TSTP Solution File: GRP037-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP037-3 : 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 12:19:04 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(product_right_cancellation,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,D,C)
| $equal(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170827784,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| $equal(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170751608,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(178976032,plain,
( ~ product(A,B,A)
| $equal(identity,B) ),
inference(resolution,[status(thm)],[170827784,170751608]),
[] ).
fof(another_right_identity,plain,
! [A] :
( ~ subgroup_member(A)
| product(A,another_identity,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170807400,plain,
( ~ subgroup_member(A)
| product(A,another_identity,A) ),
inference(rewrite,[status(thm)],[another_right_identity]),
[] ).
fof(a_is_in_subgroup,plain,
subgroup_member(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170835528,plain,
subgroup_member(a),
inference(rewrite,[status(thm)],[a_is_in_subgroup]),
[] ).
cnf(178653632,plain,
product(a,another_identity,a),
inference(resolution,[status(thm)],[170807400,170835528]),
[] ).
cnf(179191824,plain,
$equal(identity,another_identity),
inference(resolution,[status(thm)],[178976032,178653632]),
[] ).
fof(another_left_inverse,plain,
! [A] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170819072,plain,
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
inference(rewrite,[status(thm)],[another_left_inverse]),
[] ).
cnf(178675648,plain,
product(another_inverse(a),a,another_identity),
inference(resolution,[status(thm)],[170819072,170835528]),
[] ).
cnf(181963560,plain,
product(another_inverse(a),a,identity),
inference(paramodulation,[status(thm)],[179191824,178675648,theory(equality)]),
[] ).
fof(prove_two_inverses_are_equal,plain,
~ $equal(another_inverse(a),inverse(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170844192,plain,
~ $equal(another_inverse(a),inverse(a)),
inference(rewrite,[status(thm)],[prove_two_inverses_are_equal]),
[] ).
fof(product_left_cancellation,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| $equal(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170831416,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| $equal(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),
[] ).
cnf(170755256,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(179399920,plain,
( ~ product(A,B,identity)
| $equal(A,inverse(B)) ),
inference(resolution,[status(thm)],[170831416,170755256]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[181963560,170844192,179399920]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(product_right_cancellation,plain,(~product(A,B,C)|~product(A,D,C)|$equal(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170827784,plain,(~product(A,B,C)|~product(A,D,C)|$equal(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170751608,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(178976032,plain,(~product(A,B,A)|$equal(identity,B)),inference(resolution,[status(thm)],[170827784,170751608]),[]).
%
% fof(another_right_identity,plain,(~subgroup_member(A)|product(A,another_identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170807400,plain,(~subgroup_member(A)|product(A,another_identity,A)),inference(rewrite,[status(thm)],[another_right_identity]),[]).
%
% fof(a_is_in_subgroup,plain,(subgroup_member(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170835528,plain,(subgroup_member(a)),inference(rewrite,[status(thm)],[a_is_in_subgroup]),[]).
%
% cnf(178653632,plain,(product(a,another_identity,a)),inference(resolution,[status(thm)],[170807400,170835528]),[]).
%
% cnf(179191824,plain,($equal(identity,another_identity)),inference(resolution,[status(thm)],[178976032,178653632]),[]).
%
% fof(another_left_inverse,plain,(~subgroup_member(A)|product(another_inverse(A),A,another_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170819072,plain,(~subgroup_member(A)|product(another_inverse(A),A,another_identity)),inference(rewrite,[status(thm)],[another_left_inverse]),[]).
%
% cnf(178675648,plain,(product(another_inverse(a),a,another_identity)),inference(resolution,[status(thm)],[170819072,170835528]),[]).
%
% cnf(181963560,plain,(product(another_inverse(a),a,identity)),inference(paramodulation,[status(thm)],[179191824,178675648,theory(equality)]),[]).
%
% fof(prove_two_inverses_are_equal,plain,(~$equal(another_inverse(a),inverse(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170844192,plain,(~$equal(another_inverse(a),inverse(a))),inference(rewrite,[status(thm)],[prove_two_inverses_are_equal]),[]).
%
% fof(product_left_cancellation,plain,(~product(A,B,C)|~product(D,B,C)|$equal(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170831416,plain,(~product(A,B,C)|~product(D,B,C)|$equal(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP037-3.tptp',unknown),[]).
%
% cnf(170755256,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(179399920,plain,(~product(A,B,identity)|$equal(A,inverse(B))),inference(resolution,[status(thm)],[170831416,170755256]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[181963560,170844192,179399920]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------