TSTP Solution File: GRP159-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP159-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 12:29:59 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(lub_absorbtion,plain,
! [A,B] : $equal(least_upper_bound(A,greatest_lower_bound(A,B)),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
[] ).
cnf(158595400,plain,
$equal(least_upper_bound(A,greatest_lower_bound(A,B)),A),
inference(rewrite,[status(thm)],[lub_absorbtion]),
[] ).
fof(prove_ax_mono2c,plain,
~ $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
[] ).
cnf(158674480,plain,
~ $equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)),
inference(rewrite,[status(thm)],[prove_ax_mono2c]),
[] ).
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/GRP159-1.tptp',unknown),
[] ).
cnf(158607056,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(166542456,plain,
~ $equal(multiply(c,least_upper_bound(a,b)),multiply(c,b)),
inference(paramodulation,[status(thm)],[158674480,158607056,theory(equality)]),
[] ).
fof(symmetry_of_lub,plain,
! [B,A] : $equal(least_upper_bound(B,A),least_upper_bound(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
[] ).
cnf(158571992,plain,
$equal(least_upper_bound(B,A),least_upper_bound(A,B)),
inference(rewrite,[status(thm)],[symmetry_of_lub]),
[] ).
cnf(166613728,plain,
~ $equal(multiply(c,least_upper_bound(b,a)),multiply(c,b)),
inference(paramodulation,[status(thm)],[166542456,158571992,theory(equality)]),
[] ).
fof(ax_mono2c_1,plain,
$equal(greatest_lower_bound(a,b),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
[] ).
cnf(158669648,plain,
$equal(greatest_lower_bound(a,b),a),
inference(rewrite,[status(thm)],[ax_mono2c_1]),
[] ).
cnf(166662840,plain,
~ $equal(multiply(c,least_upper_bound(b,greatest_lower_bound(a,b))),multiply(c,b)),
inference(paramodulation,[status(thm)],[166613728,158669648,theory(equality)]),
[] ).
fof(symmetry_of_glb,plain,
! [B,A] : $equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
[] ).
cnf(158563216,plain,
$equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B)),
inference(rewrite,[status(thm)],[symmetry_of_glb]),
[] ).
cnf(166866696,plain,
~ $equal(multiply(c,least_upper_bound(b,greatest_lower_bound(b,a))),multiply(c,b)),
inference(paramodulation,[status(thm)],[166662840,158563216,theory(equality)]),
[] ).
cnf(167027088,plain,
~ $equal(least_upper_bound(multiply(c,b),multiply(c,greatest_lower_bound(b,a))),multiply(c,b)),
inference(paramodulation,[status(thm)],[166866696,158607056,theory(equality)]),
[] ).
fof(monotony_glb1,plain,
! [A,B,C] : $equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),
[] ).
cnf(158610848,plain,
$equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C))),
inference(rewrite,[status(thm)],[monotony_glb1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158595400,167027088,158610848,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(lub_absorbtion,plain,($equal(least_upper_bound(A,greatest_lower_bound(A,B)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
%
% cnf(158595400,plain,($equal(least_upper_bound(A,greatest_lower_bound(A,B)),A)),inference(rewrite,[status(thm)],[lub_absorbtion]),[]).
%
% fof(prove_ax_mono2c,plain,(~$equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
%
% cnf(158674480,plain,(~$equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b))),inference(rewrite,[status(thm)],[prove_ax_mono2c]),[]).
%
% fof(monotony_lub1,plain,($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/GRP159-1.tptp',unknown),[]).
%
% cnf(158607056,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_lub1]),[]).
%
% cnf(166542456,plain,(~$equal(multiply(c,least_upper_bound(a,b)),multiply(c,b))),inference(paramodulation,[status(thm)],[158674480,158607056,theory(equality)]),[]).
%
% fof(symmetry_of_lub,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
%
% cnf(158571992,plain,($equal(least_upper_bound(B,A),least_upper_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_lub]),[]).
%
% cnf(166613728,plain,(~$equal(multiply(c,least_upper_bound(b,a)),multiply(c,b))),inference(paramodulation,[status(thm)],[166542456,158571992,theory(equality)]),[]).
%
% fof(ax_mono2c_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
%
% cnf(158669648,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[ax_mono2c_1]),[]).
%
% cnf(166662840,plain,(~$equal(multiply(c,least_upper_bound(b,greatest_lower_bound(a,b))),multiply(c,b))),inference(paramodulation,[status(thm)],[166613728,158669648,theory(equality)]),[]).
%
% fof(symmetry_of_glb,plain,($equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
%
% cnf(158563216,plain,($equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_glb]),[]).
%
% cnf(166866696,plain,(~$equal(multiply(c,least_upper_bound(b,greatest_lower_bound(b,a))),multiply(c,b))),inference(paramodulation,[status(thm)],[166662840,158563216,theory(equality)]),[]).
%
% cnf(167027088,plain,(~$equal(least_upper_bound(multiply(c,b),multiply(c,greatest_lower_bound(b,a))),multiply(c,b))),inference(paramodulation,[status(thm)],[166866696,158607056,theory(equality)]),[]).
%
% fof(monotony_glb1,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP159-1.tptp',unknown),[]).
%
% cnf(158610848,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_glb1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158595400,167027088,158610848,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------