TSTP Solution File: GRP163-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP163-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:30:09 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 : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(ax_transb_1,plain,
$equal(greatest_lower_bound(a,b),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),
[] ).
cnf(143964376,plain,
$equal(greatest_lower_bound(a,b),a),
inference(rewrite,[status(thm)],[ax_transb_1]),
[] ).
fof(prove_ax_transb,plain,
~ $equal(greatest_lower_bound(a,c),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),
[] ).
cnf(143838624,plain,
~ $equal(greatest_lower_bound(a,c),a),
inference(rewrite,[status(thm)],[prove_ax_transb]),
[] ).
cnf(151792560,plain,
~ $equal(greatest_lower_bound(greatest_lower_bound(a,b),c),a),
inference(paramodulation,[status(thm)],[143838624,143964376,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/GRP163-1.tptp',unknown),
[] ).
cnf(143874768,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(152010232,plain,
~ $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),a),
inference(paramodulation,[status(thm)],[151792560,143874768,theory(equality)]),
[] ).
fof(ax_transb_2,plain,
$equal(greatest_lower_bound(b,c),b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),
[] ).
cnf(143968320,plain,
$equal(greatest_lower_bound(b,c),b),
inference(rewrite,[status(thm)],[ax_transb_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[143964376,152010232,143968320,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(ax_transb_1,plain,($equal(greatest_lower_bound(a,b),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),[]).
%
% cnf(143964376,plain,($equal(greatest_lower_bound(a,b),a)),inference(rewrite,[status(thm)],[ax_transb_1]),[]).
%
% fof(prove_ax_transb,plain,(~$equal(greatest_lower_bound(a,c),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),[]).
%
% cnf(143838624,plain,(~$equal(greatest_lower_bound(a,c),a)),inference(rewrite,[status(thm)],[prove_ax_transb]),[]).
%
% cnf(151792560,plain,(~$equal(greatest_lower_bound(greatest_lower_bound(a,b),c),a)),inference(paramodulation,[status(thm)],[143838624,143964376,theory(equality)]),[]).
%
% fof(associativity_of_glb,plain,($equal(greatest_lower_bound(greatest_lower_bound(A,B),C),greatest_lower_bound(A,greatest_lower_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),[]).
%
% cnf(143874768,plain,($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(152010232,plain,(~$equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),a)),inference(paramodulation,[status(thm)],[151792560,143874768,theory(equality)]),[]).
%
% fof(ax_transb_2,plain,($equal(greatest_lower_bound(b,c),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP163-1.tptp',unknown),[]).
%
% cnf(143968320,plain,($equal(greatest_lower_bound(b,c),b)),inference(rewrite,[status(thm)],[ax_transb_2]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[143964376,152010232,143968320,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------