TSTP Solution File: GRA002+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA002+4 : TPTP v5.0.0. Bugfixed v3.2.0.
% 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 : Sat Dec 25 09:52:57 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 16 unt; 0 def)
% Number of atoms : 129 ( 31 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 139 ( 53 ~; 48 |; 28 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 92 ( 11 sgn 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X4,X5,X6] :
( shortest_path(X4,X5,X6)
<=> ( path(X4,X5,X6)
& X4 != X5
& ! [X7] :
( path(X4,X5,X7)
=> less_or_equal(length_of(X6),length_of(X7)) ) ) ),
file('/tmp/tmpMnaoow/sel_GRA002+4.p_1',shortest_path_defn) ).
fof(9,axiom,
( complete
=> ! [X7,X4,X5] :
( shortest_path(X4,X5,X7)
=> number_of_in(sequential_pairs,X7) = number_of_in(triangles,X7) ) ),
file('/tmp/tmpMnaoow/sel_GRA002+4.p_1',triangles_and_sequential_pairs) ).
fof(10,axiom,
! [X9,X10] : less_or_equal(number_of_in(X9,X10),number_of_in(X9,graph)),
file('/tmp/tmpMnaoow/sel_GRA002+4.p_1',graph_has_them_all) ).
fof(12,axiom,
! [X4,X5,X7] :
( path(X4,X5,X7)
=> number_of_in(sequential_pairs,X7) = minus(length_of(X7),n1) ),
file('/tmp/tmpMnaoow/sel_GRA002+4.p_1',path_length_sequential_pairs) ).
fof(14,conjecture,
( complete
=> ! [X7,X4,X5] :
( shortest_path(X4,X5,X7)
=> less_or_equal(minus(length_of(X7),n1),number_of_in(triangles,graph)) ) ),
file('/tmp/tmpMnaoow/sel_GRA002+4.p_1',maximal_path_length) ).
fof(15,axiom,
! [X4,X5,X7] :
( path(X4,X5,X7)
=> length_of(X7) = number_of_in(edges,X7) ),
file('/tmp/tmpMnaoow/sel_GRA002+4.p_1',length_defn) ).
fof(16,negated_conjecture,
~ ( complete
=> ! [X7,X4,X5] :
( shortest_path(X4,X5,X7)
=> less_or_equal(minus(length_of(X7),n1),number_of_in(triangles,graph)) ) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(37,plain,
! [X4,X5,X6] :
( ( ~ shortest_path(X4,X5,X6)
| ( path(X4,X5,X6)
& X4 != X5
& ! [X7] :
( ~ path(X4,X5,X7)
| less_or_equal(length_of(X6),length_of(X7)) ) ) )
& ( ~ path(X4,X5,X6)
| X4 = X5
| ? [X7] :
( path(X4,X5,X7)
& ~ less_or_equal(length_of(X6),length_of(X7)) )
| shortest_path(X4,X5,X6) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(38,plain,
! [X8,X9,X10] :
( ( ~ shortest_path(X8,X9,X10)
| ( path(X8,X9,X10)
& X8 != X9
& ! [X11] :
( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11)) ) ) )
& ( ~ path(X8,X9,X10)
| X8 = X9
| ? [X12] :
( path(X8,X9,X12)
& ~ less_or_equal(length_of(X10),length_of(X12)) )
| shortest_path(X8,X9,X10) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X8,X9,X10] :
( ( ~ shortest_path(X8,X9,X10)
| ( path(X8,X9,X10)
& X8 != X9
& ! [X11] :
( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11)) ) ) )
& ( ~ path(X8,X9,X10)
| X8 = X9
| ( path(X8,X9,esk1_3(X8,X9,X10))
& ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10))) )
| shortest_path(X8,X9,X10) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,plain,
! [X8,X9,X10,X11] :
( ( ( ( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11)) )
& path(X8,X9,X10)
& X8 != X9 )
| ~ shortest_path(X8,X9,X10) )
& ( ~ path(X8,X9,X10)
| X8 = X9
| ( path(X8,X9,esk1_3(X8,X9,X10))
& ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10))) )
| shortest_path(X8,X9,X10) ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X8,X9,X10,X11] :
( ( ~ path(X8,X9,X11)
| less_or_equal(length_of(X10),length_of(X11))
| ~ shortest_path(X8,X9,X10) )
& ( path(X8,X9,X10)
| ~ shortest_path(X8,X9,X10) )
& ( X8 != X9
| ~ shortest_path(X8,X9,X10) )
& ( path(X8,X9,esk1_3(X8,X9,X10))
| ~ path(X8,X9,X10)
| X8 = X9
| shortest_path(X8,X9,X10) )
& ( ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10)))
| ~ path(X8,X9,X10)
| X8 = X9
| shortest_path(X8,X9,X10) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(45,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(80,plain,
( ~ complete
| ! [X7,X4,X5] :
( ~ shortest_path(X4,X5,X7)
| number_of_in(sequential_pairs,X7) = number_of_in(triangles,X7) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(81,plain,
( ~ complete
| ! [X8,X9,X10] :
( ~ shortest_path(X9,X10,X8)
| number_of_in(sequential_pairs,X8) = number_of_in(triangles,X8) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X8,X9,X10] :
( ~ shortest_path(X9,X10,X8)
| number_of_in(sequential_pairs,X8) = number_of_in(triangles,X8)
| ~ complete ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ complete
| ~ shortest_path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(84,plain,
! [X11,X12] : less_or_equal(number_of_in(X11,X12),number_of_in(X11,graph)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(85,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[84]) ).
fof(95,plain,
! [X4,X5,X7] :
( ~ path(X4,X5,X7)
| number_of_in(sequential_pairs,X7) = minus(length_of(X7),n1) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(96,plain,
! [X8,X9,X10] :
( ~ path(X8,X9,X10)
| number_of_in(sequential_pairs,X10) = minus(length_of(X10),n1) ),
inference(variable_rename,[status(thm)],[95]) ).
cnf(97,plain,
( number_of_in(sequential_pairs,X1) = minus(length_of(X1),n1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(108,negated_conjecture,
( complete
& ? [X7,X4,X5] :
( shortest_path(X4,X5,X7)
& ~ less_or_equal(minus(length_of(X7),n1),number_of_in(triangles,graph)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(109,negated_conjecture,
( complete
& ? [X8,X9,X10] :
( shortest_path(X9,X10,X8)
& ~ less_or_equal(minus(length_of(X8),n1),number_of_in(triangles,graph)) ) ),
inference(variable_rename,[status(thm)],[108]) ).
fof(110,negated_conjecture,
( complete
& shortest_path(esk7_0,esk8_0,esk6_0)
& ~ less_or_equal(minus(length_of(esk6_0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa)],[109]) ).
cnf(111,negated_conjecture,
~ less_or_equal(minus(length_of(esk6_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(112,negated_conjecture,
shortest_path(esk7_0,esk8_0,esk6_0),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(113,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[110]) ).
fof(114,plain,
! [X4,X5,X7] :
( ~ path(X4,X5,X7)
| length_of(X7) = number_of_in(edges,X7) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(115,plain,
! [X8,X9,X10] :
( ~ path(X8,X9,X10)
| length_of(X10) = number_of_in(edges,X10) ),
inference(variable_rename,[status(thm)],[114]) ).
cnf(116,plain,
( length_of(X1) = number_of_in(edges,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[115]) ).
cnf(119,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| $false
| ~ shortest_path(X2,X3,X1) ),
inference(rw,[status(thm)],[83,113,theory(equality)]) ).
cnf(120,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ shortest_path(X2,X3,X1) ),
inference(cn,[status(thm)],[119,theory(equality)]) ).
cnf(121,negated_conjecture,
number_of_in(triangles,esk6_0) = number_of_in(sequential_pairs,esk6_0),
inference(spm,[status(thm)],[120,112,theory(equality)]) ).
cnf(122,negated_conjecture,
path(esk7_0,esk8_0,esk6_0),
inference(spm,[status(thm)],[45,112,theory(equality)]) ).
cnf(172,negated_conjecture,
less_or_equal(number_of_in(sequential_pairs,esk6_0),number_of_in(triangles,graph)),
inference(spm,[status(thm)],[85,121,theory(equality)]) ).
cnf(173,negated_conjecture,
length_of(esk6_0) = number_of_in(edges,esk6_0),
inference(spm,[status(thm)],[116,122,theory(equality)]) ).
cnf(175,negated_conjecture,
minus(length_of(esk6_0),n1) = number_of_in(sequential_pairs,esk6_0),
inference(spm,[status(thm)],[97,122,theory(equality)]) ).
cnf(179,negated_conjecture,
~ less_or_equal(minus(number_of_in(edges,esk6_0),n1),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[111,173,theory(equality)]) ).
cnf(183,negated_conjecture,
minus(number_of_in(edges,esk6_0),n1) = number_of_in(sequential_pairs,esk6_0),
inference(rw,[status(thm)],[175,173,theory(equality)]) ).
cnf(184,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk6_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[179,183,theory(equality)]) ).
cnf(185,negated_conjecture,
$false,
inference(sr,[status(thm)],[172,184,theory(equality)]) ).
cnf(186,negated_conjecture,
$false,
185,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA002+4.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmpMnaoow/sel_GRA002+4.p_1 with time limit 29
% -prover status Theorem
% Problem GRA002+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA002+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA002+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
%
%------------------------------------------------------------------------------