TSTP Solution File: LCL361-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL361-1 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 13:48:30 EDT 2009
% Result : Unsatisfiable 21.5s
% Output : Refutation 21.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 52 ( 12 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_cn_10,plain,
~ is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL361-1.tptp',unknown),
[] ).
cnf(158120904,plain,
~ is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))),
inference(rewrite,[status(thm)],[prove_cn_10]),
[] ).
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/LCL361-1.tptp',unknown),
[] ).
cnf(158100048,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
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/LCL361-1.tptp',unknown),
[] ).
cnf(158104904,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(rewrite,[status(thm)],[cn_1]),
[] ).
cnf(166035832,plain,
( ~ is_a_theorem(implies(implies(implies(B,C),implies(implies(C,D),implies(B,D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158100048,158104904]),
[] ).
cnf(166016328,plain,
( ~ is_a_theorem(implies(A,B))
| is_a_theorem(implies(implies(B,C),implies(A,C))) ),
inference(resolution,[status(thm)],[158100048,158104904]),
[] ).
fof(cn_3,plain,
! [A,B] : is_a_theorem(implies(A,implies(not(A),B))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL361-1.tptp',unknown),
[] ).
cnf(158112872,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(rewrite,[status(thm)],[cn_3]),
[] ).
cnf(165964864,plain,
( ~ is_a_theorem(implies(implies(B,implies(not(B),C)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158100048,158112872]),
[] ).
cnf(166747616,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolution,[status(thm)],[165964864,158104904]),
[] ).
cnf(168979816,plain,
( ~ is_a_theorem(implies(implies(not(A),B),C))
| is_a_theorem(implies(A,C)) ),
inference(resolution,[status(thm)],[166747616,158100048]),
[] ).
cnf(168999016,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D))
| is_a_theorem(D) ),
inference(resolution,[status(thm)],[166747616,158100048]),
[] ).
cnf(167354888,plain,
is_a_theorem(implies(implies(implies(implies(C,D),implies(B,D)),A),implies(implies(B,C),A))),
inference(resolution,[status(thm)],[166016328,158104904]),
[] ).
cnf(177219816,plain,
is_a_theorem(implies(implies(C,not(A)),implies(A,implies(C,B)))),
inference(resolution,[status(thm)],[168999016,167354888]),
[] ).
cnf(177605872,plain,
is_a_theorem(implies(A,implies(B,implies(not(A),C)))),
inference(resolution,[status(thm)],[168979816,177219816]),
[] ).
cnf(178076000,plain,
is_a_theorem(implies(implies(implies(C,implies(not(A),D)),B),implies(A,B))),
inference(resolution,[status(thm)],[166016328,177605872]),
[] ).
cnf(202452792,plain,
is_a_theorem(implies(C,implies(implies(implies(not(C),D),B),implies(A,B)))),
inference(resolution,[status(thm)],[166035832,178076000]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[158120904,202452792]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 21 seconds
% START OF PROOF SEQUENCE
% fof(prove_cn_10,plain,(~is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL361-1.tptp',unknown),[]).
%
% cnf(158120904,plain,(~is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))),inference(rewrite,[status(thm)],[prove_cn_10]),[]).
%
% 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/LCL361-1.tptp',unknown),[]).
%
% cnf(158100048,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% 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/LCL361-1.tptp',unknown),[]).
%
% cnf(158104904,plain,(is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))),inference(rewrite,[status(thm)],[cn_1]),[]).
%
% cnf(166035832,plain,(~is_a_theorem(implies(implies(implies(B,C),implies(implies(C,D),implies(B,D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158100048,158104904]),[]).
%
% cnf(166016328,plain,(~is_a_theorem(implies(A,B))|is_a_theorem(implies(implies(B,C),implies(A,C)))),inference(resolution,[status(thm)],[158100048,158104904]),[]).
%
% fof(cn_3,plain,(is_a_theorem(implies(A,implies(not(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL361-1.tptp',unknown),[]).
%
% cnf(158112872,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn_3]),[]).
%
% cnf(165964864,plain,(~is_a_theorem(implies(implies(B,implies(not(B),C)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158100048,158112872]),[]).
%
% cnf(166747616,plain,(is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C)))),inference(resolution,[status(thm)],[165964864,158104904]),[]).
%
% cnf(168979816,plain,(~is_a_theorem(implies(implies(not(A),B),C))|is_a_theorem(implies(A,C))),inference(resolution,[status(thm)],[166747616,158100048]),[]).
%
% cnf(168999016,plain,(~is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),D))|is_a_theorem(D)),inference(resolution,[status(thm)],[166747616,158100048]),[]).
%
% cnf(167354888,plain,(is_a_theorem(implies(implies(implies(implies(C,D),implies(B,D)),A),implies(implies(B,C),A)))),inference(resolution,[status(thm)],[166016328,158104904]),[]).
%
% cnf(177219816,plain,(is_a_theorem(implies(implies(C,not(A)),implies(A,implies(C,B))))),inference(resolution,[status(thm)],[168999016,167354888]),[]).
%
% cnf(177605872,plain,(is_a_theorem(implies(A,implies(B,implies(not(A),C))))),inference(resolution,[status(thm)],[168979816,177219816]),[]).
%
% cnf(178076000,plain,(is_a_theorem(implies(implies(implies(C,implies(not(A),D)),B),implies(A,B)))),inference(resolution,[status(thm)],[166016328,177605872]),[]).
%
% cnf(202452792,plain,(is_a_theorem(implies(C,implies(implies(implies(not(C),D),B),implies(A,B))))),inference(resolution,[status(thm)],[166035832,178076000]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[158120904,202452792]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------