TSTP Solution File: GRA008+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA008+2 : TPTP v5.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sat Dec 25 10:01:03 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 12 unt; 0 def)
% Number of atoms : 339 ( 75 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 460 ( 191 ~; 189 |; 71 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-5 aty)
% Number of variables : 226 ( 7 sgn 67 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X2,X3] :
( sequential(X2,X3)
<=> ( edge(X2)
& edge(X3)
& X2 != X3
& head_of(X2) = tail_of(X3) ) ),
file('/tmp/tmpENJofP/sel_GRA008+2.p_1',sequential_defn) ).
fof(3,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/tmp/tmpENJofP/sel_GRA008+2.p_1',no_loops) ).
fof(9,axiom,
( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7) )
=> ? [X8] :
( edge(X8)
& tail_of(X8) = head_of(X3)
& head_of(X8) = tail_of(X2) ) ) ),
file('/tmp/tmpENJofP/sel_GRA008+2.p_1',back_edge) ).
fof(14,conjecture,
( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) ),
file('/tmp/tmpENJofP/sel_GRA008+2.p_1',sequential_is_triangle) ).
fof(15,axiom,
! [X2,X3,X8] :
( triangle(X2,X3,X8)
<=> ( edge(X2)
& edge(X3)
& edge(X8)
& sequential(X2,X3)
& sequential(X3,X8)
& sequential(X8,X2) ) ),
file('/tmp/tmpENJofP/sel_GRA008+2.p_1',triangle_defn) ).
fof(16,negated_conjecture,
~ ( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(26,plain,
! [X2,X3] :
( ( ~ sequential(X2,X3)
| ( edge(X2)
& edge(X3)
& X2 != X3
& head_of(X2) = tail_of(X3) ) )
& ( ~ edge(X2)
| ~ edge(X3)
| X2 = X3
| head_of(X2) != tail_of(X3)
| sequential(X2,X3) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(27,plain,
! [X4,X5] :
( ( ~ sequential(X4,X5)
| ( edge(X4)
& edge(X5)
& X4 != X5
& head_of(X4) = tail_of(X5) ) )
& ( ~ edge(X4)
| ~ edge(X5)
| X4 = X5
| head_of(X4) != tail_of(X5)
| sequential(X4,X5) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X4,X5] :
( ( edge(X4)
| ~ sequential(X4,X5) )
& ( edge(X5)
| ~ sequential(X4,X5) )
& ( X4 != X5
| ~ sequential(X4,X5) )
& ( head_of(X4) = tail_of(X5)
| ~ sequential(X4,X5) )
& ( ~ edge(X4)
| ~ edge(X5)
| X4 = X5
| head_of(X4) != tail_of(X5)
| sequential(X4,X5) ) ),
inference(distribute,[status(thm)],[27]) ).
cnf(29,plain,
( sequential(X1,X2)
| X1 = X2
| head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(32,plain,
( edge(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(33,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(34,plain,
! [X1] :
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(35,plain,
! [X2] :
( ~ edge(X2)
| head_of(X2) != tail_of(X2) ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(80,plain,
( ~ complete
| ! [X4,X5,X2,X3,X7] :
( ~ shortest_path(X4,X5,X7)
| ~ precedes(X2,X3,X7)
| ? [X8] :
( edge(X8)
& tail_of(X8) = head_of(X3)
& head_of(X8) = tail_of(X2) ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(81,plain,
( ~ complete
| ! [X9,X10,X11,X12,X13] :
( ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ? [X14] :
( edge(X14)
& tail_of(X14) = head_of(X12)
& head_of(X14) = tail_of(X11) ) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
( ~ complete
| ! [X9,X10,X11,X12,X13] :
( ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ( edge(esk4_5(X9,X10,X11,X12,X13))
& tail_of(esk4_5(X9,X10,X11,X12,X13)) = head_of(X12)
& head_of(esk4_5(X9,X10,X11,X12,X13)) = tail_of(X11) ) ) ),
inference(skolemize,[status(esa)],[81]) ).
fof(83,plain,
! [X9,X10,X11,X12,X13] :
( ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ( edge(esk4_5(X9,X10,X11,X12,X13))
& tail_of(esk4_5(X9,X10,X11,X12,X13)) = head_of(X12)
& head_of(esk4_5(X9,X10,X11,X12,X13)) = tail_of(X11) )
| ~ complete ),
inference(shift_quantors,[status(thm)],[82]) ).
fof(84,plain,
! [X9,X10,X11,X12,X13] :
( ( edge(esk4_5(X9,X10,X11,X12,X13))
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ~ complete )
& ( tail_of(esk4_5(X9,X10,X11,X12,X13)) = head_of(X12)
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ~ complete )
& ( head_of(esk4_5(X9,X10,X11,X12,X13)) = tail_of(X11)
| ~ shortest_path(X9,X10,X13)
| ~ precedes(X11,X12,X13)
| ~ complete ) ),
inference(distribute,[status(thm)],[83]) ).
cnf(85,plain,
( head_of(esk4_5(X4,X5,X1,X2,X3)) = tail_of(X1)
| ~ complete
| ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[84]) ).
cnf(86,plain,
( tail_of(esk4_5(X4,X5,X1,X2,X3)) = head_of(X2)
| ~ complete
| ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[84]) ).
cnf(87,plain,
( edge(esk4_5(X4,X5,X1,X2,X3))
| ~ complete
| ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(105,negated_conjecture,
( complete
& ? [X4,X5,X2,X3,X7] :
( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& sequential(X2,X3)
& ! [X8] : ~ triangle(X2,X3,X8) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(106,negated_conjecture,
( complete
& ? [X9,X10,X11,X12,X13] :
( shortest_path(X9,X10,X13)
& precedes(X11,X12,X13)
& sequential(X11,X12)
& ! [X14] : ~ triangle(X11,X12,X14) ) ),
inference(variable_rename,[status(thm)],[105]) ).
fof(107,negated_conjecture,
( complete
& shortest_path(esk7_0,esk8_0,esk11_0)
& precedes(esk9_0,esk10_0,esk11_0)
& sequential(esk9_0,esk10_0)
& ! [X14] : ~ triangle(esk9_0,esk10_0,X14) ),
inference(skolemize,[status(esa)],[106]) ).
fof(108,negated_conjecture,
! [X14] :
( ~ triangle(esk9_0,esk10_0,X14)
& shortest_path(esk7_0,esk8_0,esk11_0)
& precedes(esk9_0,esk10_0,esk11_0)
& sequential(esk9_0,esk10_0)
& complete ),
inference(shift_quantors,[status(thm)],[107]) ).
cnf(109,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[108]) ).
cnf(110,negated_conjecture,
sequential(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(111,negated_conjecture,
precedes(esk9_0,esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(112,negated_conjecture,
shortest_path(esk7_0,esk8_0,esk11_0),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(113,negated_conjecture,
~ triangle(esk9_0,esk10_0,X1),
inference(split_conjunct,[status(thm)],[108]) ).
fof(114,plain,
! [X2,X3,X8] :
( ( ~ triangle(X2,X3,X8)
| ( edge(X2)
& edge(X3)
& edge(X8)
& sequential(X2,X3)
& sequential(X3,X8)
& sequential(X8,X2) ) )
& ( ~ edge(X2)
| ~ edge(X3)
| ~ edge(X8)
| ~ sequential(X2,X3)
| ~ sequential(X3,X8)
| ~ sequential(X8,X2)
| triangle(X2,X3,X8) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(115,plain,
! [X9,X10,X11] :
( ( ~ triangle(X9,X10,X11)
| ( edge(X9)
& edge(X10)
& edge(X11)
& sequential(X9,X10)
& sequential(X10,X11)
& sequential(X11,X9) ) )
& ( ~ edge(X9)
| ~ edge(X10)
| ~ edge(X11)
| ~ sequential(X9,X10)
| ~ sequential(X10,X11)
| ~ sequential(X11,X9)
| triangle(X9,X10,X11) ) ),
inference(variable_rename,[status(thm)],[114]) ).
fof(116,plain,
! [X9,X10,X11] :
( ( edge(X9)
| ~ triangle(X9,X10,X11) )
& ( edge(X10)
| ~ triangle(X9,X10,X11) )
& ( edge(X11)
| ~ triangle(X9,X10,X11) )
& ( sequential(X9,X10)
| ~ triangle(X9,X10,X11) )
& ( sequential(X10,X11)
| ~ triangle(X9,X10,X11) )
& ( sequential(X11,X9)
| ~ triangle(X9,X10,X11) )
& ( ~ edge(X9)
| ~ edge(X10)
| ~ edge(X11)
| ~ sequential(X9,X10)
| ~ sequential(X10,X11)
| ~ sequential(X11,X9)
| triangle(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(117,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(124,negated_conjecture,
edge(esk10_0),
inference(spm,[status(thm)],[32,110,theory(equality)]) ).
cnf(125,negated_conjecture,
edge(esk9_0),
inference(spm,[status(thm)],[33,110,theory(equality)]) ).
cnf(135,plain,
( edge(esk4_5(X4,X5,X1,X2,X3))
| $false
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(rw,[status(thm)],[87,109,theory(equality)]) ).
cnf(136,plain,
( edge(esk4_5(X4,X5,X1,X2,X3))
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(cn,[status(thm)],[135,theory(equality)]) ).
cnf(138,plain,
( head_of(esk4_5(X4,X5,X1,X2,X3)) = tail_of(X1)
| $false
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(rw,[status(thm)],[85,109,theory(equality)]) ).
cnf(139,plain,
( head_of(esk4_5(X4,X5,X1,X2,X3)) = tail_of(X1)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(cn,[status(thm)],[138,theory(equality)]) ).
cnf(141,plain,
( tail_of(X3) != tail_of(esk4_5(X1,X2,X3,X4,X5))
| ~ edge(esk4_5(X1,X2,X3,X4,X5))
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5) ),
inference(spm,[status(thm)],[36,139,theory(equality)]) ).
cnf(142,plain,
( esk4_5(X1,X2,X3,X4,X5) = X6
| sequential(esk4_5(X1,X2,X3,X4,X5),X6)
| tail_of(X6) != tail_of(X3)
| ~ edge(X6)
| ~ edge(esk4_5(X1,X2,X3,X4,X5))
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5) ),
inference(spm,[status(thm)],[29,139,theory(equality)]) ).
cnf(143,plain,
( tail_of(esk4_5(X4,X5,X1,X2,X3)) = head_of(X2)
| $false
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(rw,[status(thm)],[86,109,theory(equality)]) ).
cnf(144,plain,
( tail_of(esk4_5(X4,X5,X1,X2,X3)) = head_of(X2)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(cn,[status(thm)],[143,theory(equality)]) ).
cnf(146,plain,
( X1 = esk4_5(X2,X3,X4,X5,X6)
| sequential(X1,esk4_5(X2,X3,X4,X5,X6))
| head_of(X5) != head_of(X1)
| ~ edge(esk4_5(X2,X3,X4,X5,X6))
| ~ edge(X1)
| ~ precedes(X4,X5,X6)
| ~ shortest_path(X2,X3,X6) ),
inference(spm,[status(thm)],[29,144,theory(equality)]) ).
cnf(159,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2) ),
inference(csr,[status(thm)],[117,33]) ).
cnf(160,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3) ),
inference(csr,[status(thm)],[159,33]) ).
cnf(161,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[160,33]) ).
cnf(162,negated_conjecture,
( ~ sequential(X1,esk9_0)
| ~ sequential(esk10_0,X1)
| ~ sequential(esk9_0,esk10_0) ),
inference(spm,[status(thm)],[113,161,theory(equality)]) ).
cnf(169,negated_conjecture,
( ~ sequential(X1,esk9_0)
| ~ sequential(esk10_0,X1)
| $false ),
inference(rw,[status(thm)],[162,110,theory(equality)]) ).
cnf(170,negated_conjecture,
( ~ sequential(X1,esk9_0)
| ~ sequential(esk10_0,X1) ),
inference(cn,[status(thm)],[169,theory(equality)]) ).
cnf(265,plain,
( tail_of(esk4_5(X1,X2,X3,X4,X5)) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5) ),
inference(csr,[status(thm)],[141,136]) ).
cnf(282,plain,
( esk4_5(X1,X2,X3,X4,X5) = X6
| sequential(esk4_5(X1,X2,X3,X4,X5),X6)
| tail_of(X6) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| ~ edge(X6) ),
inference(csr,[status(thm)],[142,136]) ).
cnf(287,plain,
( esk4_5(X1,X2,X3,X4,X5) = esk9_0
| ~ sequential(esk10_0,esk4_5(X1,X2,X3,X4,X5))
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[170,282,theory(equality)]) ).
cnf(288,plain,
( esk4_5(X1,X2,X3,X4,X5) = esk9_0
| ~ sequential(esk10_0,esk4_5(X1,X2,X3,X4,X5))
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| $false ),
inference(rw,[status(thm)],[287,125,theory(equality)]) ).
cnf(289,plain,
( esk4_5(X1,X2,X3,X4,X5) = esk9_0
| ~ sequential(esk10_0,esk4_5(X1,X2,X3,X4,X5))
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(326,plain,
( X1 = esk4_5(X2,X3,X4,X5,X6)
| sequential(X1,esk4_5(X2,X3,X4,X5,X6))
| head_of(X5) != head_of(X1)
| ~ precedes(X4,X5,X6)
| ~ shortest_path(X2,X3,X6)
| ~ edge(X1) ),
inference(csr,[status(thm)],[146,136]) ).
cnf(333,plain,
( esk4_5(X1,X2,X3,X4,X5) = esk9_0
| esk10_0 = esk4_5(X1,X2,X3,X4,X5)
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(X4) != head_of(esk10_0)
| ~ edge(esk10_0) ),
inference(spm,[status(thm)],[289,326,theory(equality)]) ).
cnf(334,plain,
( esk4_5(X1,X2,X3,X4,X5) = esk9_0
| esk10_0 = esk4_5(X1,X2,X3,X4,X5)
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(X4) != head_of(esk10_0)
| $false ),
inference(rw,[status(thm)],[333,124,theory(equality)]) ).
cnf(335,plain,
( esk4_5(X1,X2,X3,X4,X5) = esk9_0
| esk10_0 = esk4_5(X1,X2,X3,X4,X5)
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(X4) != head_of(esk10_0) ),
inference(cn,[status(thm)],[334,theory(equality)]) ).
cnf(362,plain,
( tail_of(esk10_0) = head_of(X4)
| esk4_5(X1,X2,X3,X4,X5) = esk9_0
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| tail_of(esk9_0) != tail_of(X3)
| head_of(X4) != head_of(esk10_0) ),
inference(spm,[status(thm)],[144,335,theory(equality)]) ).
cnf(477,plain,
( head_of(X4) = tail_of(esk10_0)
| tail_of(esk9_0) != tail_of(X3)
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(X4) != head_of(esk10_0) ),
inference(spm,[status(thm)],[265,362,theory(equality)]) ).
cnf(482,negated_conjecture,
( head_of(esk10_0) = tail_of(esk10_0)
| ~ shortest_path(X1,X2,esk11_0) ),
inference(spm,[status(thm)],[477,111,theory(equality)]) ).
cnf(489,negated_conjecture,
head_of(esk10_0) = tail_of(esk10_0),
inference(spm,[status(thm)],[482,112,theory(equality)]) ).
cnf(491,negated_conjecture,
~ edge(esk10_0),
inference(spm,[status(thm)],[36,489,theory(equality)]) ).
cnf(510,negated_conjecture,
$false,
inference(rw,[status(thm)],[491,124,theory(equality)]) ).
cnf(511,negated_conjecture,
$false,
inference(cn,[status(thm)],[510,theory(equality)]) ).
cnf(512,negated_conjecture,
$false,
511,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA008+2.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmpENJofP/sel_GRA008+2.p_1 with time limit 29
% -prover status Theorem
% Problem GRA008+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA008+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA008+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
%
%------------------------------------------------------------------------------