TSTP Solution File: LCL398-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL398-1 : TPTP v3.4.2. Released v2.3.0.
% 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 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:49:13 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 2 sgn 8 !; 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/LCL398-1.tptp',unknown),
[] ).
cnf(143219864,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(cn_3,plain,
! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
[] ).
cnf(143232688,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(rewrite,[status(thm)],[cn_3]),
[] ).
cnf(151041448,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(not(A),B)) ),
inference(resolution,[status(thm)],[143219864,143232688]),
[] ).
fof(prove_cn_64,plain,
~ is_a_theorem(implies(not(implies(x,x)),y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
[] ).
cnf(143240456,plain,
~ is_a_theorem(implies(not(implies(x,x)),y)),
inference(rewrite,[status(thm)],[prove_cn_64]),
[] ).
cnf(151115360,plain,
~ is_a_theorem(implies(x,x)),
inference(resolution,[status(thm)],[151041448,143240456]),
[] ).
cnf(151135568,plain,
( ~ is_a_theorem(implies(A,implies(x,x)))
| ~ is_a_theorem(A) ),
inference(resolution,[status(thm)],[143219864,151115360]),
[] ).
fof(cn_2,plain,
! [A] : is_a_theorem(implies(implies(not(A),A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
[] ).
cnf(143228712,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(rewrite,[status(thm)],[cn_2]),
[] ).
cnf(151587904,plain,
~ is_a_theorem(implies(implies(implies(not(A),A),A),implies(x,x))),
inference(resolution,[status(thm)],[151135568,143228712]),
[] ).
fof(cn_1,plain,
! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),
[] ).
cnf(143224720,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_1]),
[] ).
cnf(151276224,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(implies(B,C),implies(A,C))) ),
inference(resolution,[status(thm)],[143219864,143224720]),
[] ).
cnf(154438640,plain,
~ is_a_theorem(implies(x,implies(not(x),x))),
inference(resolution,[status(thm)],[151587904,151276224]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[154438640,143232688]),
[] ).
%------------------------------------------------------------------------------
%----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/LCL398-1.tptp',unknown),[]).
%
% cnf(143219864,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
%
% cnf(143232688,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
%
% cnf(151041448,plain,(~is_a_theorem(A)|is_a_theorem(implies(not(A),B))),inference(resolution,[status(thm)],[143219864,143232688]),[]).
%
% fof(prove_cn_64,plain,(~is_a_theorem(implies(not(implies(x,x)),y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
%
% cnf(143240456,plain,(~is_a_theorem(implies(not(implies(x,x)),y))),inference(rewrite,[status(thm)],[prove_cn_64]),[]).
%
% cnf(151115360,plain,(~is_a_theorem(implies(x,x))),inference(resolution,[status(thm)],[151041448,143240456]),[]).
%
% cnf(151135568,plain,(~is_a_theorem(implies(A,implies(x,x)))|~is_a_theorem(A)),inference(resolution,[status(thm)],[143219864,151115360]),[]).
%
% fof(cn_2,plain,(is_a_theorem(implies(implies(not(A),A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
%
% cnf(143228712,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn_2]),[]).
%
% cnf(151587904,plain,(~is_a_theorem(implies(implies(implies(not(A),A),A),implies(x,x)))),inference(resolution,[status(thm)],[151135568,143228712]),[]).
%
% fof(cn_1,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL398-1.tptp',unknown),[]).
%
% cnf(143224720,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
%
% cnf(151276224,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[143219864,143224720]),[]).
%
% cnf(154438640,plain,(~is_a_theorem(implies(x,implies(not(x),x)))),inference(resolution,[status(thm)],[151587904,151276224]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[154438640,143232688]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------