TSTP Solution File: LCL104-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL104-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 13:42:12 EDT 2009
% Result : Unsatisfiable 4.5s
% Output : Refutation 4.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_p_1,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),
[] ).
cnf(162383000,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(rewrite,[status(thm)],[prove_p_1]),
[] ).
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),
[] ).
cnf(162365584,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(q_3,plain,
! [A,B,C] : is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C)),C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),
[] ).
cnf(162374904,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C)),C)),
inference(rewrite,[status(thm)],[q_3]),
[] ).
cnf(170158760,plain,
( ~ is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162365584,162374904]),
[] ).
fof(p_4,plain,
! [A,B,C,D] : is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),
[] ).
cnf(162370512,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))),
inference(rewrite,[status(thm)],[p_4]),
[] ).
cnf(170206728,plain,
is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(A,B),equivalent(A,C)))),
inference(resolution,[status(thm)],[170158760,162370512]),
[] ).
cnf(170279968,plain,
( ~ is_a_theorem(equivalent(B,C))
| is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolution,[status(thm)],[162365584,170206728]),
[] ).
cnf(170696784,plain,
( ~ is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(A,B))
| is_a_theorem(equivalent(A,C)) ),
inference(resolution,[status(thm)],[170279968,162365584]),
[] ).
cnf(173241440,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),A))
| is_a_theorem(equivalent(equivalent(C,D),A)) ),
inference(resolution,[status(thm)],[170696784,170206728]),
[] ).
cnf(170423192,plain,
( ~ is_a_theorem(equivalent(equivalent(B,equivalent(equivalent(equivalent(equivalent(C,D),equivalent(C,E)),equivalent(D,E)),B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[162365584,162370512]),
[] ).
cnf(170350784,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(C,D),equivalent(equivalent(D,C),B))),equivalent(A,B))),
inference(resolution,[status(thm)],[170279968,162374904]),
[] ).
cnf(173025864,plain,
( ~ is_a_theorem(equivalent(A,equivalent(equivalent(C,D),equivalent(equivalent(D,C),B))))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[170350784,162365584]),
[] ).
cnf(170730232,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(C,D)),equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))))),
inference(resolution,[status(thm)],[170279968,170206728]),
[] ).
cnf(176159008,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
inference(resolution,[status(thm)],[173025864,170730232]),
[] ).
cnf(176258824,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(C,D)))),
inference(resolution,[status(thm)],[170279968,176159008]),
[] ).
cnf(177472128,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D))),
inference(resolution,[status(thm)],[170423192,176258824]),
[] ).
cnf(178491056,plain,
is_a_theorem(equivalent(equivalent(equivalent(B,D),A),equivalent(equivalent(C,D),equivalent(equivalent(B,C),A)))),
inference(resolution,[status(thm)],[173241440,177472128]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162383000,178491056]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 seconds
% START OF PROOF SEQUENCE
% fof(prove_p_1,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),[]).
%
% cnf(162383000,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),inference(rewrite,[status(thm)],[prove_p_1]),[]).
%
% fof(condensed_detachment,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),[]).
%
% cnf(162365584,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(q_3,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C)),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),[]).
%
% cnf(162374904,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C)),C))),inference(rewrite,[status(thm)],[q_3]),[]).
%
% cnf(170158760,plain,(~is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))|is_a_theorem(A)),inference(resolution,[status(thm)],[162365584,162374904]),[]).
%
% fof(p_4,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL104-1.tptp',unknown),[]).
%
% cnf(162370512,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A)))),inference(rewrite,[status(thm)],[p_4]),[]).
%
% cnf(170206728,plain,(is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(A,B),equivalent(A,C))))),inference(resolution,[status(thm)],[170158760,162370512]),[]).
%
% cnf(170279968,plain,(~is_a_theorem(equivalent(B,C))|is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C)))),inference(resolution,[status(thm)],[162365584,170206728]),[]).
%
% cnf(170696784,plain,(~is_a_theorem(equivalent(B,C))|~is_a_theorem(equivalent(A,B))|is_a_theorem(equivalent(A,C))),inference(resolution,[status(thm)],[170279968,162365584]),[]).
%
% cnf(173241440,plain,(~is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),A))|is_a_theorem(equivalent(equivalent(C,D),A))),inference(resolution,[status(thm)],[170696784,170206728]),[]).
%
% cnf(170423192,plain,(~is_a_theorem(equivalent(equivalent(B,equivalent(equivalent(equivalent(equivalent(C,D),equivalent(C,E)),equivalent(D,E)),B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[162365584,162370512]),[]).
%
% cnf(170350784,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(C,D),equivalent(equivalent(D,C),B))),equivalent(A,B)))),inference(resolution,[status(thm)],[170279968,162374904]),[]).
%
% cnf(173025864,plain,(~is_a_theorem(equivalent(A,equivalent(equivalent(C,D),equivalent(equivalent(D,C),B))))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[170350784,162365584]),[]).
%
% cnf(170730232,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(C,D)),equivalent(A,equivalent(equivalent(B,C),equivalent(B,D)))))),inference(resolution,[status(thm)],[170279968,170206728]),[]).
%
% cnf(176159008,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)))),inference(resolution,[status(thm)],[173025864,170730232]),[]).
%
% cnf(176258824,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(C,D))))),inference(resolution,[status(thm)],[170279968,176159008]),[]).
%
% cnf(177472128,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)))),inference(resolution,[status(thm)],[170423192,176258824]),[]).
%
% cnf(178491056,plain,(is_a_theorem(equivalent(equivalent(equivalent(B,D),A),equivalent(equivalent(C,D),equivalent(equivalent(B,C),A))))),inference(resolution,[status(thm)],[173241440,177472128]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162383000,178491056]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------