%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP042-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 12:19:20 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 : 13 ( 8 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 22 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(product_substitution3,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),
[] ).
cnf(173852792,plain,
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
inference(rewrite,[status(thm)],[product_substitution3]),
[] ).
fof(a_equals_b,plain,
equalish(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),
[] ).
cnf(173861424,plain,
equalish(a,b),
inference(rewrite,[status(thm)],[a_equals_b]),
[] ).
cnf(181644552,plain,
( ~ product(A,B,a)
| product(A,B,b) ),
inference(resolution,[status(thm)],[173852792,173861424]),
[] ).
fof(total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),
[] ).
cnf(173834304,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(prove_symmetry,plain,
~ equalish(b,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),
[] ).
cnf(173865424,plain,
~ equalish(b,a),
inference(rewrite,[status(thm)],[prove_symmetry]),
[] ).
cnf(181778808,plain,
~ product(A,B,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[181644552,173834304,173865424]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),
[] ).
cnf(173818416,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[181778808,173818416]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(product_substitution3,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),[]).
%
% cnf(173852792,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),inference(rewrite,[status(thm)],[product_substitution3]),[]).
%
% fof(a_equals_b,plain,(equalish(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),[]).
%
% cnf(173861424,plain,(equalish(a,b)),inference(rewrite,[status(thm)],[a_equals_b]),[]).
%
% cnf(181644552,plain,(~product(A,B,a)|product(A,B,b)),inference(resolution,[status(thm)],[173852792,173861424]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),[]).
%
% cnf(173834304,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(prove_symmetry,plain,(~equalish(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),[]).
%
% cnf(173865424,plain,(~equalish(b,a)),inference(rewrite,[status(thm)],[prove_symmetry]),[]).
%
% cnf(181778808,plain,(~product(A,B,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[181644552,173834304,173865424]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP042-2.tptp',unknown),[]).
%
% cnf(173818416,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[181778808,173818416]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------