%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : BOO011-1 : 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 11:26:41 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(additive_inverse2,plain,
! [A] : sum(A,inverse(A),multiplicative_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),
[] ).
cnf(151438616,plain,
sum(A,inverse(A),multiplicative_identity),
inference(rewrite,[status(thm)],[additive_inverse2]),
[] ).
fof(addition_is_well_defined,plain,
! [A,B,C,D] :
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),
[] ).
cnf(151555560,plain,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[addition_is_well_defined]),
[] ).
fof(additive_identity1,plain,
! [A] : sum(additive_identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),
[] ).
cnf(151464912,plain,
sum(additive_identity,A,A),
inference(rewrite,[status(thm)],[additive_identity1]),
[] ).
cnf(159358480,plain,
( ~ sum(additive_identity,A,B)
| $equal(A,B) ),
inference(resolution,[status(thm)],[151555560,151464912]),
[] ).
fof(prove_equation,plain,
~ $equal(inverse(additive_identity),multiplicative_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),
[] ).
cnf(151569072,plain,
~ $equal(inverse(additive_identity),multiplicative_identity),
inference(rewrite,[status(thm)],[prove_equation]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[151438616,159358480,151569072]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(additive_inverse2,plain,(sum(A,inverse(A),multiplicative_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),[]).
%
% cnf(151438616,plain,(sum(A,inverse(A),multiplicative_identity)),inference(rewrite,[status(thm)],[additive_inverse2]),[]).
%
% fof(addition_is_well_defined,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),[]).
%
% cnf(151555560,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[addition_is_well_defined]),[]).
%
% fof(additive_identity1,plain,(sum(additive_identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),[]).
%
% cnf(151464912,plain,(sum(additive_identity,A,A)),inference(rewrite,[status(thm)],[additive_identity1]),[]).
%
% cnf(159358480,plain,(~sum(additive_identity,A,B)|$equal(A,B)),inference(resolution,[status(thm)],[151555560,151464912]),[]).
%
% fof(prove_equation,plain,(~$equal(inverse(additive_identity),multiplicative_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO011-1.tptp',unknown),[]).
%
% cnf(151569072,plain,(~$equal(inverse(additive_identity),multiplicative_identity)),inference(rewrite,[status(thm)],[prove_equation]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[151438616,159358480,151569072]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------