TSTP Solution File: GRA005+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA005+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 : Sat Dec 25 09:54:32 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 93 ( 36 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 117 ( 54 ~; 29 |; 28 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 81 ( 10 sgn 47 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X4,X5,X1,X2,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X1,X2,X7) )
=> ( ~ ? [X8] :
( tail_of(X8) = tail_of(X1)
& head_of(X8) = head_of(X2) )
& ~ precedes(X2,X1,X7) ) ),
file('/tmp/tmpMbBRuG/sel_GRA005+1.p_1',shortest_path_properties) ).
fof(7,conjecture,
! [X4,X5,X1,X2,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X1,X2,X7) )
=> ~ ? [X8] :
( edge(X8)
& tail_of(X8) = tail_of(X1)
& head_of(X8) = head_of(X2) ) ),
file('/tmp/tmpMbBRuG/sel_GRA005+1.p_1',no_short_cut_edge) ).
fof(13,negated_conjecture,
~ ! [X4,X5,X1,X2,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X1,X2,X7) )
=> ~ ? [X8] :
( edge(X8)
& tail_of(X8) = tail_of(X1)
& head_of(X8) = head_of(X2) ) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(15,plain,
! [X4,X5,X1,X2,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X1,X2,X7) )
=> ( ~ ? [X8] :
( tail_of(X8) = tail_of(X1)
& head_of(X8) = head_of(X2) )
& ~ precedes(X2,X1,X7) ) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(48,plain,
! [X4,X5,X1,X2,X7] :
( ~ shortest_path(X4,X5,X7)
| ~ precedes(X1,X2,X7)
| ( ! [X8] :
( tail_of(X8) != tail_of(X1)
| head_of(X8) != head_of(X2) )
& ~ precedes(X2,X1,X7) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(49,plain,
! [X9,X10,X11,X12,X13] :
( ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ( ! [X14] :
( tail_of(X14) != tail_of(X11)
| head_of(X14) != head_of(X12) )
& ~ precedes(X12,X11,X13) ) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ( tail_of(X14) != tail_of(X11)
| head_of(X14) != head_of(X12) )
& ~ precedes(X12,X11,X13) )
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13) ),
inference(shift_quantors,[status(thm)],[49]) ).
fof(51,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( tail_of(X14) != tail_of(X11)
| head_of(X14) != head_of(X12)
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13) )
& ( ~ precedes(X12,X11,X13)
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13) ) ),
inference(distribute,[status(thm)],[50]) ).
cnf(53,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| head_of(X6) != head_of(X2)
| tail_of(X6) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(60,negated_conjecture,
? [X4,X5,X1,X2,X7] :
( shortest_path(X4,X5,X7)
& precedes(X1,X2,X7)
& ? [X8] :
( edge(X8)
& tail_of(X8) = tail_of(X1)
& head_of(X8) = head_of(X2) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(61,negated_conjecture,
? [X9,X10,X11,X12,X13] :
( shortest_path(X9,X10,X13)
& precedes(X11,X12,X13)
& ? [X14] :
( edge(X14)
& tail_of(X14) = tail_of(X11)
& head_of(X14) = head_of(X12) ) ),
inference(variable_rename,[status(thm)],[60]) ).
fof(62,negated_conjecture,
( shortest_path(esk3_0,esk4_0,esk7_0)
& precedes(esk5_0,esk6_0,esk7_0)
& edge(esk8_0)
& tail_of(esk8_0) = tail_of(esk5_0)
& head_of(esk8_0) = head_of(esk6_0) ),
inference(skolemize,[status(esa)],[61]) ).
cnf(63,negated_conjecture,
head_of(esk8_0) = head_of(esk6_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(64,negated_conjecture,
tail_of(esk8_0) = tail_of(esk5_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(66,negated_conjecture,
precedes(esk5_0,esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(67,negated_conjecture,
shortest_path(esk3_0,esk4_0,esk7_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(112,negated_conjecture,
( head_of(esk6_0) != head_of(X1)
| tail_of(esk5_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk7_0) ),
inference(spm,[status(thm)],[53,66,theory(equality)]) ).
cnf(113,negated_conjecture,
( head_of(esk8_0) != head_of(X1)
| tail_of(esk5_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk7_0) ),
inference(rw,[status(thm)],[112,63,theory(equality)]) ).
cnf(114,negated_conjecture,
( head_of(esk8_0) != head_of(X1)
| tail_of(esk8_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk7_0) ),
inference(rw,[status(thm)],[113,64,theory(equality)]) ).
fof(142,plain,
( ~ epred1_0
<=> ! [X1] :
( tail_of(esk8_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ) ),
introduced(definition),
[split] ).
cnf(143,plain,
( epred1_0
| tail_of(esk8_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ),
inference(split_equiv,[status(thm)],[142]) ).
fof(144,plain,
( ~ epred2_0
<=> ! [X3,X2] : ~ shortest_path(X2,X3,esk7_0) ),
introduced(definition),
[split] ).
cnf(145,plain,
( epred2_0
| ~ shortest_path(X2,X3,esk7_0) ),
inference(split_equiv,[status(thm)],[144]) ).
cnf(146,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[114,142,theory(equality)]),144,theory(equality)]),
[split] ).
cnf(147,negated_conjecture,
epred2_0,
inference(spm,[status(thm)],[145,67,theory(equality)]) ).
cnf(149,negated_conjecture,
( $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[146,147,theory(equality)]) ).
cnf(150,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[149,theory(equality)]) ).
cnf(151,negated_conjecture,
epred1_0,
inference(er,[status(thm)],[143,theory(equality)]) ).
cnf(153,negated_conjecture,
$false,
inference(sr,[status(thm)],[151,150,theory(equality)]) ).
cnf(154,negated_conjecture,
$false,
153,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA005+1.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmpMbBRuG/sel_GRA005+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRA005+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA005+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA005+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
%
%------------------------------------------------------------------------------