TSTP Solution File: GRP003-2 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP003-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 12:17:25 EDT 2009
% Result : Unsatisfiable 8.6s
% Output : Refutation 8.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 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 : 41 ( 0 sgn 14 !; 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/GRP003-2.tptp',unknown),
[] ).
cnf(173976000,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP003-2.tptp',unknown),
[] ).
cnf(173949176,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(181857792,plain,
( ~ product(A,identity,B)
| ~ product(A,C,D)
| product(B,C,D) ),
inference(resolution,[status(thm)],[173976000,173949176]),
[] ).
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/GRP003-2.tptp',unknown),
[] ).
cnf(173971736,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
cnf(181847944,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[173971736,173949176]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP003-2.tptp',unknown),
[] ).
cnf(173953256,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(181879616,plain,
( ~ product(A,B,C)
| product(inverse(A),C,B) ),
inference(resolution,[status(thm)],[181847944,173953256]),
[] ).
cnf(187649528,plain,
product(inverse(inverse(A)),identity,A),
inference(resolution,[status(thm)],[181879616,173953256]),
[] ).
cnf(257576512,plain,
product(A,identity,A),
inference(resolution,[status(thm)],[181857792,187649528]),
[] ).
fof(prove_left_identity,plain,
~ product(a,identity,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP003-2.tptp',unknown),
[] ).
cnf(173991328,plain,
~ product(a,identity,a),
inference(rewrite,[status(thm)],[prove_left_identity]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[257576512,173991328]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 9 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/GRP003-2.tptp',unknown),[]).
%
% cnf(173976000,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP003-2.tptp',unknown),[]).
%
% cnf(173949176,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(181857792,plain,(~product(A,identity,B)|~product(A,C,D)|product(B,C,D)),inference(resolution,[status(thm)],[173976000,173949176]),[]).
%
% 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/GRP003-2.tptp',unknown),[]).
%
% cnf(173971736,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% cnf(181847944,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[173971736,173949176]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP003-2.tptp',unknown),[]).
%
% cnf(173953256,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(181879616,plain,(~product(A,B,C)|product(inverse(A),C,B)),inference(resolution,[status(thm)],[181847944,173953256]),[]).
%
% cnf(187649528,plain,(product(inverse(inverse(A)),identity,A)),inference(resolution,[status(thm)],[181879616,173953256]),[]).
%
% cnf(257576512,plain,(product(A,identity,A)),inference(resolution,[status(thm)],[181857792,187649528]),[]).
%
% fof(prove_left_identity,plain,(~product(a,identity,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP003-2.tptp',unknown),[]).
%
% cnf(173991328,plain,(~product(a,identity,a)),inference(rewrite,[status(thm)],[prove_left_identity]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[257576512,173991328]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------