relation(esk12_0)
& in(ordered_pair(esk10_0,esk11_0),esk12_0)
& ( ~ in(esk10_0,relation_dom(esk12_0))
| ~ in(esk11_0,relation_rng(esk12_0)) ) ),
inference(skolemize,[status(esa)],[285]) ).
cnf(287,negated_conjecture,
( ~ in(esk11_0,relation_rng(esk12_0))
| ~ in(esk10_0,relation_dom(esk12_0)) ),
inference(split_conjunct,[status(thm)],[286]) ).
cnf(288,negated_conjecture,
in(ordered_pair(esk10_0,esk11_0),esk12_0),
inference(split_conjunct,[status(thm)],[286]) ).
cnf(289,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[286]) ).
fof(299,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[39]) ).
cnf(300,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[299]) ).
fof(450,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[80]) ).
cnf(451,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[450]) ).
fof(477,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_dom(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) )
& ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) ) )
| X2 = relation_dom(X1) ) ) ),
inference(fof_nnf,[status(thm)],[88]) ).
fof(478,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X7,X8),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X10,X12),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(variable_rename,[status(thm)],[477]) ).
fof(479,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk20_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk21_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk21_2(X5,X6),X11),X5) )
& ( in(esk21_2(X5,X6),X6)
| in(ordered_pair(esk21_2(X5,X6),esk22_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[478]) ).
fof(480,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk21_2(X5,X6),X11),X5)
| ~ in(esk21_2(X5,X6),X6) )
& ( in(esk21_2(X5,X6),X6)
| in(ordered_pair(esk21_2(X5,X6),esk22_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk20_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[479]) ).
fof(481,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk21_2(X5,X6),X11),X5)
| ~ in(esk21_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk21_2(X5,X6),X6)
| in(ordered_pair(esk21_2(X5,X6),esk22_2(X5,X6)),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk20_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[480]) ).
cnf(483,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[481]) ).
fof(512,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[98]) ).
cnf(513,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[512]) ).
cnf(710,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[513,300,theory(equality)]),
[unfolding] ).
cnf(754,negated_conjecture,
in(unordered_pair(unordered_pair(esk10_0,esk11_0),unordered_pair(esk10_0,esk10_0)),esk12_0),
inference(rw,[status(thm)],[288,710,theory(equality)]),
[unfolding] ).
cnf(767,plain,
( in(X3,X2)
| relation_rng(X1) != X2
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X1) ),
inference(rw,[status(thm)],[171,710,theory(equality)]),
[unfolding] ).
cnf(768,plain,
( in(X3,X2)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[483,710,theory(equality)]),
[unfolding] ).
cnf(787,negated_conjecture,
in(unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,esk11_0)),esk12_0),
inference(rw,[status(thm)],[754,451,theory(equality)]) ).
cnf(1385,plain,
( in(X1,X2)
| relation_rng(X3) != X2
| ~ in(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,X1)),X3)
| ~ relation(X3) ),
inference(spm,[status(thm)],[767,451,theory(equality)]) ).
cnf(1394,plain,
( in(X1,X2)
| relation_dom(X3) != X2
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X4)),X3)
| ~ relation(X3) ),
inference(spm,[status(thm)],[768,451,theory(equality)]) ).
cnf(31626,negated_conjecture,
( in(esk11_0,X1)
| relation_rng(esk12_0) != X1
| ~ relation(esk12_0) ),
inference(spm,[status(thm)],[1385,787,theory(equality)]) ).
cnf(31780,negated_conjecture,
( in(esk11_0,X1)
| relation_rng(esk12_0) != X1
| $false ),
inference(rw,[status(thm)],[31626,289,theory(equality)]) ).
cnf(31781,negated_conjecture,
( in(esk11_0,X1)
| relation_rng(esk12_0) != X1 ),
inference(cn,[status(thm)],[31780,theory(equality)]) ).
cnf(31784,negated_conjecture,
in(esk11_0,relation_rng(esk12_0)),
inference(er,[status(thm)],[31781,theory(equality)]) ).
cnf(31815,negated_conjecture,
( ~ in(esk10_0,relation_dom(esk12_0))
| $false ),
inference(rw,[status(thm)],[287,31784,theory(equality)]) ).
cnf(31816,negated_conjecture,
~ in(esk10_0,relation_dom(esk12_0)),
inference(cn,[status(thm)],[31815,theory(equality)]) ).
cnf(32558,negated_conjecture,
( in(esk10_0,X1)
| relation_dom(esk12_0) != X1
| ~ relation(esk12_0) ),
inference(spm,[status(thm)],[1394,787,theory(equality)]) ).
cnf(32712,negated_conjecture,
( in(esk10_0,X1)
| relation_dom(esk12_0) != X1
| $false ),
inference(rw,[status(thm)],[32558,289,theory(equality)]) ).
cnf(32713,negated_conjecture,
( in(esk10_0,X1)
| relation_dom(esk12_0) != X1 ),
inference(cn,[status(thm)],[32712,theory(equality)]) ).
cnf(32729,negated_conjecture,
in(esk10_0,relation_dom(esk12_0)),
inference(er,[status(thm)],[32713,theory(equality)]) ).
cnf(32732,negated_conjecture,
$false,
inference(sr,[status(thm)],[32729,31816,theory(equality)]) ).
cnf(32733,negated_conjecture,
$false,
32732,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU177+2.p
% --creating new selector for []
% -running prover on /tmp/tmpqyBnAY/sel_SEU177+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU177+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU177+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU177+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
%
%------------------------------------------------------------------------------