%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP546-1 : TPTP v3.4.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 13:07:45 EDT 2009
% Result : Unsatisfiable 1.3s
% Output : Refutation 1.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 19 ( 0 sgn 7 !; 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/GRP546-1.tptp',unknown),
[] ).
cnf(153526880,plain,
~ $equal(multiply(multiply(inverse(b2),b2),a2),a2),
inference(rewrite,[status(thm)],[prove_these_axioms_2]),
[] ).
fof(multiply,plain,
! [A,B] : $equal(divide(A,divide(identity,B)),multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),
[] ).
cnf(153510496,plain,
$equal(divide(A,divide(identity,B)),multiply(A,B)),
inference(rewrite,[status(thm)],[multiply]),
[] ).
cnf(161377088,plain,
~ $equal(multiply(divide(inverse(b2),divide(identity,b2)),a2),a2),
inference(paramodulation,[status(thm)],[153526880,153510496,theory(equality)]),
[] ).
fof(inverse,plain,
! [A] : $equal(divide(identity,A),inverse(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),
[] ).
cnf(153514360,plain,
$equal(divide(identity,A),inverse(A)),
inference(rewrite,[status(thm)],[inverse]),
[] ).
cnf(161594472,plain,
~ $equal(multiply(divide(inverse(b2),inverse(b2)),a2),a2),
inference(paramodulation,[status(thm)],[161377088,153514360,theory(equality)]),
[] ).
fof(identity,plain,
! [A] : $equal(divide(A,A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),
[] ).
cnf(153518272,plain,
$equal(divide(A,A),identity),
inference(rewrite,[status(thm)],[identity]),
[] ).
cnf(161674120,plain,
~ $equal(multiply(identity,a2),a2),
inference(paramodulation,[status(thm)],[161594472,153518272,theory(equality)]),
[] ).
cnf(161745016,plain,
~ $equal(multiply(divide(A,A),a2),a2),
inference(paramodulation,[status(thm)],[161674120,153518272,theory(equality)]),
[] ).
cnf(161798312,plain,
~ $equal(multiply(inverse(identity),a2),a2),
inference(paramodulation,[status(thm)],[161745016,153514360,theory(equality)]),
[] ).
cnf(161900064,plain,
~ $equal(multiply(divide(identity,identity),a2),a2),
inference(paramodulation,[status(thm)],[161798312,153514360,theory(equality)]),
[] ).
cnf(162121736,plain,
~ $equal(multiply(divide(identity,divide(A,A)),a2),a2),
inference(paramodulation,[status(thm)],[161900064,153518272,theory(equality)]),
[] ).
cnf(163657728,plain,
~ $equal(divide(divide(identity,divide(A,A)),divide(identity,a2)),a2),
inference(paramodulation,[status(thm)],[162121736,153510496,theory(equality)]),
[] ).
cnf(170625624,plain,
~ $equal(divide(divide(identity,divide(A,A)),divide(divide(B,B),a2)),a2),
inference(paramodulation,[status(thm)],[163657728,153518272,theory(equality)]),
[] ).
fof(single_axiom,plain,
! [A,B,C] : $equal(divide(divide(identity,divide(A,B)),divide(divide(B,C),A)),C),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),
[] ).
cnf(153506296,plain,
$equal(divide(divide(identity,divide(A,B)),divide(divide(B,C),A)),C),
inference(rewrite,[status(thm)],[single_axiom]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[170625624,153506296]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_these_axioms_2,plain,(~$equal(multiply(multiply(inverse(b2),b2),a2),a2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),[]).
%
% cnf(153526880,plain,(~$equal(multiply(multiply(inverse(b2),b2),a2),a2)),inference(rewrite,[status(thm)],[prove_these_axioms_2]),[]).
%
% fof(multiply,plain,($equal(divide(A,divide(identity,B)),multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),[]).
%
% cnf(153510496,plain,($equal(divide(A,divide(identity,B)),multiply(A,B))),inference(rewrite,[status(thm)],[multiply]),[]).
%
% cnf(161377088,plain,(~$equal(multiply(divide(inverse(b2),divide(identity,b2)),a2),a2)),inference(paramodulation,[status(thm)],[153526880,153510496,theory(equality)]),[]).
%
% fof(inverse,plain,($equal(divide(identity,A),inverse(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),[]).
%
% cnf(153514360,plain,($equal(divide(identity,A),inverse(A))),inference(rewrite,[status(thm)],[inverse]),[]).
%
% cnf(161594472,plain,(~$equal(multiply(divide(inverse(b2),inverse(b2)),a2),a2)),inference(paramodulation,[status(thm)],[161377088,153514360,theory(equality)]),[]).
%
% fof(identity,plain,($equal(divide(A,A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),[]).
%
% cnf(153518272,plain,($equal(divide(A,A),identity)),inference(rewrite,[status(thm)],[identity]),[]).
%
% cnf(161674120,plain,(~$equal(multiply(identity,a2),a2)),inference(paramodulation,[status(thm)],[161594472,153518272,theory(equality)]),[]).
%
% cnf(161745016,plain,(~$equal(multiply(divide(A,A),a2),a2)),inference(paramodulation,[status(thm)],[161674120,153518272,theory(equality)]),[]).
%
% cnf(161798312,plain,(~$equal(multiply(inverse(identity),a2),a2)),inference(paramodulation,[status(thm)],[161745016,153514360,theory(equality)]),[]).
%
% cnf(161900064,plain,(~$equal(multiply(divide(identity,identity),a2),a2)),inference(paramodulation,[status(thm)],[161798312,153514360,theory(equality)]),[]).
%
% cnf(162121736,plain,(~$equal(multiply(divide(identity,divide(A,A)),a2),a2)),inference(paramodulation,[status(thm)],[161900064,153518272,theory(equality)]),[]).
%
% cnf(163657728,plain,(~$equal(divide(divide(identity,divide(A,A)),divide(identity,a2)),a2)),inference(paramodulation,[status(thm)],[162121736,153510496,theory(equality)]),[]).
%
% cnf(170625624,plain,(~$equal(divide(divide(identity,divide(A,A)),divide(divide(B,B),a2)),a2)),inference(paramodulation,[status(thm)],[163657728,153518272,theory(equality)]),[]).
%
% fof(single_axiom,plain,($equal(divide(divide(identity,divide(A,B)),divide(divide(B,C),A)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP546-1.tptp',unknown),[]).
%
% cnf(153506296,plain,($equal(divide(divide(identity,divide(A,B)),divide(divide(B,C),A)),C)),inference(rewrite,[status(thm)],[single_axiom]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[170625624,153506296]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------