TSTP Solution File: GRP137-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP137-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 12:29:08 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP137-1.tptp',unknown),
[] ).
cnf(144449280,plain,
$equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B)),
inference(rewrite,[status(thm)],[symmetry_of_glb]),
[] ).
fof(prove_ax_antisymb,plain,
~ $equal(b,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),
[] ).
cnf(144429944,plain,
~ $equal(b,a),
inference(rewrite,[status(thm)],[prove_ax_antisymb]),
[] ).
fof(ax_antisymb_1,plain,
$equal(greatest_lower_bound(a,b),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),
[] ).
cnf(144555712,plain,
$equal(greatest_lower_bound(a,b),a),
inference(rewrite,[status(thm)],[ax_antisymb_1]),
[] ).
cnf(152372216,plain,
~ $equal(b,greatest_lower_bound(a,b)),
inference(paramodulation,[status(thm)],[144429944,144555712,theory(equality)]),
[] ).
cnf(152442464,plain,
~ $equal(b,greatest_lower_bound(b,a)),
inference(paramodulation,[status(thm)],[152372216,144449280,theory(equality)]),
[] ).
fof(ax_antisymb_2,plain,
$equal(greatest_lower_bound(a,b),b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),
[] ).
cnf(144559624,plain,
$equal(greatest_lower_bound(a,b),b),
inference(rewrite,[status(thm)],[ax_antisymb_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[144449280,152442464,144559624,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(symmetry_of_glb,plain,($equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),[]).
%
% cnf(144449280,plain,($equal(greatest_lower_bound(B,A),greatest_lower_bound(A,B))),inference(rewrite,[status(thm)],[symmetry_of_glb]),[]).
%
% fof(prove_ax_antisymb,plain,(~$equal(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),[]).
%
% cnf(144429944,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[prove_ax_antisymb]),[]).
%
% fof(ax_antisymb_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),[]).
%
% cnf(144555712,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[ax_antisymb_1]),[]).
%
% cnf(152372216,plain,(~$equal(b,greatest_lower_bound(a,b))),inference(paramodulation,[status(thm)],[144429944,144555712,theory(equality)]),[]).
%
% cnf(152442464,plain,(~$equal(b,greatest_lower_bound(b,a))),inference(paramodulation,[status(thm)],[152372216,144449280,theory(equality)]),[]).
%
% fof(ax_antisymb_2,plain,($equal(greatest_lower_bound(a,b),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP137-1.tptp',unknown),[]).
%
% cnf(144559624,plain,($equal(greatest_lower_bound(a,b),b)),inference(rewrite,[status(thm)],[ax_antisymb_2]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[144449280,152442464,144559624,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------