%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO057-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 11:54:15 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-4 aty)
% Number of variables : 22 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(identity_for_equidistance,plain,
! [A,B,C] :
( ~ equidistant(A,B,C,C)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),
[] ).
cnf(148419456,plain,
( ~ equidistant(A,B,C,C)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[identity_for_equidistance]),
[] ).
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/GEO057-2.tptp',unknown),
[] ).
cnf(148432768,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(rewrite,[status(thm)],[segment_construction2]),
[] ).
cnf(158325728,plain,
$equal(extension(C,A,B,B),A),
inference(resolution,[status(thm)],[148419456,148432768]),
[] ).
fof(reflection,plain,
! [A,B] : $equal(extension(A,B,A,B),reflection(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),
[] ).
cnf(148631824,plain,
$equal(extension(A,B,A,B),reflection(A,B)),
inference(rewrite,[status(thm)],[reflection]),
[] ).
cnf(158343040,plain,
$equal(reflection(A,A),A),
inference(paramodulation,[status(thm)],[158325728,148631824,theory(equality)]),
[] ).
fof(prove_null_extension_by_reflection,plain,
~ $equal(reflection(u,u),u),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),
[] ).
cnf(148636608,plain,
~ $equal(reflection(u,u),u),
inference(rewrite,[status(thm)],[prove_null_extension_by_reflection]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[158343040,148636608]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(identity_for_equidistance,plain,(~equidistant(A,B,C,C)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),[]).
%
% cnf(148419456,plain,(~equidistant(A,B,C,C)|$equal(B,A)),inference(rewrite,[status(thm)],[identity_for_equidistance]),[]).
%
% fof(segment_construction2,plain,(equidistant(A,extension(B,A,C,D),C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),[]).
%
% cnf(148432768,plain,(equidistant(A,extension(B,A,C,D),C,D)),inference(rewrite,[status(thm)],[segment_construction2]),[]).
%
% cnf(158325728,plain,($equal(extension(C,A,B,B),A)),inference(resolution,[status(thm)],[148419456,148432768]),[]).
%
% fof(reflection,plain,($equal(extension(A,B,A,B),reflection(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),[]).
%
% cnf(148631824,plain,($equal(extension(A,B,A,B),reflection(A,B))),inference(rewrite,[status(thm)],[reflection]),[]).
%
% cnf(158343040,plain,($equal(reflection(A,A),A)),inference(paramodulation,[status(thm)],[158325728,148631824,theory(equality)]),[]).
%
% fof(prove_null_extension_by_reflection,plain,(~$equal(reflection(u,u),u)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO057-2.tptp',unknown),[]).
%
% cnf(148636608,plain,(~$equal(reflection(u,u),u)),inference(rewrite,[status(thm)],[prove_null_extension_by_reflection]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[158343040,148636608]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------