TSTP Solution File: GEO020-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO020-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 11:52:44 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 8 !; 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/GEO020-2.tptp',unknown),
[] ).
cnf(165837296,plain,
( ~ equidistant(A,B,C,D)
| ~ equidistant(A,B,E,F)
| equidistant(C,D,E,F) ),
inference(rewrite,[status(thm)],[transitivity_for_equidistance]),
[] ).
fof(u_to_v_equals_w_to_x,plain,
equidistant(u,v,w,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),
[] ).
cnf(166059592,plain,
equidistant(u,v,w,x),
inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),
[] ).
cnf(174133608,plain,
( ~ equidistant(u,v,A,B)
| equidistant(w,x,A,B) ),
inference(resolution,[status(thm)],[165837296,166059592]),
[] ).
fof(reflexivity_for_equidistance,plain,
! [A,B] : equidistant(A,B,B,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),
[] ).
cnf(165828576,plain,
equidistant(A,B,B,A),
inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),
[] ).
cnf(173889608,plain,
equidistant(B,A,B,A),
inference(resolution,[status(thm)],[165837296,165828576]),
[] ).
cnf(176209176,plain,
equidistant(w,x,u,v),
inference(resolution,[status(thm)],[174133608,173889608]),
[] ).
cnf(173880672,plain,
( ~ equidistant(A,B,C,D)
| equidistant(B,A,C,D) ),
inference(resolution,[status(thm)],[165837296,165828576]),
[] ).
fof(prove_symmetry,plain,
~ equidistant(x,w,u,v),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),
[] ).
cnf(166067472,plain,
~ equidistant(x,w,u,v),
inference(rewrite,[status(thm)],[prove_symmetry]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[176209176,173880672,166067472]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(transitivity_for_equidistance,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),[]).
%
% cnf(165837296,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),inference(rewrite,[status(thm)],[transitivity_for_equidistance]),[]).
%
% fof(u_to_v_equals_w_to_x,plain,(equidistant(u,v,w,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),[]).
%
% cnf(166059592,plain,(equidistant(u,v,w,x)),inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),[]).
%
% cnf(174133608,plain,(~equidistant(u,v,A,B)|equidistant(w,x,A,B)),inference(resolution,[status(thm)],[165837296,166059592]),[]).
%
% fof(reflexivity_for_equidistance,plain,(equidistant(A,B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),[]).
%
% cnf(165828576,plain,(equidistant(A,B,B,A)),inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),[]).
%
% cnf(173889608,plain,(equidistant(B,A,B,A)),inference(resolution,[status(thm)],[165837296,165828576]),[]).
%
% cnf(176209176,plain,(equidistant(w,x,u,v)),inference(resolution,[status(thm)],[174133608,173889608]),[]).
%
% cnf(173880672,plain,(~equidistant(A,B,C,D)|equidistant(B,A,C,D)),inference(resolution,[status(thm)],[165837296,165828576]),[]).
%
% fof(prove_symmetry,plain,(~equidistant(x,w,u,v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO020-2.tptp',unknown),[]).
%
% cnf(166067472,plain,(~equidistant(x,w,u,v)),inference(rewrite,[status(thm)],[prove_symmetry]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[176209176,173880672,166067472]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------