TSTP Solution File: GRP017-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP017-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:18:00 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP017-1.tptp',unknown),
[] ).
cnf(155511584,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/GRP017-1.tptp',unknown),
[] ).
cnf(155478368,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(163388928,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[155511584,155478368]),
[] ).
fof(b_times_a_is_identity,plain,
product(b,a,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
[] ).
cnf(155475880,plain,
product(b,a,identity),
inference(rewrite,[status(thm)],[b_times_a_is_identity]),
[] ).
cnf(163469136,plain,
( ~ product(a,A,B)
| product(b,B,A) ),
inference(resolution,[status(thm)],[163388928,155475880]),
[] ).
fof(a_times_c_is_identity,plain,
product(a,c,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
[] ).
cnf(155530704,plain,
product(a,c,identity),
inference(rewrite,[status(thm)],[a_times_c_is_identity]),
[] ).
cnf(163594256,plain,
product(b,identity,c),
inference(resolution,[status(thm)],[163469136,155530704]),
[] ).
fof(prove_b_equals_c,plain,
~ $equal(c,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
[] ).
cnf(155538888,plain,
~ $equal(c,b),
inference(rewrite,[status(thm)],[prove_b_equals_c]),
[] ).
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/GRP017-1.tptp',unknown),
[] ).
cnf(155504816,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
[] ).
cnf(155482472,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(164280072,plain,
( ~ product(A,identity,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[155504816,155482472]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[163594256,155538888,164280072]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(associativity1,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155511584,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155478368,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(163388928,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[155511584,155478368]),[]).
%
% fof(b_times_a_is_identity,plain,(product(b,a,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155475880,plain,(product(b,a,identity)),inference(rewrite,[status(thm)],[b_times_a_is_identity]),[]).
%
% cnf(163469136,plain,(~product(a,A,B)|product(b,B,A)),inference(resolution,[status(thm)],[163388928,155475880]),[]).
%
% fof(a_times_c_is_identity,plain,(product(a,c,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155530704,plain,(product(a,c,identity)),inference(rewrite,[status(thm)],[a_times_c_is_identity]),[]).
%
% cnf(163594256,plain,(product(b,identity,c)),inference(resolution,[status(thm)],[163469136,155530704]),[]).
%
% fof(prove_b_equals_c,plain,(~$equal(c,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155538888,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[prove_b_equals_c]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155504816,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
%
% cnf(155482472,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(164280072,plain,(~product(A,identity,B)|$equal(B,A)),inference(resolution,[status(thm)],[155504816,155482472]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163594256,155538888,164280072]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------