TSTP Solution File: LCL076-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL076-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:41:18 EDT 2009
% Result : Unsatisfiable 0.7s
% Output : Refutation 0.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 11 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_40,plain,
~ is_a_theorem(implies(a,not(not(a)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),
[] ).
cnf(173704064,plain,
~ is_a_theorem(implies(a,not(not(a)))),
inference(rewrite,[status(thm)],[prove_cn_40]),
[] ).
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),
[] ).
cnf(173678016,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_49,plain,
! [A,B] : is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),
[] ).
cnf(173690800,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(rewrite,[status(thm)],[cn_49]),
[] ).
cnf(181864704,plain,
( ~ is_a_theorem(implies(not(A),not(B)))
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[173678016,173690800]),
[] ).
fof(transitivity,plain,
! [A,B,C] :
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(B,C))
| is_a_theorem(implies(A,C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),
[] ).
cnf(173700512,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(B,C))
| is_a_theorem(implies(A,C)) ),
inference(rewrite,[status(thm)],[transitivity]),
[] ).
fof(cn_18,plain,
! [A,B] : is_a_theorem(implies(A,implies(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),
[] ).
cnf(173682768,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(rewrite,[status(thm)],[cn_18]),
[] ).
cnf(181500976,plain,
( ~ is_a_theorem(implies(implies(C,A),B))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[173700512,173682768]),
[] ).
cnf(183756088,plain,
is_a_theorem(implies(not(B),implies(B,A))),
inference(resolution,[status(thm)],[181500976,173690800]),
[] ).
cnf(184284752,plain,
( ~ is_a_theorem(implies(implies(B,A),C))
| is_a_theorem(implies(not(B),C)) ),
inference(resolution,[status(thm)],[183756088,173700512]),
[] ).
cnf(196129096,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolution,[status(thm)],[184284752,173690800]),
[] ).
cnf(197031808,plain,
( ~ is_a_theorem(implies(implies(C,B),A))
| is_a_theorem(implies(not(not(B)),A)) ),
inference(resolution,[status(thm)],[173700512,196129096]),
[] ).
cnf(181481608,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[173678016,173682768]),
[] ).
fof(cn_35,plain,
! [A,B,C] : is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),
[] ).
cnf(173686896,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_35]),
[] ).
cnf(182157144,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolution,[status(thm)],[181481608,173686896]),
[] ).
cnf(182220904,plain,
is_a_theorem(implies(A,A)),
inference(resolution,[status(thm)],[182157144,181481608]),
[] ).
cnf(181462232,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[173678016,173682768]),
[] ).
cnf(182235232,plain,
is_a_theorem(implies(B,implies(A,A))),
inference(resolution,[status(thm)],[182220904,181462232]),
[] ).
cnf(182299432,plain,
( ~ is_a_theorem(implies(implies(B,implies(A,A)),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[182235232,173678016]),
[] ).
cnf(182255208,plain,
( ~ is_a_theorem(implies(implies(A,A),B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[182220904,173678016]),
[] ).
cnf(183081952,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolution,[status(thm)],[182255208,173686896]),
[] ).
cnf(197554592,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolution,[status(thm)],[182299432,183081952]),
[] ).
cnf(199168848,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolution,[status(thm)],[197031808,197554592]),
[] ).
cnf(199467152,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolution,[status(thm)],[181864704,199168848]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[173704064,199467152]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_40,plain,(~is_a_theorem(implies(a,not(not(a))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),[]).
%
% cnf(173704064,plain,(~is_a_theorem(implies(a,not(not(a))))),inference(rewrite,[status(thm)],[prove_cn_40]),[]).
%
% fof(condensed_detachment,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),[]).
%
% cnf(173678016,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_49,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),[]).
%
% cnf(173690800,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),inference(rewrite,[status(thm)],[cn_49]),[]).
%
% cnf(181864704,plain,(~is_a_theorem(implies(not(A),not(B)))|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[173678016,173690800]),[]).
%
% fof(transitivity,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(implies(B,C))|is_a_theorem(implies(A,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),[]).
%
% cnf(173700512,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(implies(B,C))|is_a_theorem(implies(A,C))),inference(rewrite,[status(thm)],[transitivity]),[]).
%
% fof(cn_18,plain,(is_a_theorem(implies(A,implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),[]).
%
% cnf(173682768,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[cn_18]),[]).
%
% cnf(181500976,plain,(~is_a_theorem(implies(implies(C,A),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[173700512,173682768]),[]).
%
% cnf(183756088,plain,(is_a_theorem(implies(not(B),implies(B,A)))),inference(resolution,[status(thm)],[181500976,173690800]),[]).
%
% cnf(184284752,plain,(~is_a_theorem(implies(implies(B,A),C))|is_a_theorem(implies(not(B),C))),inference(resolution,[status(thm)],[183756088,173700512]),[]).
%
% cnf(196129096,plain,(is_a_theorem(implies(not(not(A)),implies(B,A)))),inference(resolution,[status(thm)],[184284752,173690800]),[]).
%
% cnf(197031808,plain,(~is_a_theorem(implies(implies(C,B),A))|is_a_theorem(implies(not(not(B)),A))),inference(resolution,[status(thm)],[173700512,196129096]),[]).
%
% cnf(181481608,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[173678016,173682768]),[]).
%
% fof(cn_35,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL076-3.tptp',unknown),[]).
%
% cnf(173686896,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),inference(rewrite,[status(thm)],[cn_35]),[]).
%
% cnf(182157144,plain,(is_a_theorem(implies(implies(A,B),implies(A,A)))),inference(resolution,[status(thm)],[181481608,173686896]),[]).
%
% cnf(182220904,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[182157144,181481608]),[]).
%
% cnf(181462232,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[173678016,173682768]),[]).
%
% cnf(182235232,plain,(is_a_theorem(implies(B,implies(A,A)))),inference(resolution,[status(thm)],[182220904,181462232]),[]).
%
% cnf(182299432,plain,(~is_a_theorem(implies(implies(B,implies(A,A)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[182235232,173678016]),[]).
%
% cnf(182255208,plain,(~is_a_theorem(implies(implies(A,A),B))|is_a_theorem(B)),inference(resolution,[status(thm)],[182220904,173678016]),[]).
%
% cnf(183081952,plain,(is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B)))),inference(resolution,[status(thm)],[182255208,173686896]),[]).
%
% cnf(197554592,plain,(is_a_theorem(implies(implies(implies(A,A),B),B))),inference(resolution,[status(thm)],[182299432,183081952]),[]).
%
% cnf(199168848,plain,(is_a_theorem(implies(not(not(A)),A))),inference(resolution,[status(thm)],[197031808,197554592]),[]).
%
% cnf(199467152,plain,(is_a_theorem(implies(A,not(not(A))))),inference(resolution,[status(thm)],[181864704,199168848]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[173704064,199467152]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------