TSTP Solution File: GEO018-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO018-3 : 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 11:52:38 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 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 : 34 ( 0 sgn 16 !; 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/GEO018-3.tptp',unknown),
[] ).
cnf(150738016,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/GEO018-3.tptp',unknown),
[] ).
cnf(150980664,plain,
equidistant(u,v,w,x),
inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),
[] ).
cnf(159174000,plain,
( ~ equidistant(u,v,A,B)
| equidistant(w,x,A,B) ),
inference(resolution,[status(thm)],[150738016,150980664]),
[] ).
fof(reflexivity_for_equidistance,plain,
! [A,B] : equidistant(A,B,B,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),
[] ).
cnf(150729296,plain,
equidistant(A,B,B,A),
inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),
[] ).
cnf(159200192,plain,
equidistant(w,x,v,u),
inference(resolution,[status(thm)],[159174000,150729296]),
[] ).
fof(d3,plain,
! [A,B,C,D] :
( ~ equidistant(A,B,C,D)
| equidistant(B,A,C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),
[] ).
cnf(150977400,plain,
( ~ equidistant(A,B,C,D)
| equidistant(B,A,C,D) ),
inference(rewrite,[status(thm)],[d3]),
[] ).
fof(d2,plain,
! [A,B,C,D] :
( ~ equidistant(A,B,C,D)
| equidistant(C,D,A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),
[] ).
cnf(150969016,plain,
( ~ equidistant(A,B,C,D)
| equidistant(C,D,A,B) ),
inference(rewrite,[status(thm)],[d2]),
[] ).
fof(prove_symmetry,plain,
~ equidistant(v,u,x,w),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),
[] ).
cnf(150984488,plain,
~ equidistant(v,u,x,w),
inference(rewrite,[status(thm)],[prove_symmetry]),
[] ).
cnf(160095016,plain,
~ equidistant(x,w,v,u),
inference(resolution,[status(thm)],[150969016,150984488]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[159200192,150977400,160095016]),
[] ).
%------------------------------------------------------------------------------
%----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/GEO018-3.tptp',unknown),[]).
%
% cnf(150738016,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/GEO018-3.tptp',unknown),[]).
%
% cnf(150980664,plain,(equidistant(u,v,w,x)),inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),[]).
%
% cnf(159174000,plain,(~equidistant(u,v,A,B)|equidistant(w,x,A,B)),inference(resolution,[status(thm)],[150738016,150980664]),[]).
%
% fof(reflexivity_for_equidistance,plain,(equidistant(A,B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),[]).
%
% cnf(150729296,plain,(equidistant(A,B,B,A)),inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),[]).
%
% cnf(159200192,plain,(equidistant(w,x,v,u)),inference(resolution,[status(thm)],[159174000,150729296]),[]).
%
% fof(d3,plain,(~equidistant(A,B,C,D)|equidistant(B,A,C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),[]).
%
% cnf(150977400,plain,(~equidistant(A,B,C,D)|equidistant(B,A,C,D)),inference(rewrite,[status(thm)],[d3]),[]).
%
% fof(d2,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),[]).
%
% cnf(150969016,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),inference(rewrite,[status(thm)],[d2]),[]).
%
% fof(prove_symmetry,plain,(~equidistant(v,u,x,w)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-3.tptp',unknown),[]).
%
% cnf(150984488,plain,(~equidistant(v,u,x,w)),inference(rewrite,[status(thm)],[prove_symmetry]),[]).
%
% cnf(160095016,plain,(~equidistant(x,w,v,u)),inference(resolution,[status(thm)],[150969016,150984488]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[159200192,150977400,160095016]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------