TSTP Solution File: GRP036-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP036-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 12:19:02 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),
[] ).
cnf(166635744,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
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/GRP036-3.tptp',unknown),
[] ).
cnf(166658528,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(associativity1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),
[] ).
cnf(166665328,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),
[] ).
cnf(166627960,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(174854720,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[166665328,166627960]),
[] ).
fof(another_left_identity,plain,
! [A] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),
[] ).
cnf(166687744,plain,
( ~ subgroup_member(A)
| product(another_identity,A,A) ),
inference(rewrite,[status(thm)],[another_left_identity]),
[] ).
fof(another_identity_in_subgroup,plain,
subgroup_member(another_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),
[] ).
cnf(166712600,plain,
subgroup_member(another_identity),
inference(rewrite,[status(thm)],[another_identity_in_subgroup]),
[] ).
cnf(174508952,plain,
product(another_identity,another_identity,another_identity),
inference(resolution,[status(thm)],[166687744,166712600]),
[] ).
cnf(175027064,plain,
( ~ product(A,another_identity,identity)
| product(A,another_identity,another_identity) ),
inference(resolution,[status(thm)],[174854720,174508952]),
[] ).
cnf(175083040,plain,
product(inverse(another_identity),another_identity,another_identity),
inference(resolution,[status(thm)],[175027064,166635744]),
[] ).
cnf(175361808,plain,
( ~ product(inverse(another_identity),another_identity,A)
| $equal(another_identity,A) ),
inference(resolution,[status(thm)],[166658528,175083040]),
[] ).
fof(prove_identity_equals_another_identity,plain,
~ $equal(another_identity,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),
[] ).
cnf(166717272,plain,
~ $equal(another_identity,identity),
inference(rewrite,[status(thm)],[prove_identity_equals_another_identity]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[166635744,175361808,166717272]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166635744,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166658528,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(associativity1,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166665328,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166627960,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(174854720,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[166665328,166627960]),[]).
%
% fof(another_left_identity,plain,(~subgroup_member(A)|product(another_identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166687744,plain,(~subgroup_member(A)|product(another_identity,A,A)),inference(rewrite,[status(thm)],[another_left_identity]),[]).
%
% fof(another_identity_in_subgroup,plain,(subgroup_member(another_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166712600,plain,(subgroup_member(another_identity)),inference(rewrite,[status(thm)],[another_identity_in_subgroup]),[]).
%
% cnf(174508952,plain,(product(another_identity,another_identity,another_identity)),inference(resolution,[status(thm)],[166687744,166712600]),[]).
%
% cnf(175027064,plain,(~product(A,another_identity,identity)|product(A,another_identity,another_identity)),inference(resolution,[status(thm)],[174854720,174508952]),[]).
%
% cnf(175083040,plain,(product(inverse(another_identity),another_identity,another_identity)),inference(resolution,[status(thm)],[175027064,166635744]),[]).
%
% cnf(175361808,plain,(~product(inverse(another_identity),another_identity,A)|$equal(another_identity,A)),inference(resolution,[status(thm)],[166658528,175083040]),[]).
%
% fof(prove_identity_equals_another_identity,plain,(~$equal(another_identity,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP036-3.tptp',unknown),[]).
%
% cnf(166717272,plain,(~$equal(another_identity,identity)),inference(rewrite,[status(thm)],[prove_identity_equals_another_identity]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[166635744,175361808,166717272]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------