TSTP Solution File: GEO059-2 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO059-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 11:54:23 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(transitivity_for_equidistance,plain,
! [A,B,C,D,E,F] :
( ~ equidistant(A,B,C,D)
| ~ equidistant(A,B,E,F)
| equidistant(C,D,E,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),
[] ).
cnf(165313992,plain,
( ~ equidistant(A,B,C,D)
| ~ equidistant(A,B,E,F)
| equidistant(C,D,E,F) ),
inference(rewrite,[status(thm)],[transitivity_for_equidistance]),
[] ).
fof(reflexivity_for_equidistance,plain,
! [A,B] : equidistant(A,B,B,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),
[] ).
cnf(165305304,plain,
equidistant(A,B,B,A),
inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),
[] ).
cnf(173352672,plain,
( ~ equidistant(A,B,C,D)
| equidistant(B,A,C,D) ),
inference(resolution,[status(thm)],[165313992,165305304]),
[] ).
fof(segment_construction2,plain,
! [A,B,C,D] : equidistant(A,extension(B,A,C,D),C,D),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),
[] ).
cnf(165336416,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(rewrite,[status(thm)],[segment_construction2]),
[] ).
cnf(177627512,plain,
equidistant(extension(D,A,B,C),A,B,C),
inference(resolution,[status(thm)],[173352672,165336416]),
[] ).
fof(reflection,plain,
! [A,B] : $equal(extension(A,B,A,B),reflection(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),
[] ).
cnf(165539904,plain,
$equal(extension(A,B,A,B),reflection(A,B)),
inference(rewrite,[status(thm)],[reflection]),
[] ).
cnf(177866480,plain,
equidistant(reflection(B,A),A,B,A),
inference(paramodulation,[status(thm)],[177627512,165539904,theory(equality)]),
[] ).
cnf(177923400,plain,
( ~ equidistant(reflection(B,A),A,C,D)
| equidistant(B,A,C,D) ),
inference(resolution,[status(thm)],[177866480,165313992]),
[] ).
cnf(173363584,plain,
( ~ equidistant(A,B,C,D)
| equidistant(C,D,B,A) ),
inference(resolution,[status(thm)],[165313992,165305304]),
[] ).
cnf(177894856,plain,
equidistant(B,A,A,reflection(B,A)),
inference(resolution,[status(thm)],[177866480,173363584]),
[] ).
cnf(179586920,plain,
equidistant(B,A,A,reflection(reflection(B,A),A)),
inference(resolution,[status(thm)],[177923400,177894856]),
[] ).
fof(prove_congruence,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),
[] ).
cnf(165544072,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(rewrite,[status(thm)],[prove_congruence]),
[] ).
cnf(177642576,plain,
~ equidistant(u,v,v,reflection(reflection(u,v),v)),
inference(resolution,[status(thm)],[173352672,165544072]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[179586920,177642576]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(transitivity_for_equidistance,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),[]).
%
% cnf(165313992,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),inference(rewrite,[status(thm)],[transitivity_for_equidistance]),[]).
%
% fof(reflexivity_for_equidistance,plain,(equidistant(A,B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),[]).
%
% cnf(165305304,plain,(equidistant(A,B,B,A)),inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),[]).
%
% cnf(173352672,plain,(~equidistant(A,B,C,D)|equidistant(B,A,C,D)),inference(resolution,[status(thm)],[165313992,165305304]),[]).
%
% fof(segment_construction2,plain,(equidistant(A,extension(B,A,C,D),C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),[]).
%
% cnf(165336416,plain,(equidistant(A,extension(B,A,C,D),C,D)),inference(rewrite,[status(thm)],[segment_construction2]),[]).
%
% cnf(177627512,plain,(equidistant(extension(D,A,B,C),A,B,C)),inference(resolution,[status(thm)],[173352672,165336416]),[]).
%
% fof(reflection,plain,($equal(extension(A,B,A,B),reflection(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),[]).
%
% cnf(165539904,plain,($equal(extension(A,B,A,B),reflection(A,B))),inference(rewrite,[status(thm)],[reflection]),[]).
%
% cnf(177866480,plain,(equidistant(reflection(B,A),A,B,A)),inference(paramodulation,[status(thm)],[177627512,165539904,theory(equality)]),[]).
%
% cnf(177923400,plain,(~equidistant(reflection(B,A),A,C,D)|equidistant(B,A,C,D)),inference(resolution,[status(thm)],[177866480,165313992]),[]).
%
% cnf(173363584,plain,(~equidistant(A,B,C,D)|equidistant(C,D,B,A)),inference(resolution,[status(thm)],[165313992,165305304]),[]).
%
% cnf(177894856,plain,(equidistant(B,A,A,reflection(B,A))),inference(resolution,[status(thm)],[177866480,173363584]),[]).
%
% cnf(179586920,plain,(equidistant(B,A,A,reflection(reflection(B,A),A))),inference(resolution,[status(thm)],[177923400,177894856]),[]).
%
% fof(prove_congruence,plain,(~equidistant(v,u,v,reflection(reflection(u,v),v))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO059-2.tptp',unknown),[]).
%
% cnf(165544072,plain,(~equidistant(v,u,v,reflection(reflection(u,v),v))),inference(rewrite,[status(thm)],[prove_congruence]),[]).
%
% cnf(177642576,plain,(~equidistant(u,v,v,reflection(reflection(u,v),v))),inference(resolution,[status(thm)],[173352672,165544072]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[179586920,177642576]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------