TSTP Solution File: GRA002+4 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRA002+4 : TPTP v3.4.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:16:02 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 42 ( 18 ~; 18 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 26 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(graph_has_them_all,plain,
! [A,B] : less_or_equal(number_of_in(A,B),number_of_in(A,graph)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),
[] ).
cnf(157289008,plain,
less_or_equal(number_of_in(A,B),number_of_in(A,graph)),
inference(rewrite,[status(thm)],[graph_has_them_all]),
[] ).
fof(path_length_sequential_pairs,plain,
! [A,B,C] :
( ~ path(A,B,C)
| $equal(minus(length_of(C),n1),number_of_in(sequential_pairs,C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),
[] ).
cnf(157229944,plain,
( ~ path(A,B,C)
| $equal(minus(length_of(C),n1),number_of_in(sequential_pairs,C)) ),
inference(rewrite,[status(thm)],[path_length_sequential_pairs]),
[] ).
fof(shortest_path_defn,plain,
! [B,A,C,D] :
( ( ~ $equal(B,A)
| ~ shortest_path(A,B,C) )
& ( ~ path(A,B,D)
| less_or_equal(length_of(C),length_of(D))
| ~ shortest_path(A,B,C) )
& ( path(A,B,C)
| ~ shortest_path(A,B,C) )
& ( ~ less_or_equal(length_of(C),length_of(p(A,B,C,D)))
| $equal(B,A)
| ~ path(A,B,C)
| shortest_path(A,B,C) )
& ( path(A,B,p(A,B,C,D))
| $equal(B,A)
| ~ path(A,B,C)
| shortest_path(A,B,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),
[] ).
cnf(157093968,plain,
( path(A,B,C)
| ~ shortest_path(A,B,C) ),
inference(rewrite,[status(thm)],[shortest_path_defn]),
[] ).
fof(maximal_path_length,plain,
( complete
& shortest_path(v1,v2,p)
& ~ less_or_equal(minus(length_of(p),n1),number_of_in(triangles,graph)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),
[] ).
cnf(157373832,plain,
shortest_path(v1,v2,p),
inference(rewrite,[status(thm)],[maximal_path_length]),
[] ).
cnf(170732776,plain,
path(v1,v2,p),
inference(resolution,[status(thm)],[157093968,157373832]),
[] ).
cnf(170942960,plain,
$equal(minus(length_of(p),n1),number_of_in(sequential_pairs,p)),
inference(resolution,[status(thm)],[157229944,170732776]),
[] ).
fof(triangles_and_sequential_pairs,plain,
! [B,C,A] :
( ~ complete
| ~ shortest_path(B,C,A)
| $equal(number_of_in(triangles,A),number_of_in(sequential_pairs,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),
[] ).
cnf(157298192,plain,
( ~ complete
| ~ shortest_path(B,C,A)
| $equal(number_of_in(triangles,A),number_of_in(sequential_pairs,A)) ),
inference(rewrite,[status(thm)],[triangles_and_sequential_pairs]),
[] ).
cnf(157383728,plain,
complete,
inference(rewrite,[status(thm)],[maximal_path_length]),
[] ).
cnf(170723944,plain,
( ~ shortest_path(B,C,A)
| $equal(number_of_in(triangles,A),number_of_in(sequential_pairs,A)) ),
inference(resolution,[status(thm)],[157298192,157383728]),
[] ).
cnf(174815056,plain,
$equal(number_of_in(triangles,p),number_of_in(sequential_pairs,p)),
inference(resolution,[status(thm)],[170723944,157373832]),
[] ).
cnf(177368904,plain,
$equal(number_of_in(triangles,p),minus(length_of(p),n1)),
inference(paramodulation,[status(thm)],[170942960,174815056,theory(equality)]),
[] ).
cnf(157359952,plain,
~ less_or_equal(minus(length_of(p),n1),number_of_in(triangles,graph)),
inference(rewrite,[status(thm)],[maximal_path_length]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157289008,177368904,157359952,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(graph_has_them_all,plain,(less_or_equal(number_of_in(A,B),number_of_in(A,graph))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),[]).
%
% cnf(157289008,plain,(less_or_equal(number_of_in(A,B),number_of_in(A,graph))),inference(rewrite,[status(thm)],[graph_has_them_all]),[]).
%
% fof(path_length_sequential_pairs,plain,(~path(A,B,C)|$equal(minus(length_of(C),n1),number_of_in(sequential_pairs,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),[]).
%
% cnf(157229944,plain,(~path(A,B,C)|$equal(minus(length_of(C),n1),number_of_in(sequential_pairs,C))),inference(rewrite,[status(thm)],[path_length_sequential_pairs]),[]).
%
% fof(shortest_path_defn,plain,(((~$equal(B,A)|~shortest_path(A,B,C))&(~path(A,B,D)|less_or_equal(length_of(C),length_of(D))|~shortest_path(A,B,C))&(path(A,B,C)|~shortest_path(A,B,C))&(~less_or_equal(length_of(C),length_of(p(A,B,C,D)))|$equal(B,A)|~path(A,B,C)|shortest_path(A,B,C))&(path(A,B,p(A,B,C,D))|$equal(B,A)|~path(A,B,C)|shortest_path(A,B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),[]).
%
% cnf(157093968,plain,(path(A,B,C)|~shortest_path(A,B,C)),inference(rewrite,[status(thm)],[shortest_path_defn]),[]).
%
% fof(maximal_path_length,plain,((complete&shortest_path(v1,v2,p)&~less_or_equal(minus(length_of(p),n1),number_of_in(triangles,graph)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),[]).
%
% cnf(157373832,plain,(shortest_path(v1,v2,p)),inference(rewrite,[status(thm)],[maximal_path_length]),[]).
%
% cnf(170732776,plain,(path(v1,v2,p)),inference(resolution,[status(thm)],[157093968,157373832]),[]).
%
% cnf(170942960,plain,($equal(minus(length_of(p),n1),number_of_in(sequential_pairs,p))),inference(resolution,[status(thm)],[157229944,170732776]),[]).
%
% fof(triangles_and_sequential_pairs,plain,(~complete|~shortest_path(B,C,A)|$equal(number_of_in(triangles,A),number_of_in(sequential_pairs,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA002+4.tptp',unknown),[]).
%
% cnf(157298192,plain,(~complete|~shortest_path(B,C,A)|$equal(number_of_in(triangles,A),number_of_in(sequential_pairs,A))),inference(rewrite,[status(thm)],[triangles_and_sequential_pairs]),[]).
%
% cnf(157383728,plain,(complete),inference(rewrite,[status(thm)],[maximal_path_length]),[]).
%
% cnf(170723944,plain,(~shortest_path(B,C,A)|$equal(number_of_in(triangles,A),number_of_in(sequential_pairs,A))),inference(resolution,[status(thm)],[157298192,157383728]),[]).
%
% cnf(174815056,plain,($equal(number_of_in(triangles,p),number_of_in(sequential_pairs,p))),inference(resolution,[status(thm)],[170723944,157373832]),[]).
%
% cnf(177368904,plain,($equal(number_of_in(triangles,p),minus(length_of(p),n1))),inference(paramodulation,[status(thm)],[170942960,174815056,theory(equality)]),[]).
%
% cnf(157359952,plain,(~less_or_equal(minus(length_of(p),n1),number_of_in(triangles,graph))),inference(rewrite,[status(thm)],[maximal_path_length]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157289008,177368904,157359952,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------