TSTP Solution File: GRP019-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP019-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 12:18:04 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 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 7 !; 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/GRP019-1.tptp',unknown),
[] ).
cnf(172723832,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/GRP019-1.tptp',unknown),
[] ).
cnf(172697424,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(180512392,plain,
( ~ product(identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[172723832,172697424]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP019-1.tptp',unknown),
[] ).
cnf(172712528,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(181298840,plain,
$equal(multiply(identity,A),A),
inference(resolution,[status(thm)],[180512392,172712528]),
[] ).
fof(prove_id_times_X_is_X,plain,
~ $equal(multiply(identity,a),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP019-1.tptp',unknown),
[] ).
cnf(172742944,plain,
~ $equal(multiply(identity,a),a),
inference(rewrite,[status(thm)],[prove_id_times_X_is_X]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[181298840,172742944]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP019-1.tptp',unknown),[]).
%
% cnf(172723832,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP019-1.tptp',unknown),[]).
%
% cnf(172697424,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(180512392,plain,(~product(identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[172723832,172697424]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP019-1.tptp',unknown),[]).
%
% cnf(172712528,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(181298840,plain,($equal(multiply(identity,A),A)),inference(resolution,[status(thm)],[180512392,172712528]),[]).
%
% fof(prove_id_times_X_is_X,plain,(~$equal(multiply(identity,a),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP019-1.tptp',unknown),[]).
%
% cnf(172742944,plain,(~$equal(multiply(identity,a),a)),inference(rewrite,[status(thm)],[prove_id_times_X_is_X]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[181298840,172742944]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------