TSTP Solution File: LCL077-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL077-2 : 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 13:41:21 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 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 : 57 ( 11 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_39,plain,
~ is_a_theorem(implies(not(not(a)),a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),
[] ).
cnf(155194280,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(rewrite,[status(thm)],[prove_cn_39]),
[] ).
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/LCL077-2.tptp',unknown),
[] ).
cnf(155190728,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/LCL077-2.tptp',unknown),
[] ).
cnf(155172984,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(rewrite,[status(thm)],[cn_18]),
[] ).
cnf(162991360,plain,
( ~ is_a_theorem(implies(implies(C,A),B))
| is_a_theorem(implies(A,B)) ),
inference(resolution,[status(thm)],[155190728,155172984]),
[] ).
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/LCL077-2.tptp',unknown),
[] ).
cnf(155181016,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(rewrite,[status(thm)],[cn_49]),
[] ).
cnf(165816360,plain,
is_a_theorem(implies(not(B),implies(B,A))),
inference(resolution,[status(thm)],[162991360,155181016]),
[] ).
cnf(166270640,plain,
( ~ is_a_theorem(implies(implies(B,A),C))
| is_a_theorem(implies(not(B),C)) ),
inference(resolution,[status(thm)],[165816360,155190728]),
[] ).
cnf(174701128,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolution,[status(thm)],[166270640,155181016]),
[] ).
cnf(175367752,plain,
( ~ is_a_theorem(implies(implies(C,B),A))
| is_a_theorem(implies(not(not(B)),A)) ),
inference(resolution,[status(thm)],[155190728,174701128]),
[] ).
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/LCL077-2.tptp',unknown),
[] ).
cnf(155168232,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
cnf(162971976,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[155168232,155172984]),
[] ).
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/LCL077-2.tptp',unknown),
[] ).
cnf(155177112,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_35]),
[] ).
cnf(163743920,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolution,[status(thm)],[162971976,155177112]),
[] ).
cnf(163821392,plain,
is_a_theorem(implies(A,A)),
inference(resolution,[status(thm)],[163743920,162971976]),
[] ).
cnf(162952600,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[155168232,155172984]),
[] ).
cnf(163835736,plain,
is_a_theorem(implies(B,implies(A,A))),
inference(resolution,[status(thm)],[163821392,162952600]),
[] ).
cnf(163921712,plain,
( ~ is_a_theorem(implies(implies(B,implies(A,A)),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[163835736,155168232]),
[] ).
cnf(163855712,plain,
( ~ is_a_theorem(implies(implies(A,A),B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[163821392,155168232]),
[] ).
cnf(164600280,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolution,[status(thm)],[163855712,155177112]),
[] ).
cnf(176501080,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolution,[status(thm)],[163921712,164600280]),
[] ).
cnf(178089600,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolution,[status(thm)],[175367752,176501080]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[155194280,178089600]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_39,plain,(~is_a_theorem(implies(not(not(a)),a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL077-2.tptp',unknown),[]).
%
% cnf(155194280,plain,(~is_a_theorem(implies(not(not(a)),a))),inference(rewrite,[status(thm)],[prove_cn_39]),[]).
%
% 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/LCL077-2.tptp',unknown),[]).
%
% cnf(155190728,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/LCL077-2.tptp',unknown),[]).
%
% cnf(155172984,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[cn_18]),[]).
%
% cnf(162991360,plain,(~is_a_theorem(implies(implies(C,A),B))|is_a_theorem(implies(A,B))),inference(resolution,[status(thm)],[155190728,155172984]),[]).
%
% 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/LCL077-2.tptp',unknown),[]).
%
% cnf(155181016,plain,(is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))),inference(rewrite,[status(thm)],[cn_49]),[]).
%
% cnf(165816360,plain,(is_a_theorem(implies(not(B),implies(B,A)))),inference(resolution,[status(thm)],[162991360,155181016]),[]).
%
% cnf(166270640,plain,(~is_a_theorem(implies(implies(B,A),C))|is_a_theorem(implies(not(B),C))),inference(resolution,[status(thm)],[165816360,155190728]),[]).
%
% cnf(174701128,plain,(is_a_theorem(implies(not(not(A)),implies(B,A)))),inference(resolution,[status(thm)],[166270640,155181016]),[]).
%
% cnf(175367752,plain,(~is_a_theorem(implies(implies(C,B),A))|is_a_theorem(implies(not(not(B)),A))),inference(resolution,[status(thm)],[155190728,174701128]),[]).
%
% 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/LCL077-2.tptp',unknown),[]).
%
% cnf(155168232,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% cnf(162971976,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[155168232,155172984]),[]).
%
% 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/LCL077-2.tptp',unknown),[]).
%
% cnf(155177112,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),inference(rewrite,[status(thm)],[cn_35]),[]).
%
% cnf(163743920,plain,(is_a_theorem(implies(implies(A,B),implies(A,A)))),inference(resolution,[status(thm)],[162971976,155177112]),[]).
%
% cnf(163821392,plain,(is_a_theorem(implies(A,A))),inference(resolution,[status(thm)],[163743920,162971976]),[]).
%
% cnf(162952600,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[155168232,155172984]),[]).
%
% cnf(163835736,plain,(is_a_theorem(implies(B,implies(A,A)))),inference(resolution,[status(thm)],[163821392,162952600]),[]).
%
% cnf(163921712,plain,(~is_a_theorem(implies(implies(B,implies(A,A)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[163835736,155168232]),[]).
%
% cnf(163855712,plain,(~is_a_theorem(implies(implies(A,A),B))|is_a_theorem(B)),inference(resolution,[status(thm)],[163821392,155168232]),[]).
%
% cnf(164600280,plain,(is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B)))),inference(resolution,[status(thm)],[163855712,155177112]),[]).
%
% cnf(176501080,plain,(is_a_theorem(implies(implies(implies(A,A),B),B))),inference(resolution,[status(thm)],[163921712,164600280]),[]).
%
% cnf(178089600,plain,(is_a_theorem(implies(not(not(A)),A))),inference(resolution,[status(thm)],[175367752,176501080]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[155194280,178089600]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------