TSTP Solution File: GRP020-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP020-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 12:18:06 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 : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 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(prove_inverse_X_times_X_is_id,plain,
~ $equal(multiply(inverse(a),a),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),
[] ).
cnf(148504520,plain,
~ $equal(multiply(inverse(a),a),identity),
inference(rewrite,[status(thm)],[prove_inverse_X_times_X_is_id]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),
[] ).
cnf(148474104,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
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/GRP020-1.tptp',unknown),
[] ).
cnf(148485408,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),
[] ).
cnf(148466688,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(156468528,plain,
( ~ product(inverse(A),A,B)
| $equal(B,identity) ),
inference(resolution,[status(thm)],[148485408,148466688]),
[] ).
cnf(157404536,plain,
$equal(multiply(inverse(A),A),identity),
inference(resolution,[status(thm)],[148474104,156468528]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[148504520,157404536]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_inverse_X_times_X_is_id,plain,(~$equal(multiply(inverse(a),a),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),[]).
%
% cnf(148504520,plain,(~$equal(multiply(inverse(a),a),identity)),inference(rewrite,[status(thm)],[prove_inverse_X_times_X_is_id]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),[]).
%
% cnf(148474104,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),[]).
%
% cnf(148485408,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP020-1.tptp',unknown),[]).
%
% cnf(148466688,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(156468528,plain,(~product(inverse(A),A,B)|$equal(B,identity)),inference(resolution,[status(thm)],[148485408,148466688]),[]).
%
% cnf(157404536,plain,($equal(multiply(inverse(A),A),identity)),inference(resolution,[status(thm)],[148474104,156468528]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[148504520,157404536]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------