TSTP Solution File: GRA010+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA010+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 09:57:19 EST 2010
% Result : Theorem 0.32s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 121 ( 24 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 146 ( 52 ~; 50 |; 36 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 87 ( 5 sgn 43 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,conjecture,
( complete
=> ! [X7,X4,X5] :
( ( path(X4,X5,X7)
& ! [X2,X3] :
( ( on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) )
=> number_of_in(sequential_pairs,X7) = number_of_in(triangles,X7) ) ),
file('/tmp/tmptyWy9g/sel_GRA010+1.p_1',complete_means_sequential_pairs_and_triangles) ).
fof(12,axiom,
! [X7,X4,X5] :
( ( path(X4,X5,X7)
& ! [X2,X3] :
( ( on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) )
=> number_of_in(sequential_pairs,X7) = number_of_in(triangles,X7) ),
file('/tmp/tmptyWy9g/sel_GRA010+1.p_1',sequential_pairs_and_triangles) ).
fof(15,negated_conjecture,
~ ( complete
=> ! [X7,X4,X5] :
( ( path(X4,X5,X7)
& ! [X2,X3] :
( ( on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) )
=> number_of_in(sequential_pairs,X7) = number_of_in(triangles,X7) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(79,negated_conjecture,
( complete
& ? [X7,X4,X5] :
( path(X4,X5,X7)
& ! [X2,X3] :
( ~ on_path(X2,X7)
| ~ on_path(X3,X7)
| ~ sequential(X2,X3)
| ? [X8] : triangle(X2,X3,X8) )
& number_of_in(sequential_pairs,X7) != number_of_in(triangles,X7) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(80,negated_conjecture,
( complete
& ? [X9,X10,X11] :
( path(X10,X11,X9)
& ! [X12,X13] :
( ~ on_path(X12,X9)
| ~ on_path(X13,X9)
| ~ sequential(X12,X13)
| ? [X14] : triangle(X12,X13,X14) )
& number_of_in(sequential_pairs,X9) != number_of_in(triangles,X9) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,negated_conjecture,
( complete
& path(esk5_0,esk6_0,esk4_0)
& ! [X12,X13] :
( ~ on_path(X12,esk4_0)
| ~ on_path(X13,esk4_0)
| ~ sequential(X12,X13)
| triangle(X12,X13,esk7_2(X12,X13)) )
& number_of_in(sequential_pairs,esk4_0) != number_of_in(triangles,esk4_0) ),
inference(skolemize,[status(esa)],[80]) ).
fof(82,negated_conjecture,
! [X12,X13] :
( ( ~ on_path(X12,esk4_0)
| ~ on_path(X13,esk4_0)
| ~ sequential(X12,X13)
| triangle(X12,X13,esk7_2(X12,X13)) )
& path(esk5_0,esk6_0,esk4_0)
& number_of_in(sequential_pairs,esk4_0) != number_of_in(triangles,esk4_0)
& complete ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(84,negated_conjecture,
number_of_in(sequential_pairs,esk4_0) != number_of_in(triangles,esk4_0),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(85,negated_conjecture,
path(esk5_0,esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(86,negated_conjecture,
( triangle(X1,X2,esk7_2(X1,X2))
| ~ sequential(X1,X2)
| ~ on_path(X2,esk4_0)
| ~ on_path(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(92,plain,
! [X7,X4,X5] :
( ~ path(X4,X5,X7)
| ? [X2,X3] :
( on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3)
& ! [X8] : ~ triangle(X2,X3,X8) )
| number_of_in(sequential_pairs,X7) = number_of_in(triangles,X7) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(93,plain,
! [X9,X10,X11] :
( ~ path(X10,X11,X9)
| ? [X12,X13] :
( on_path(X12,X9)
& on_path(X13,X9)
& sequential(X12,X13)
& ! [X14] : ~ triangle(X12,X13,X14) )
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,plain,
! [X9,X10,X11] :
( ~ path(X10,X11,X9)
| ( on_path(esk8_3(X9,X10,X11),X9)
& on_path(esk9_3(X9,X10,X11),X9)
& sequential(esk8_3(X9,X10,X11),esk9_3(X9,X10,X11))
& ! [X14] : ~ triangle(esk8_3(X9,X10,X11),esk9_3(X9,X10,X11),X14) )
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) ),
inference(skolemize,[status(esa)],[93]) ).
fof(95,plain,
! [X9,X10,X11,X14] :
( ( ~ triangle(esk8_3(X9,X10,X11),esk9_3(X9,X10,X11),X14)
& on_path(esk8_3(X9,X10,X11),X9)
& on_path(esk9_3(X9,X10,X11),X9)
& sequential(esk8_3(X9,X10,X11),esk9_3(X9,X10,X11)) )
| ~ path(X10,X11,X9)
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) ),
inference(shift_quantors,[status(thm)],[94]) ).
fof(96,plain,
! [X9,X10,X11,X14] :
( ( ~ triangle(esk8_3(X9,X10,X11),esk9_3(X9,X10,X11),X14)
| ~ path(X10,X11,X9)
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) )
& ( on_path(esk8_3(X9,X10,X11),X9)
| ~ path(X10,X11,X9)
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) )
& ( on_path(esk9_3(X9,X10,X11),X9)
| ~ path(X10,X11,X9)
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) )
& ( sequential(esk8_3(X9,X10,X11),esk9_3(X9,X10,X11))
| ~ path(X10,X11,X9)
| number_of_in(sequential_pairs,X9) = number_of_in(triangles,X9) ) ),
inference(distribute,[status(thm)],[95]) ).
cnf(97,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| sequential(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3))
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(98,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk9_3(X1,X2,X3),X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(99,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk8_3(X1,X2,X3),X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(100,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(156,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1)
| ~ on_path(esk9_3(X1,X2,X3),esk4_0)
| ~ on_path(esk8_3(X1,X2,X3),esk4_0)
| ~ sequential(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)) ),
inference(spm,[status(thm)],[100,86,theory(equality)]) ).
cnf(390,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ on_path(esk9_3(X1,X2,X3),esk4_0)
| ~ on_path(esk8_3(X1,X2,X3),esk4_0)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[156,97]) ).
cnf(391,negated_conjecture,
( number_of_in(triangles,esk4_0) = number_of_in(sequential_pairs,esk4_0)
| ~ on_path(esk8_3(esk4_0,X1,X2),esk4_0)
| ~ path(X1,X2,esk4_0) ),
inference(spm,[status(thm)],[390,98,theory(equality)]) ).
cnf(393,negated_conjecture,
( ~ on_path(esk8_3(esk4_0,X1,X2),esk4_0)
| ~ path(X1,X2,esk4_0) ),
inference(sr,[status(thm)],[391,84,theory(equality)]) ).
cnf(395,negated_conjecture,
( number_of_in(triangles,esk4_0) = number_of_in(sequential_pairs,esk4_0)
| ~ path(X1,X2,esk4_0) ),
inference(spm,[status(thm)],[393,99,theory(equality)]) ).
cnf(396,negated_conjecture,
~ path(X1,X2,esk4_0),
inference(sr,[status(thm)],[395,84,theory(equality)]) ).
cnf(397,negated_conjecture,
$false,
inference(sr,[status(thm)],[85,396,theory(equality)]) ).
cnf(398,negated_conjecture,
$false,
397,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA010+1.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmptyWy9g/sel_GRA010+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRA010+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA010+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA010+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
%
%------------------------------------------------------------------------------