%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP023-1 : 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 12:18:13 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),
[] ).
cnf(163592944,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),
[] ).
cnf(163566568,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(171380400,plain,
( ~ product(identity,A,B)
| $equal(A,B) ),
inference(resolution,[status(thm)],[163592944,163566568]),
[] ).
fof(right_inverse,plain,
! [A] : product(A,inverse(A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),
[] ).
cnf(163578064,plain,
product(A,inverse(A),identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
cnf(171667272,plain,
$equal(inverse(identity),identity),
inference(resolution,[status(thm)],[171380400,163578064]),
[] ).
fof(prove_inverse_of_id_is_id,plain,
~ $equal(inverse(identity),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),
[] ).
cnf(163611992,plain,
~ $equal(inverse(identity),identity),
inference(rewrite,[status(thm)],[prove_inverse_of_id_is_id]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[171667272,163611992]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),[]).
%
% cnf(163592944,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),[]).
%
% cnf(163566568,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(171380400,plain,(~product(identity,A,B)|$equal(A,B)),inference(resolution,[status(thm)],[163592944,163566568]),[]).
%
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),[]).
%
% cnf(163578064,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% cnf(171667272,plain,($equal(inverse(identity),identity)),inference(resolution,[status(thm)],[171380400,163578064]),[]).
%
% fof(prove_inverse_of_id_is_id,plain,(~$equal(inverse(identity),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP023-1.tptp',unknown),[]).
%
% cnf(163611992,plain,(~$equal(inverse(identity),identity)),inference(rewrite,[status(thm)],[prove_inverse_of_id_is_id]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[171667272,163611992]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------