%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRA005+1 : TPTP v3.4.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:16:08 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   10 (   5 unt;   0 def)
%            Number of atoms       :   26 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   32 (  16   ~;  11   |;   5   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :   17 (   4 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(no_short_cut_edge,plain,
    ( shortest_path(v1,v2,p)
    & precedes(e1,e2,p)
    & edge(e3)
    & $equal(tail_of(e1),tail_of(e3))
    & $equal(head_of(e2),head_of(e3)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA005+1.tptp',unknown),
    [] ).

cnf(159335656,plain,
    $equal(tail_of(e1),tail_of(e3)),
    inference(rewrite,[status(thm)],[no_short_cut_edge]),
    [] ).

fof(shortest_path_properties,plain,
    ! [D,C,E,A,B,F] :
      ( ( ~ precedes(D,C,E)
        | ~ shortest_path(A,B,E)
        | ~ precedes(C,D,E) )
      & ( ~ $equal(tail_of(C),tail_of(F))
        | ~ $equal(head_of(D),head_of(F))
        | ~ shortest_path(A,B,E)
        | ~ precedes(C,D,E) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA005+1.tptp',unknown),
    [] ).

cnf(159084744,plain,
    ( ~ $equal(tail_of(C),tail_of(F))
    | ~ $equal(head_of(D),head_of(F))
    | ~ shortest_path(A,B,E)
    | ~ precedes(C,D,E) ),
    inference(rewrite,[status(thm)],[shortest_path_properties]),
    [] ).

cnf(159323328,plain,
    $equal(head_of(e2),head_of(e3)),
    inference(rewrite,[status(thm)],[no_short_cut_edge]),
    [] ).

cnf(181038368,plain,
    ( ~ $equal(tail_of(C),tail_of(e3))
    | ~ shortest_path(A,B,D)
    | ~ precedes(C,e2,D) ),
    inference(resolution,[status(thm)],[159084744,159323328]),
    [] ).

cnf(159369272,plain,
    shortest_path(v1,v2,p),
    inference(rewrite,[status(thm)],[no_short_cut_edge]),
    [] ).

cnf(181049056,plain,
    ( ~ $equal(tail_of(A),tail_of(e3))
    | ~ precedes(A,e2,p) ),
    inference(resolution,[status(thm)],[181038368,159369272]),
    [] ).

cnf(159359440,plain,
    precedes(e1,e2,p),
    inference(rewrite,[status(thm)],[no_short_cut_edge]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[159335656,181049056,159359440]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(no_short_cut_edge,plain,((shortest_path(v1,v2,p)&precedes(e1,e2,p)&edge(e3)&$equal(tail_of(e1),tail_of(e3))&$equal(head_of(e2),head_of(e3)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA005+1.tptp',unknown),[]).
% 
% cnf(159335656,plain,($equal(tail_of(e1),tail_of(e3))),inference(rewrite,[status(thm)],[no_short_cut_edge]),[]).
% 
% fof(shortest_path_properties,plain,(((~precedes(D,C,E)|~shortest_path(A,B,E)|~precedes(C,D,E))&(~$equal(tail_of(C),tail_of(F))|~$equal(head_of(D),head_of(F))|~shortest_path(A,B,E)|~precedes(C,D,E)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRA/GRA005+1.tptp',unknown),[]).
% 
% cnf(159084744,plain,(~$equal(tail_of(C),tail_of(F))|~$equal(head_of(D),head_of(F))|~shortest_path(A,B,E)|~precedes(C,D,E)),inference(rewrite,[status(thm)],[shortest_path_properties]),[]).
% 
% cnf(159323328,plain,($equal(head_of(e2),head_of(e3))),inference(rewrite,[status(thm)],[no_short_cut_edge]),[]).
% 
% cnf(181038368,plain,(~$equal(tail_of(C),tail_of(e3))|~shortest_path(A,B,D)|~precedes(C,e2,D)),inference(resolution,[status(thm)],[159084744,159323328]),[]).
% 
% cnf(159369272,plain,(shortest_path(v1,v2,p)),inference(rewrite,[status(thm)],[no_short_cut_edge]),[]).
% 
% cnf(181049056,plain,(~$equal(tail_of(A),tail_of(e3))|~precedes(A,e2,p)),inference(resolution,[status(thm)],[181038368,159369272]),[]).
% 
% cnf(159359440,plain,(precedes(e1,e2,p)),inference(rewrite,[status(thm)],[no_short_cut_edge]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[159335656,181049056,159359440]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------