TSTP Solution File: GRP538-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP538-1 : TPTP v3.4.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 13:07:27 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 22 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_these_axioms_2,plain,
~ $equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),
[] ).
cnf(158231640,plain,
~ $equal(multiply(multiply(inverse(b2),b2),a2),a2),
inference(rewrite,[status(thm)],[prove_these_axioms_2]),
[] ).
fof(multiply,plain,
! [A,C,B] : $equal(divide(A,divide(divide(C,C),B)),multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),
[] ).
cnf(158200480,plain,
$equal(divide(A,divide(divide(C,C),B)),multiply(A,B)),
inference(rewrite,[status(thm)],[multiply]),
[] ).
cnf(166081944,plain,
~ $equal(multiply(divide(inverse(b2),divide(divide(A,A),b2)),a2),a2),
inference(paramodulation,[status(thm)],[158231640,158200480,theory(equality)]),
[] ).
fof(inverse,plain,
! [B,A] : $equal(divide(divide(B,B),A),inverse(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),
[] ).
cnf(158219080,plain,
$equal(divide(divide(B,B),A),inverse(A)),
inference(rewrite,[status(thm)],[inverse]),
[] ).
cnf(166588184,plain,
~ $equal(multiply(divide(inverse(b2),inverse(b2)),a2),a2),
inference(paramodulation,[status(thm)],[166081944,158219080,theory(equality)]),
[] ).
fof(identity,plain,
! [A] : $equal(divide(A,A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),
[] ).
cnf(158222944,plain,
$equal(divide(A,A),identity),
inference(rewrite,[status(thm)],[identity]),
[] ).
cnf(166666648,plain,
~ $equal(multiply(identity,a2),a2),
inference(paramodulation,[status(thm)],[166588184,158222944,theory(equality)]),
[] ).
cnf(166741632,plain,
~ $equal(multiply(divide(A,A),a2),a2),
inference(paramodulation,[status(thm)],[166666648,158222944,theory(equality)]),
[] ).
cnf(166824600,plain,
~ $equal(divide(divide(A,A),divide(divide(B,B),a2)),a2),
inference(paramodulation,[status(thm)],[166741632,158200480,theory(equality)]),
[] ).
fof(single_axiom,plain,
! [A,B,C] : $equal(divide(divide(A,B),divide(divide(A,C),B)),C),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),
[] ).
cnf(158178312,plain,
$equal(divide(divide(A,B),divide(divide(A,C),B)),C),
inference(rewrite,[status(thm)],[single_axiom]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[166824600,158178312]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_these_axioms_2,plain,(~$equal(multiply(multiply(inverse(b2),b2),a2),a2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),[]).
%
% cnf(158231640,plain,(~$equal(multiply(multiply(inverse(b2),b2),a2),a2)),inference(rewrite,[status(thm)],[prove_these_axioms_2]),[]).
%
% fof(multiply,plain,($equal(divide(A,divide(divide(C,C),B)),multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),[]).
%
% cnf(158200480,plain,($equal(divide(A,divide(divide(C,C),B)),multiply(A,B))),inference(rewrite,[status(thm)],[multiply]),[]).
%
% cnf(166081944,plain,(~$equal(multiply(divide(inverse(b2),divide(divide(A,A),b2)),a2),a2)),inference(paramodulation,[status(thm)],[158231640,158200480,theory(equality)]),[]).
%
% fof(inverse,plain,($equal(divide(divide(B,B),A),inverse(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),[]).
%
% cnf(158219080,plain,($equal(divide(divide(B,B),A),inverse(A))),inference(rewrite,[status(thm)],[inverse]),[]).
%
% cnf(166588184,plain,(~$equal(multiply(divide(inverse(b2),inverse(b2)),a2),a2)),inference(paramodulation,[status(thm)],[166081944,158219080,theory(equality)]),[]).
%
% fof(identity,plain,($equal(divide(A,A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),[]).
%
% cnf(158222944,plain,($equal(divide(A,A),identity)),inference(rewrite,[status(thm)],[identity]),[]).
%
% cnf(166666648,plain,(~$equal(multiply(identity,a2),a2)),inference(paramodulation,[status(thm)],[166588184,158222944,theory(equality)]),[]).
%
% cnf(166741632,plain,(~$equal(multiply(divide(A,A),a2),a2)),inference(paramodulation,[status(thm)],[166666648,158222944,theory(equality)]),[]).
%
% cnf(166824600,plain,(~$equal(divide(divide(A,A),divide(divide(B,B),a2)),a2)),inference(paramodulation,[status(thm)],[166741632,158200480,theory(equality)]),[]).
%
% fof(single_axiom,plain,($equal(divide(divide(A,B),divide(divide(A,C),B)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP538-1.tptp',unknown),[]).
%
% cnf(158178312,plain,($equal(divide(divide(A,B),divide(divide(A,C),B)),C)),inference(rewrite,[status(thm)],[single_axiom]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[166824600,158178312]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------