TSTP Solution File: GRP001-5 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP001-5 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 12:17:09 EDT 2009
% Result : Unsatisfiable 0.9s
% Output : Refutation 0.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 23 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_b_times_a_is_c,plain,
~ product(b,a,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),
[] ).
cnf(157804608,plain,
~ product(b,a,c),
inference(rewrite,[status(thm)],[prove_b_times_a_is_c]),
[] ).
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/GRP001-5.tptp',unknown),
[] ).
cnf(157793888,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),
[] ).
cnf(157779840,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(165706176,plain,
( ~ product(A,B,C)
| ~ product(B,D,identity)
| product(C,D,A) ),
inference(resolution,[status(thm)],[157793888,157779840]),
[] ).
fof(square_element,plain,
! [A] : product(A,A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),
[] ).
cnf(157797152,plain,
product(A,A,identity),
inference(rewrite,[status(thm)],[square_element]),
[] ).
cnf(168092704,plain,
( ~ product(A,B,C)
| product(C,B,A) ),
inference(resolution,[status(thm)],[165706176,157797152]),
[] ).
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/GRP001-5.tptp',unknown),
[] ).
cnf(157789496,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/GRP001-5.tptp',unknown),
[] ).
cnf(157775864,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(165616800,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[157789496,157775864]),
[] ).
cnf(168013560,plain,
( ~ product(A,B,C)
| product(A,C,B) ),
inference(resolution,[status(thm)],[165616800,157797152]),
[] ).
fof(a_times_b_is_c,plain,
product(a,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),
[] ).
cnf(157800664,plain,
product(a,b,c),
inference(rewrite,[status(thm)],[a_times_b_is_c]),
[] ).
cnf(165869560,plain,
( ~ product(b,A,B)
| ~ product(a,B,C)
| product(c,A,C) ),
inference(resolution,[status(thm)],[157793888,157800664]),
[] ).
cnf(165979664,plain,
( ~ product(b,A,identity)
| product(c,A,a) ),
inference(resolution,[status(thm)],[165869560,157779840]),
[] ).
cnf(167236968,plain,
product(c,b,a),
inference(resolution,[status(thm)],[165979664,157797152]),
[] ).
cnf(169039472,plain,
product(c,a,b),
inference(resolution,[status(thm)],[168013560,167236968]),
[] ).
cnf(171110488,plain,
product(b,a,c),
inference(resolution,[status(thm)],[168092704,169039472]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[157804608,171110488]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_b_times_a_is_c,plain,(~product(b,a,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),[]).
%
% cnf(157804608,plain,(~product(b,a,c)),inference(rewrite,[status(thm)],[prove_b_times_a_is_c]),[]).
%
% 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/GRP001-5.tptp',unknown),[]).
%
% cnf(157793888,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),[]).
%
% cnf(157779840,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(165706176,plain,(~product(A,B,C)|~product(B,D,identity)|product(C,D,A)),inference(resolution,[status(thm)],[157793888,157779840]),[]).
%
% fof(square_element,plain,(product(A,A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),[]).
%
% cnf(157797152,plain,(product(A,A,identity)),inference(rewrite,[status(thm)],[square_element]),[]).
%
% cnf(168092704,plain,(~product(A,B,C)|product(C,B,A)),inference(resolution,[status(thm)],[165706176,157797152]),[]).
%
% 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/GRP001-5.tptp',unknown),[]).
%
% cnf(157789496,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/GRP001-5.tptp',unknown),[]).
%
% cnf(157775864,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(165616800,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[157789496,157775864]),[]).
%
% cnf(168013560,plain,(~product(A,B,C)|product(A,C,B)),inference(resolution,[status(thm)],[165616800,157797152]),[]).
%
% fof(a_times_b_is_c,plain,(product(a,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP001-5.tptp',unknown),[]).
%
% cnf(157800664,plain,(product(a,b,c)),inference(rewrite,[status(thm)],[a_times_b_is_c]),[]).
%
% cnf(165869560,plain,(~product(b,A,B)|~product(a,B,C)|product(c,A,C)),inference(resolution,[status(thm)],[157793888,157800664]),[]).
%
% cnf(165979664,plain,(~product(b,A,identity)|product(c,A,a)),inference(resolution,[status(thm)],[165869560,157779840]),[]).
%
% cnf(167236968,plain,(product(c,b,a)),inference(resolution,[status(thm)],[165979664,157797152]),[]).
%
% cnf(169039472,plain,(product(c,a,b)),inference(resolution,[status(thm)],[168013560,167236968]),[]).
%
% cnf(171110488,plain,(product(b,a,c)),inference(resolution,[status(thm)],[168092704,169039472]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[157804608,171110488]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------