%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP170-3 : TPTP v3.4.2. Bugfixed v1.2.1.
% 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 12:30:46 EDT 2009
% Result : Unsatisfiable 2.9s
% Output : Refutation 2.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_p03c,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171621296,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
inference(rewrite,[status(thm)],[prove_p03c]),
[] ).
fof(p03c_1,plain,
$equal(least_upper_bound(a,b),b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171746968,plain,
$equal(least_upper_bound(a,b),b),
inference(rewrite,[status(thm)],[p03c_1]),
[] ).
cnf(179589088,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(least_upper_bound(a,b),d)),multiply(a,c)),
inference(paramodulation,[status(thm)],[171621296,171746968,theory(equality)]),
[] ).
fof(monotony_lub2,plain,
! [A,C,B] : $equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171717376,plain,
$equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C)),
inference(rewrite,[status(thm)],[monotony_lub2]),
[] ).
cnf(179856888,plain,
~ $equal(greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(a,d),multiply(b,d))),multiply(a,c)),
inference(paramodulation,[status(thm)],[179589088,171717376,theory(equality)]),
[] ).
fof(p03c_2,plain,
$equal(least_upper_bound(c,d),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171750944,plain,
$equal(least_upper_bound(c,d),d),
inference(rewrite,[status(thm)],[p03c_2]),
[] ).
cnf(180916104,plain,
~ $equal(greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(a,least_upper_bound(c,d)),multiply(b,d))),multiply(a,c)),
inference(paramodulation,[status(thm)],[179856888,171750944,theory(equality)]),
[] ).
fof(monotony_lub1,plain,
! [A,B,C] : $equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171684376,plain,
$equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C))),
inference(rewrite,[status(thm)],[monotony_lub1]),
[] ).
cnf(185052424,plain,
~ $equal(greatest_lower_bound(multiply(a,c),least_upper_bound(least_upper_bound(multiply(a,c),multiply(a,d)),multiply(b,d))),multiply(a,c)),
inference(paramodulation,[status(thm)],[180916104,171684376,theory(equality)]),
[] ).
fof(associativity_of_lub,plain,
! [A,B,C] : $equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171661320,plain,
$equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C))),
inference(rewrite,[status(thm)],[associativity_of_lub]),
[] ).
cnf(204021360,plain,
~ $equal(greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(a,c),least_upper_bound(multiply(a,d),multiply(b,d)))),multiply(a,c)),
inference(paramodulation,[status(thm)],[185052424,171661320,theory(equality)]),
[] ).
fof(glb_absorbtion,plain,
! [A,B] : $equal(greatest_lower_bound(A,least_upper_bound(A,B)),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),
[] ).
cnf(171680640,plain,
$equal(greatest_lower_bound(A,least_upper_bound(A,B)),A),
inference(rewrite,[status(thm)],[glb_absorbtion]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[204021360,171680640]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(prove_p03c,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171621296,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c))),inference(rewrite,[status(thm)],[prove_p03c]),[]).
%
% fof(p03c_1,plain,($equal(least_upper_bound(a,b),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171746968,plain,($equal(least_upper_bound(a,b),b)),inference(rewrite,[status(thm)],[p03c_1]),[]).
%
% cnf(179589088,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(least_upper_bound(a,b),d)),multiply(a,c))),inference(paramodulation,[status(thm)],[171621296,171746968,theory(equality)]),[]).
%
% fof(monotony_lub2,plain,($equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171717376,plain,($equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_lub2]),[]).
%
% cnf(179856888,plain,(~$equal(greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(a,d),multiply(b,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[179589088,171717376,theory(equality)]),[]).
%
% fof(p03c_2,plain,($equal(least_upper_bound(c,d),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171750944,plain,($equal(least_upper_bound(c,d),d)),inference(rewrite,[status(thm)],[p03c_2]),[]).
%
% cnf(180916104,plain,(~$equal(greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(a,least_upper_bound(c,d)),multiply(b,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[179856888,171750944,theory(equality)]),[]).
%
% fof(monotony_lub1,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171684376,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_lub1]),[]).
%
% cnf(185052424,plain,(~$equal(greatest_lower_bound(multiply(a,c),least_upper_bound(least_upper_bound(multiply(a,c),multiply(a,d)),multiply(b,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[180916104,171684376,theory(equality)]),[]).
%
% fof(associativity_of_lub,plain,($equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171661320,plain,($equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[associativity_of_lub]),[]).
%
% cnf(204021360,plain,(~$equal(greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(a,c),least_upper_bound(multiply(a,d),multiply(b,d)))),multiply(a,c))),inference(paramodulation,[status(thm)],[185052424,171661320,theory(equality)]),[]).
%
% fof(glb_absorbtion,plain,($equal(greatest_lower_bound(A,least_upper_bound(A,B)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-3.tptp',unknown),[]).
%
% cnf(171680640,plain,($equal(greatest_lower_bound(A,least_upper_bound(A,B)),A)),inference(rewrite,[status(thm)],[glb_absorbtion]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[204021360,171680640]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------