TSTP Solution File: GRP031-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP031-2 : 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 12:18:49 EDT 2009
% Result : Unsatisfiable 2.0s
% Output : Refutation 2.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 45 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associativity2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),
[] ).
cnf(150400936,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(right_inverse,plain,
! [A] : product(A,inverse(A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),
[] ).
cnf(150404200,plain,
product(A,inverse(A),identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
cnf(158455952,plain,
( ~ product(inverse(A),B,C)
| ~ product(A,C,D)
| product(identity,B,D) ),
inference(resolution,[status(thm)],[150400936,150404200]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),
[] ).
cnf(150407960,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(158539792,plain,
( ~ product(inverse(A),B,identity)
| product(identity,B,A) ),
inference(resolution,[status(thm)],[158455952,150407960]),
[] ).
cnf(163144272,plain,
product(identity,inverse(inverse(A)),A),
inference(resolution,[status(thm)],[158539792,150404200]),
[] ).
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/GRP031-2.tptp',unknown),
[] ).
cnf(150396672,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
cnf(158391688,plain,
( ~ product(A,B,C)
| ~ product(B,inverse(C),D)
| product(A,D,identity) ),
inference(resolution,[status(thm)],[150396672,150404200]),
[] ).
fof(prove_a_has_a_left_inverse,plain,
! [A] : ~ product(A,a,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),
[] ).
cnf(150411728,plain,
~ product(A,a,identity),
inference(rewrite,[status(thm)],[prove_a_has_a_left_inverse]),
[] ).
cnf(158622152,plain,
( ~ product(A,B,C)
| ~ product(B,inverse(C),a) ),
inference(resolution,[status(thm)],[158391688,150411728]),
[] ).
cnf(158635736,plain,
~ product(identity,inverse(A),a),
inference(resolution,[status(thm)],[158622152,150407960]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[163144272,158635736]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(associativity2,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),[]).
%
% cnf(150400936,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),[]).
%
% cnf(150404200,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% cnf(158455952,plain,(~product(inverse(A),B,C)|~product(A,C,D)|product(identity,B,D)),inference(resolution,[status(thm)],[150400936,150404200]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),[]).
%
% cnf(150407960,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(158539792,plain,(~product(inverse(A),B,identity)|product(identity,B,A)),inference(resolution,[status(thm)],[158455952,150407960]),[]).
%
% cnf(163144272,plain,(product(identity,inverse(inverse(A)),A)),inference(resolution,[status(thm)],[158539792,150404200]),[]).
%
% 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/GRP031-2.tptp',unknown),[]).
%
% cnf(150396672,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% cnf(158391688,plain,(~product(A,B,C)|~product(B,inverse(C),D)|product(A,D,identity)),inference(resolution,[status(thm)],[150396672,150404200]),[]).
%
% fof(prove_a_has_a_left_inverse,plain,(~product(A,a,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP031-2.tptp',unknown),[]).
%
% cnf(150411728,plain,(~product(A,a,identity)),inference(rewrite,[status(thm)],[prove_a_has_a_left_inverse]),[]).
%
% cnf(158622152,plain,(~product(A,B,C)|~product(B,inverse(C),a)),inference(resolution,[status(thm)],[158391688,150411728]),[]).
%
% cnf(158635736,plain,(~product(identity,inverse(A),a)),inference(resolution,[status(thm)],[158622152,150407960]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[163144272,158635736]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------