%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO041-3 : 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 11:53:41 EDT 2009
% Result : Unsatisfiable 3.5s
% Output : Refutation 3.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(w_between_u_and_v,plain,
between(u,w,v),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144276808,plain,
between(u,w,v),
inference(rewrite,[status(thm)],[w_between_u_and_v]),
[] ).
fof(t1,plain,
! [A,B,C] :
( ~ between(A,B,C)
| between(C,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144257232,plain,
( ~ between(A,B,C)
| between(C,B,A) ),
inference(rewrite,[status(thm)],[t1]),
[] ).
cnf(159070400,plain,
between(v,w,u),
inference(resolution,[status(thm)],[144276808,144257232]),
[] ).
fof(b2,plain,
! [A,B,C] :
( ~ between(A,B,C)
| ~ between(B,A,C)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144265232,plain,
( ~ between(A,B,C)
| ~ between(B,A,C)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[b2]),
[] ).
fof(v_between_u_and_w,plain,
between(u,v,w),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144273032,plain,
between(u,v,w),
inference(rewrite,[status(thm)],[v_between_u_and_w]),
[] ).
cnf(159061952,plain,
between(w,v,u),
inference(resolution,[status(thm)],[144273032,144257232]),
[] ).
cnf(240120736,plain,
$equal(v,w),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159070400,144265232,159061952]),
[] ).
fof(b1,plain,
! [A,B,C,D] :
( ~ between(A,B,C)
| ~ $equal(C,A)
| between(D,B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144252080,plain,
( ~ between(A,B,C)
| ~ $equal(C,A)
| between(D,B,C) ),
inference(rewrite,[status(thm)],[b1]),
[] ).
fof(t2,plain,
! [A,B] : between(A,A,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144261336,plain,
between(A,A,B),
inference(rewrite,[status(thm)],[t2]),
[] ).
cnf(152508544,plain,
( ~ $equal(B,A)
| between(C,A,B) ),
inference(resolution,[status(thm)],[144252080,144261336]),
[] ).
fof(prove_v_is_w,plain,
~ $equal(w,v),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(144280344,plain,
~ $equal(w,v),
inference(rewrite,[status(thm)],[prove_v_is_w]),
[] ).
fof(identity_for_betweeness,plain,
! [A,B] :
( ~ between(A,B,A)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),
[] ).
cnf(143891224,plain,
( ~ between(A,B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[identity_for_betweeness]),
[] ).
cnf(156494824,plain,
~ between(v,w,v),
inference(resolution,[status(thm)],[144280344,143891224]),
[] ).
cnf(156963088,plain,
~ $equal(v,w),
inference(resolution,[status(thm)],[152508544,156494824]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[240120736,156963088]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(w_between_u_and_v,plain,(between(u,w,v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144276808,plain,(between(u,w,v)),inference(rewrite,[status(thm)],[w_between_u_and_v]),[]).
%
% fof(t1,plain,(~between(A,B,C)|between(C,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144257232,plain,(~between(A,B,C)|between(C,B,A)),inference(rewrite,[status(thm)],[t1]),[]).
%
% cnf(159070400,plain,(between(v,w,u)),inference(resolution,[status(thm)],[144276808,144257232]),[]).
%
% fof(b2,plain,(~between(A,B,C)|~between(B,A,C)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144265232,plain,(~between(A,B,C)|~between(B,A,C)|$equal(B,A)),inference(rewrite,[status(thm)],[b2]),[]).
%
% fof(v_between_u_and_w,plain,(between(u,v,w)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144273032,plain,(between(u,v,w)),inference(rewrite,[status(thm)],[v_between_u_and_w]),[]).
%
% cnf(159061952,plain,(between(w,v,u)),inference(resolution,[status(thm)],[144273032,144257232]),[]).
%
% cnf(240120736,plain,($equal(v,w)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159070400,144265232,159061952]),[]).
%
% fof(b1,plain,(~between(A,B,C)|~$equal(C,A)|between(D,B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144252080,plain,(~between(A,B,C)|~$equal(C,A)|between(D,B,C)),inference(rewrite,[status(thm)],[b1]),[]).
%
% fof(t2,plain,(between(A,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144261336,plain,(between(A,A,B)),inference(rewrite,[status(thm)],[t2]),[]).
%
% cnf(152508544,plain,(~$equal(B,A)|between(C,A,B)),inference(resolution,[status(thm)],[144252080,144261336]),[]).
%
% fof(prove_v_is_w,plain,(~$equal(w,v)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(144280344,plain,(~$equal(w,v)),inference(rewrite,[status(thm)],[prove_v_is_w]),[]).
%
% fof(identity_for_betweeness,plain,(~between(A,B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO041-3.tptp',unknown),[]).
%
% cnf(143891224,plain,(~between(A,B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[identity_for_betweeness]),[]).
%
% cnf(156494824,plain,(~between(v,w,v)),inference(resolution,[status(thm)],[144280344,143891224]),[]).
%
% cnf(156963088,plain,(~$equal(v,w)),inference(resolution,[status(thm)],[152508544,156494824]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[240120736,156963088]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------