TSTP Solution File: GRP170-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP170-2 : 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 12:30:45 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 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; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(monotony_glb2,plain,
! [A,C,B] : $equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
[] ).
cnf(158406744,plain,
$equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C)),
inference(rewrite,[status(thm)],[monotony_glb2]),
[] ).
fof(prove_p03b,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
[] ).
cnf(158288896,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
inference(rewrite,[status(thm)],[prove_p03b]),
[] ).
fof(p03b_1,plain,
$equal(greatest_lower_bound(a,b),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
[] ).
cnf(158414488,plain,
$equal(greatest_lower_bound(a,b),a),
inference(rewrite,[status(thm)],[p03b_1]),
[] ).
cnf(166258392,plain,
~ $equal(greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,d)),multiply(a,c)),
inference(paramodulation,[status(thm)],[158288896,158414488,theory(equality)]),
[] ).
cnf(166602184,plain,
~ $equal(greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(b,d)),multiply(a,c)),
inference(paramodulation,[status(thm)],[166258392,158406744,theory(equality)]),
[] ).
fof(associativity_of_glb,plain,
! [A,B,C] : $equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
[] ).
cnf(158324880,plain,
$equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C))),
inference(rewrite,[status(thm)],[associativity_of_glb]),
[] ).
cnf(168743464,plain,
~ $equal(greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),multiply(b,d))),multiply(a,c)),
inference(paramodulation,[status(thm)],[166602184,158324880,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/GRP170-2.tptp',unknown),
[] ).
cnf(158355688,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(174853936,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))),multiply(a,c)),
inference(paramodulation,[status(thm)],[168743464,158355688,theory(equality)]),
[] ).
fof(p03b_2,plain,
$equal(greatest_lower_bound(c,d),c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),
[] ).
cnf(158418464,plain,
$equal(greatest_lower_bound(c,d),c),
inference(rewrite,[status(thm)],[p03b_2]),
[] ).
cnf(175744672,plain,
~ $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c)),
inference(paramodulation,[status(thm)],[174853936,158418464,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158406744,175744672,158414488,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(monotony_glb2,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
%
% cnf(158406744,plain,($equal(greatest_lower_bound(multiply(A,C),multiply(B,C)),multiply(greatest_lower_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_glb2]),[]).
%
% fof(prove_p03b,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
%
% cnf(158288896,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c))),inference(rewrite,[status(thm)],[prove_p03b]),[]).
%
% fof(p03b_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
%
% cnf(158414488,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[p03b_1]),[]).
%
% cnf(166258392,plain,(~$equal(greatest_lower_bound(multiply(greatest_lower_bound(a,b),c),multiply(b,d)),multiply(a,c))),inference(paramodulation,[status(thm)],[158288896,158414488,theory(equality)]),[]).
%
% cnf(166602184,plain,(~$equal(greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(b,d)),multiply(a,c))),inference(paramodulation,[status(thm)],[166258392,158406744,theory(equality)]),[]).
%
% fof(associativity_of_glb,plain,($equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
%
% cnf(158324880,plain,($equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[associativity_of_glb]),[]).
%
% cnf(168743464,plain,(~$equal(greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),multiply(b,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[166602184,158324880,theory(equality)]),[]).
%
% fof(monotony_glb1,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
%
% cnf(158355688,plain,($equal(greatest_lower_bound(multiply(A,B),multiply(A,C)),multiply(A,greatest_lower_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_glb1]),[]).
%
% cnf(174853936,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))),multiply(a,c))),inference(paramodulation,[status(thm)],[168743464,158355688,theory(equality)]),[]).
%
% fof(p03b_2,plain,($equal(greatest_lower_bound(c,d),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP170-2.tptp',unknown),[]).
%
% cnf(158418464,plain,($equal(greatest_lower_bound(c,d),c)),inference(rewrite,[status(thm)],[p03b_2]),[]).
%
% cnf(175744672,plain,(~$equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c))),inference(paramodulation,[status(thm)],[174853936,158418464,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[158406744,175744672,158414488,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------