%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : FLD071-4 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 11:51:24 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(not_less_or_equal_7,plain,
~ less_or_equal(additive_identity,u),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),
[] ).
cnf(171379464,plain,
~ less_or_equal(additive_identity,u),
inference(rewrite,[status(thm)],[not_less_or_equal_7]),
[] ).
fof(less_or_equal_4,plain,
less_or_equal(additive_identity,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),
[] ).
cnf(171362472,plain,
less_or_equal(additive_identity,a),
inference(rewrite,[status(thm)],[less_or_equal_4]),
[] ).
fof(less_or_equal_5,plain,
less_or_equal(additive_identity,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),
[] ).
cnf(171366600,plain,
less_or_equal(additive_identity,b),
inference(rewrite,[status(thm)],[less_or_equal_5]),
[] ).
fof(compatibility_of_order_relation_and_multiplication,plain,
! [A,B,C] :
( less_or_equal(additive_identity,A)
| ~ less_or_equal(additive_identity,B)
| ~ less_or_equal(additive_identity,C)
| ~ product(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),
[] ).
cnf(171338048,plain,
( less_or_equal(additive_identity,A)
| ~ less_or_equal(additive_identity,B)
| ~ less_or_equal(additive_identity,C)
| ~ product(B,C,A) ),
inference(rewrite,[status(thm)],[compatibility_of_order_relation_and_multiplication]),
[] ).
fof(commutativity_multiplication,plain,
! [A,B,C] :
( product(A,B,C)
| ~ product(B,A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),
[] ).
cnf(171207248,plain,
( product(A,B,C)
| ~ product(B,A,C) ),
inference(rewrite,[status(thm)],[commutativity_multiplication]),
[] ).
fof(product_6,plain,
product(a,b,u),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),
[] ).
cnf(171370488,plain,
product(a,b,u),
inference(rewrite,[status(thm)],[product_6]),
[] ).
cnf(188465288,plain,
product(b,a,u),
inference(resolution,[status(thm)],[171207248,171370488]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[171379464,171362472,171366600,171338048,188465288]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(not_less_or_equal_7,plain,(~less_or_equal(additive_identity,u)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),[]).
%
% cnf(171379464,plain,(~less_or_equal(additive_identity,u)),inference(rewrite,[status(thm)],[not_less_or_equal_7]),[]).
%
% fof(less_or_equal_4,plain,(less_or_equal(additive_identity,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),[]).
%
% cnf(171362472,plain,(less_or_equal(additive_identity,a)),inference(rewrite,[status(thm)],[less_or_equal_4]),[]).
%
% fof(less_or_equal_5,plain,(less_or_equal(additive_identity,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),[]).
%
% cnf(171366600,plain,(less_or_equal(additive_identity,b)),inference(rewrite,[status(thm)],[less_or_equal_5]),[]).
%
% fof(compatibility_of_order_relation_and_multiplication,plain,(less_or_equal(additive_identity,A)|~less_or_equal(additive_identity,B)|~less_or_equal(additive_identity,C)|~product(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),[]).
%
% cnf(171338048,plain,(less_or_equal(additive_identity,A)|~less_or_equal(additive_identity,B)|~less_or_equal(additive_identity,C)|~product(B,C,A)),inference(rewrite,[status(thm)],[compatibility_of_order_relation_and_multiplication]),[]).
%
% fof(commutativity_multiplication,plain,(product(A,B,C)|~product(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),[]).
%
% cnf(171207248,plain,(product(A,B,C)|~product(B,A,C)),inference(rewrite,[status(thm)],[commutativity_multiplication]),[]).
%
% fof(product_6,plain,(product(a,b,u)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD071-4.tptp',unknown),[]).
%
% cnf(171370488,plain,(product(a,b,u)),inference(rewrite,[status(thm)],[product_6]),[]).
%
% cnf(188465288,plain,(product(b,a,u)),inference(resolution,[status(thm)],[171207248,171370488]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171379464,171362472,171366600,171338048,188465288]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------