TSTP Solution File: GEO058-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO058-2 : 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 11:54:19 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 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 : 49 ( 2 sgn 17 !; 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/GEO058-2.tptp',unknown),
[] ).
cnf(163280072,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/GEO058-2.tptp',unknown),
[] ).
cnf(163271384,plain,
equidistant(A,B,B,A),
inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),
[] ).
cnf(171462760,plain,
( ~ equidistant(A,B,C,D)
| equidistant(B,A,C,D) ),
inference(resolution,[status(thm)],[163280072,163271384]),
[] ).
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/GEO058-2.tptp',unknown),
[] ).
cnf(163302496,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(rewrite,[status(thm)],[segment_construction2]),
[] ).
cnf(173499112,plain,
equidistant(extension(D,A,B,C),A,B,C),
inference(resolution,[status(thm)],[171462760,163302496]),
[] ).
fof(reflection,plain,
! [A,B] : $equal(extension(A,B,A,B),reflection(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),
[] ).
cnf(163505984,plain,
$equal(extension(A,B,A,B),reflection(A,B)),
inference(rewrite,[status(thm)],[reflection]),
[] ).
cnf(174073600,plain,
equidistant(reflection(B,A),A,B,A),
inference(paramodulation,[status(thm)],[173499112,163505984,theory(equality)]),
[] ).
fof(v_equals_reflection,plain,
$equal(reflection(u,v),v),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),
[] ).
cnf(163510008,plain,
$equal(reflection(u,v),v),
inference(rewrite,[status(thm)],[v_equals_reflection]),
[] ).
cnf(174149512,plain,
equidistant(v,v,u,v),
inference(paramodulation,[status(thm)],[174073600,163510008,theory(equality)]),
[] ).
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/GEO058-2.tptp',unknown),
[] ).
cnf(163289120,plain,
( ~ equidistant(A,B,C,C)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[identity_for_equidistance]),
[] ).
fof(prove_u_equals_v,plain,
~ $equal(v,u),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),
[] ).
cnf(163518816,plain,
~ $equal(v,u),
inference(rewrite,[status(thm)],[prove_u_equals_v]),
[] ).
cnf(171346576,plain,
~ equidistant(u,v,A,A),
inference(resolution,[status(thm)],[163289120,163518816]),
[] ).
cnf(172181112,plain,
( ~ equidistant(A,B,u,v)
| ~ equidistant(A,B,C,C) ),
inference(resolution,[status(thm)],[163280072,171346576]),
[] ).
cnf(172214072,plain,
~ equidistant(A,A,u,v),
inference(resolution,[status(thm)],[172181112,163271384]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[174149512,172214072]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(transitivity_for_equidistance,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163280072,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),inference(rewrite,[status(thm)],[transitivity_for_equidistance]),[]).
%
% fof(reflexivity_for_equidistance,plain,(equidistant(A,B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163271384,plain,(equidistant(A,B,B,A)),inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),[]).
%
% cnf(171462760,plain,(~equidistant(A,B,C,D)|equidistant(B,A,C,D)),inference(resolution,[status(thm)],[163280072,163271384]),[]).
%
% fof(segment_construction2,plain,(equidistant(A,extension(B,A,C,D),C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163302496,plain,(equidistant(A,extension(B,A,C,D),C,D)),inference(rewrite,[status(thm)],[segment_construction2]),[]).
%
% cnf(173499112,plain,(equidistant(extension(D,A,B,C),A,B,C)),inference(resolution,[status(thm)],[171462760,163302496]),[]).
%
% fof(reflection,plain,($equal(extension(A,B,A,B),reflection(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163505984,plain,($equal(extension(A,B,A,B),reflection(A,B))),inference(rewrite,[status(thm)],[reflection]),[]).
%
% cnf(174073600,plain,(equidistant(reflection(B,A),A,B,A)),inference(paramodulation,[status(thm)],[173499112,163505984,theory(equality)]),[]).
%
% fof(v_equals_reflection,plain,($equal(reflection(u,v),v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163510008,plain,($equal(reflection(u,v),v)),inference(rewrite,[status(thm)],[v_equals_reflection]),[]).
%
% cnf(174149512,plain,(equidistant(v,v,u,v)),inference(paramodulation,[status(thm)],[174073600,163510008,theory(equality)]),[]).
%
% fof(identity_for_equidistance,plain,(~equidistant(A,B,C,C)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163289120,plain,(~equidistant(A,B,C,C)|$equal(B,A)),inference(rewrite,[status(thm)],[identity_for_equidistance]),[]).
%
% fof(prove_u_equals_v,plain,(~$equal(v,u)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-2.tptp',unknown),[]).
%
% cnf(163518816,plain,(~$equal(v,u)),inference(rewrite,[status(thm)],[prove_u_equals_v]),[]).
%
% cnf(171346576,plain,(~equidistant(u,v,A,A)),inference(resolution,[status(thm)],[163289120,163518816]),[]).
%
% cnf(172181112,plain,(~equidistant(A,B,u,v)|~equidistant(A,B,C,C)),inference(resolution,[status(thm)],[163280072,171346576]),[]).
%
% cnf(172214072,plain,(~equidistant(A,A,u,v)),inference(resolution,[status(thm)],[172181112,163271384]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[174149512,172214072]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------