%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL079-1 : 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 13:41:25 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 5 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/LCL079-1.tptp',unknown),
[] ).
cnf(148296384,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_18,plain,
! [A,B] : is_a_theorem(implies(A,implies(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),
[] ).
cnf(148301200,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(rewrite,[status(thm)],[cn_18]),
[] ).
cnf(156134560,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[148296384,148301200]),
[] ).
fof(b_implies_c,plain,
is_a_theorem(implies(b,c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),
[] ).
cnf(148320904,plain,
is_a_theorem(implies(b,c)),
inference(rewrite,[status(thm)],[b_implies_c]),
[] ).
cnf(156463088,plain,
is_a_theorem(implies(A,implies(b,c))),
inference(resolution,[status(thm)],[156134560,148320904]),
[] ).
cnf(156777008,plain,
( ~ is_a_theorem(implies(implies(A,implies(b,c)),B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[156463088,148296384]),
[] ).
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/LCL079-1.tptp',unknown),
[] ).
cnf(148305392,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_35]),
[] ).
cnf(168285936,plain,
is_a_theorem(implies(implies(A,b),implies(A,c))),
inference(resolution,[status(thm)],[156777008,148305392]),
[] ).
fof(a_implies_b,plain,
is_a_theorem(implies(a,b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),
[] ).
cnf(148317032,plain,
is_a_theorem(implies(a,b)),
inference(rewrite,[status(thm)],[a_implies_b]),
[] ).
cnf(156124304,plain,
( ~ is_a_theorem(implies(implies(a,b),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[148296384,148317032]),
[] ).
cnf(156905016,plain,
( ~ is_a_theorem(implies(implies(a,b),A))
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[156124304,156134560]),
[] ).
fof(prove_transitivity,plain,
~ is_a_theorem(implies(a,c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),
[] ).
cnf(148324736,plain,
~ is_a_theorem(implies(a,c)),
inference(rewrite,[status(thm)],[prove_transitivity]),
[] ).
cnf(156896264,plain,
~ is_a_theorem(implies(implies(a,b),implies(a,c))),
inference(resolution,[status(thm)],[156124304,148324736]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[168285936,156905016,156896264]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/LCL079-1.tptp',unknown),[]).
%
% cnf(148296384,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_18,plain,(is_a_theorem(implies(A,implies(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),[]).
%
% cnf(148301200,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[cn_18]),[]).
%
% cnf(156134560,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[148296384,148301200]),[]).
%
% fof(b_implies_c,plain,(is_a_theorem(implies(b,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),[]).
%
% cnf(148320904,plain,(is_a_theorem(implies(b,c))),inference(rewrite,[status(thm)],[b_implies_c]),[]).
%
% cnf(156463088,plain,(is_a_theorem(implies(A,implies(b,c)))),inference(resolution,[status(thm)],[156134560,148320904]),[]).
%
% cnf(156777008,plain,(~is_a_theorem(implies(implies(A,implies(b,c)),B))|is_a_theorem(B)),inference(resolution,[status(thm)],[156463088,148296384]),[]).
%
% 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/LCL079-1.tptp',unknown),[]).
%
% cnf(148305392,plain,(is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))),inference(rewrite,[status(thm)],[cn_35]),[]).
%
% cnf(168285936,plain,(is_a_theorem(implies(implies(A,b),implies(A,c)))),inference(resolution,[status(thm)],[156777008,148305392]),[]).
%
% fof(a_implies_b,plain,(is_a_theorem(implies(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),[]).
%
% cnf(148317032,plain,(is_a_theorem(implies(a,b))),inference(rewrite,[status(thm)],[a_implies_b]),[]).
%
% cnf(156124304,plain,(~is_a_theorem(implies(implies(a,b),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[148296384,148317032]),[]).
%
% cnf(156905016,plain,(~is_a_theorem(implies(implies(a,b),A))|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[156124304,156134560]),[]).
%
% fof(prove_transitivity,plain,(~is_a_theorem(implies(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL079-1.tptp',unknown),[]).
%
% cnf(148324736,plain,(~is_a_theorem(implies(a,c))),inference(rewrite,[status(thm)],[prove_transitivity]),[]).
%
% cnf(156896264,plain,(~is_a_theorem(implies(implies(a,b),implies(a,c)))),inference(resolution,[status(thm)],[156124304,148324736]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[168285936,156905016,156896264]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------