%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP034-4 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 12:18:58 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 13 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_inverse_is_in_subgroup,plain,
~ subgroup_member(inverse(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),
[] ).
cnf(169075736,plain,
~ subgroup_member(inverse(a)),
inference(rewrite,[status(thm)],[prove_inverse_is_in_subgroup]),
[] ).
fof(closure_of_subgroup,plain,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(B,inverse(A),C)
| subgroup_member(C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),
[] ).
cnf(169063032,plain,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(B,inverse(A),C)
| subgroup_member(C) ),
inference(rewrite,[status(thm)],[closure_of_subgroup]),
[] ).
fof(a_is_in_subgroup,plain,
subgroup_member(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),
[] ).
cnf(169071760,plain,
subgroup_member(a),
inference(rewrite,[status(thm)],[a_is_in_subgroup]),
[] ).
cnf(176846856,plain,
( ~ subgroup_member(A)
| ~ product(A,inverse(a),B)
| subgroup_member(B) ),
inference(resolution,[status(thm)],[169063032,169071760]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),
[] ).
cnf(169019104,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(176899920,plain,
~ subgroup_member(identity),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169075736,176846856,169019104]),
[] ).
fof(right_inverse,plain,
! [A] : product(A,inverse(A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),
[] ).
cnf(169026608,plain,
product(A,inverse(A),identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
cnf(178001296,plain,
~ subgroup_member(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[176899920,169063032,169026608]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[178001296,169071760]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_inverse_is_in_subgroup,plain,(~subgroup_member(inverse(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),[]).
%
% cnf(169075736,plain,(~subgroup_member(inverse(a))),inference(rewrite,[status(thm)],[prove_inverse_is_in_subgroup]),[]).
%
% fof(closure_of_subgroup,plain,(~subgroup_member(A)|~subgroup_member(B)|~product(B,inverse(A),C)|subgroup_member(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),[]).
%
% cnf(169063032,plain,(~subgroup_member(A)|~subgroup_member(B)|~product(B,inverse(A),C)|subgroup_member(C)),inference(rewrite,[status(thm)],[closure_of_subgroup]),[]).
%
% fof(a_is_in_subgroup,plain,(subgroup_member(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),[]).
%
% cnf(169071760,plain,(subgroup_member(a)),inference(rewrite,[status(thm)],[a_is_in_subgroup]),[]).
%
% cnf(176846856,plain,(~subgroup_member(A)|~product(A,inverse(a),B)|subgroup_member(B)),inference(resolution,[status(thm)],[169063032,169071760]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),[]).
%
% cnf(169019104,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(176899920,plain,(~subgroup_member(identity)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169075736,176846856,169019104]),[]).
%
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP034-4.tptp',unknown),[]).
%
% cnf(169026608,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% cnf(178001296,plain,(~subgroup_member(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[176899920,169063032,169026608]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[178001296,169071760]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------