TSTP Solution File: GRP549-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP549-1 : TPTP v3.4.2. Released v2.6.0.
% 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 13:07:54 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(identity,plain,
! [A] : $equal(divide(A,A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
[] ).
cnf(145135400,plain,
$equal(divide(A,A),identity),
inference(rewrite,[status(thm)],[identity]),
[] ).
fof(prove_these_axioms_1,plain,
~ $equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
[] ).
cnf(145144016,plain,
~ $equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(rewrite,[status(thm)],[prove_these_axioms_1]),
[] ).
fof(multiply,plain,
! [A,B] : $equal(divide(A,divide(identity,B)),multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
[] ).
cnf(145127656,plain,
$equal(divide(A,divide(identity,B)),multiply(A,B)),
inference(rewrite,[status(thm)],[multiply]),
[] ).
cnf(152980920,plain,
~ $equal(multiply(inverse(b1),b1),divide(inverse(a1),divide(identity,a1))),
inference(paramodulation,[status(thm)],[145144016,145127656,theory(equality)]),
[] ).
fof(inverse,plain,
! [A] : $equal(divide(identity,A),inverse(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
[] ).
cnf(145131520,plain,
$equal(divide(identity,A),inverse(A)),
inference(rewrite,[status(thm)],[inverse]),
[] ).
cnf(153171464,plain,
~ $equal(multiply(inverse(b1),b1),divide(inverse(a1),inverse(a1))),
inference(paramodulation,[status(thm)],[152980920,145131520,theory(equality)]),
[] ).
cnf(153254552,plain,
~ $equal(multiply(inverse(b1),b1),identity),
inference(paramodulation,[status(thm)],[153171464,145135400,theory(equality)]),
[] ).
cnf(153353584,plain,
~ $equal(divide(inverse(b1),divide(identity,b1)),identity),
inference(paramodulation,[status(thm)],[153254552,145127656,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145135400,153353584,145131520,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(identity,plain,($equal(divide(A,A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
%
% cnf(145135400,plain,($equal(divide(A,A),identity)),inference(rewrite,[status(thm)],[identity]),[]).
%
% fof(prove_these_axioms_1,plain,(~$equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
%
% cnf(145144016,plain,(~$equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))),inference(rewrite,[status(thm)],[prove_these_axioms_1]),[]).
%
% fof(multiply,plain,($equal(divide(A,divide(identity,B)),multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
%
% cnf(145127656,plain,($equal(divide(A,divide(identity,B)),multiply(A,B))),inference(rewrite,[status(thm)],[multiply]),[]).
%
% cnf(152980920,plain,(~$equal(multiply(inverse(b1),b1),divide(inverse(a1),divide(identity,a1)))),inference(paramodulation,[status(thm)],[145144016,145127656,theory(equality)]),[]).
%
% fof(inverse,plain,($equal(divide(identity,A),inverse(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
%
% cnf(145131520,plain,($equal(divide(identity,A),inverse(A))),inference(rewrite,[status(thm)],[inverse]),[]).
%
% cnf(153171464,plain,(~$equal(multiply(inverse(b1),b1),divide(inverse(a1),inverse(a1)))),inference(paramodulation,[status(thm)],[152980920,145131520,theory(equality)]),[]).
%
% cnf(153254552,plain,(~$equal(multiply(inverse(b1),b1),identity)),inference(paramodulation,[status(thm)],[153171464,145135400,theory(equality)]),[]).
%
% cnf(153353584,plain,(~$equal(divide(inverse(b1),divide(identity,b1)),identity)),inference(paramodulation,[status(thm)],[153254552,145127656,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145135400,153353584,145131520,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------