TSTP Solution File: GRP148-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP148-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 12:29:35 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP148-1.tptp',unknown),
[] ).
cnf(150977712,plain,
$equal(greatest_lower_bound(A,least_upper_bound(A,B)),A),
inference(rewrite,[status(thm)],[glb_absorbtion]),
[] ).
fof(prove_ax_lub1c,plain,
~ $equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),
[] ).
cnf(150918448,plain,
~ $equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b)),
inference(rewrite,[status(thm)],[prove_ax_lub1c]),
[] ).
fof(ax_lub1c_1,plain,
$equal(least_upper_bound(a,c),c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),
[] ).
cnf(151044040,plain,
$equal(least_upper_bound(a,c),c),
inference(rewrite,[status(thm)],[ax_lub1c_1]),
[] ).
cnf(158877248,plain,
~ $equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),least_upper_bound(a,b)),
inference(paramodulation,[status(thm)],[150918448,151044040,theory(equality)]),
[] ).
fof(ax_lub1c_2,plain,
$equal(least_upper_bound(b,c),c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),
[] ).
cnf(151047984,plain,
$equal(least_upper_bound(b,c),c),
inference(rewrite,[status(thm)],[ax_lub1c_2]),
[] ).
cnf(159494688,plain,
~ $equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,least_upper_bound(b,c))),least_upper_bound(a,b)),
inference(paramodulation,[status(thm)],[158877248,151047984,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/GRP148-1.tptp',unknown),
[] ).
cnf(150958392,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(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[150977712,159494688,150958392,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(glb_absorbtion,plain,($equal(greatest_lower_bound(A,least_upper_bound(A,B)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),[]).
%
% cnf(150977712,plain,($equal(greatest_lower_bound(A,least_upper_bound(A,B)),A)),inference(rewrite,[status(thm)],[glb_absorbtion]),[]).
%
% fof(prove_ax_lub1c,plain,(~$equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),[]).
%
% cnf(150918448,plain,(~$equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b))),inference(rewrite,[status(thm)],[prove_ax_lub1c]),[]).
%
% fof(ax_lub1c_1,plain,($equal(least_upper_bound(a,c),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),[]).
%
% cnf(151044040,plain,($equal(least_upper_bound(a,c),c)),inference(rewrite,[status(thm)],[ax_lub1c_1]),[]).
%
% cnf(158877248,plain,(~$equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),least_upper_bound(a,b))),inference(paramodulation,[status(thm)],[150918448,151044040,theory(equality)]),[]).
%
% fof(ax_lub1c_2,plain,($equal(least_upper_bound(b,c),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP148-1.tptp',unknown),[]).
%
% cnf(151047984,plain,($equal(least_upper_bound(b,c),c)),inference(rewrite,[status(thm)],[ax_lub1c_2]),[]).
%
% cnf(159494688,plain,(~$equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,least_upper_bound(b,c))),least_upper_bound(a,b))),inference(paramodulation,[status(thm)],[158877248,151047984,theory(equality)]),[]).
%
% fof(associativity_of_lub,plain,($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/GRP148-1.tptp',unknown),[]).
%
% cnf(150958392,plain,($equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[associativity_of_lub]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[150977712,159494688,150958392,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------