%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO058-3 : 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 11:54:21 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GEO058-3.tptp',unknown),
[] ).
cnf(170201744,plain,
( ~ equidistant(A,B,C,D)
| equidistant(C,D,A,B) ),
inference(rewrite,[status(thm)],[d2]),
[] ).
fof(r2_2,plain,
! [A,B] : equidistant(A,reflection(B,A),B,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-3.tptp',unknown),
[] ).
cnf(170268488,plain,
equidistant(A,reflection(B,A),B,A),
inference(rewrite,[status(thm)],[r2_2]),
[] ).
cnf(180380256,plain,
equidistant(B,A,A,reflection(B,A)),
inference(resolution,[status(thm)],[170201744,170268488]),
[] ).
fof(v_equals_reflection,plain,
$equal(reflection(u,v),v),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-3.tptp',unknown),
[] ).
cnf(170290456,plain,
$equal(reflection(u,v),v),
inference(rewrite,[status(thm)],[v_equals_reflection]),
[] ).
cnf(180444560,plain,
equidistant(u,v,v,v),
inference(paramodulation,[status(thm)],[180380256,170290456,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/GEO058-3.tptp',unknown),
[] ).
cnf(169976096,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/GEO058-3.tptp',unknown),
[] ).
cnf(170294152,plain,
~ $equal(v,u),
inference(rewrite,[status(thm)],[prove_u_equals_v]),
[] ).
cnf(178126584,plain,
~ equidistant(u,v,A,A),
inference(resolution,[status(thm)],[169976096,170294152]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[180444560,178126584]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(d2,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-3.tptp',unknown),[]).
%
% cnf(170201744,plain,(~equidistant(A,B,C,D)|equidistant(C,D,A,B)),inference(rewrite,[status(thm)],[d2]),[]).
%
% fof(r2_2,plain,(equidistant(A,reflection(B,A),B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-3.tptp',unknown),[]).
%
% cnf(170268488,plain,(equidistant(A,reflection(B,A),B,A)),inference(rewrite,[status(thm)],[r2_2]),[]).
%
% cnf(180380256,plain,(equidistant(B,A,A,reflection(B,A))),inference(resolution,[status(thm)],[170201744,170268488]),[]).
%
% fof(v_equals_reflection,plain,($equal(reflection(u,v),v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-3.tptp',unknown),[]).
%
% cnf(170290456,plain,($equal(reflection(u,v),v)),inference(rewrite,[status(thm)],[v_equals_reflection]),[]).
%
% cnf(180444560,plain,(equidistant(u,v,v,v)),inference(paramodulation,[status(thm)],[180380256,170290456,theory(equality)]),[]).
%
% fof(identity_for_equidistance,plain,(~equidistant(A,B,C,C)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO058-3.tptp',unknown),[]).
%
% cnf(169976096,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/GEO058-3.tptp',unknown),[]).
%
% cnf(170294152,plain,(~$equal(v,u)),inference(rewrite,[status(thm)],[prove_u_equals_v]),[]).
%
% cnf(178126584,plain,(~equidistant(u,v,A,A)),inference(resolution,[status(thm)],[169976096,170294152]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[180444560,178126584]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------