TSTP Solution File: LCL107-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL107-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 13:42:17 EDT 2009
% Result : Unsatisfiable 2.4s
% Output : Refutation 2.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 16 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 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 : 129 ( 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/LCL107-1.tptp',unknown),
[] ).
cnf(166853664,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/LCL107-1.tptp',unknown),
[] ).
cnf(166839952,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(lg_27_1690,plain,
! [A,B,C,D,E,F,G] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL107-1.tptp',unknown),
[] ).
cnf(166845096,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G)))),
inference(rewrite,[status(thm)],[lg_27_1690]),
[] ).
cnf(174688040,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),H))),equivalent(D,equivalent(equivalent(C,B),H))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166839952,166845096]),
[] ).
cnf(174668080,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))))
| is_a_theorem(equivalent(C,equivalent(equivalent(B,A),G))) ),
inference(resolution,[status(thm)],[166839952,166845096]),
[] ).
cnf(177427088,plain,
is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),D)),equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B))),D))),
inference(resolution,[status(thm)],[174668080,166845096]),
[] ).
cnf(177549128,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)),equivalent(equivalent(B,A),D))),
inference(resolution,[status(thm)],[174668080,177427088]),
[] ).
cnf(177572376,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)))
| is_a_theorem(equivalent(equivalent(B,A),D)) ),
inference(resolution,[status(thm)],[166839952,177549128]),
[] ).
cnf(177744920,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A),A)),
inference(resolution,[status(thm)],[177572376,177549128]),
[] ).
cnf(177879312,plain,
is_a_theorem(equivalent(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))),equivalent(equivalent(B,A),D))),
inference(resolution,[status(thm)],[174688040,177744920]),
[] ).
cnf(178283136,plain,
( ~ is_a_theorem(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))))
| is_a_theorem(equivalent(equivalent(B,A),D)) ),
inference(resolution,[status(thm)],[166839952,177879312]),
[] ).
cnf(178455384,plain,
is_a_theorem(equivalent(equivalent(equivalent(E,equivalent(B,C)),A),equivalent(equivalent(E,equivalent(equivalent(D,B),equivalent(D,C))),A))),
inference(resolution,[status(thm)],[178283136,177427088]),
[] ).
cnf(178571280,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(F,equivalent(C,D)),B),equivalent(equivalent(F,equivalent(equivalent(E,C),equivalent(E,D))),B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166839952,178455384]),
[] ).
cnf(178989520,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),D),equivalent(equivalent(equivalent(C,A),equivalent(equivalent(E,C),equivalent(E,B))),D))),
inference(resolution,[status(thm)],[178571280,177549128]),
[] ).
cnf(179046368,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),E),equivalent(equivalent(equivalent(D,B),equivalent(equivalent(F,D),equivalent(F,C))),E)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166839952,178989520]),
[] ).
cnf(177762296,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166839952,177744920]),
[] ).
cnf(177927472,plain,
is_a_theorem(equivalent(equivalent(equivalent(D,equivalent(C,A)),equivalent(equivalent(F,equivalent(E,D)),equivalent(F,equivalent(E,equivalent(C,B))))),equivalent(A,B))),
inference(resolution,[status(thm)],[177762296,177744920]),
[] ).
cnf(179775832,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,C),equivalent(equivalent(C,A),D)),D)),
inference(resolution,[status(thm)],[179046368,177927472]),
[] ).
cnf(179899568,plain,
( ~ is_a_theorem(equivalent(equivalent(B,D),equivalent(equivalent(D,B),A)))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166839952,179775832]),
[] ).
cnf(179935576,plain,
is_a_theorem(equivalent(B,B)),
inference(resolution,[status(thm)],[179899568,178455384]),
[] ).
cnf(180143216,plain,
( ~ is_a_theorem(equivalent(equivalent(C,C),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166839952,179935576]),
[] ).
cnf(180165016,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(D,C),equivalent(D,B)),E),equivalent(equivalent(C,B),E))),
inference(resolution,[status(thm)],[180143216,166845096]),
[] ).
cnf(181392952,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(D,C),equivalent(D,B)),E))
| is_a_theorem(equivalent(equivalent(C,B),E)) ),
inference(resolution,[status(thm)],[166839952,180165016]),
[] ).
cnf(181525368,plain,
is_a_theorem(equivalent(equivalent(equivalent(F,D),B),equivalent(equivalent(E,D),equivalent(equivalent(F,E),B)))),
inference(resolution,[status(thm)],[181392952,180165016]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[166853664,181525368]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 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/LCL107-1.tptp',unknown),[]).
%
% cnf(166853664,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/LCL107-1.tptp',unknown),[]).
%
% cnf(166839952,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(lg_27_1690,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL107-1.tptp',unknown),[]).
%
% cnf(166845096,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G))))),inference(rewrite,[status(thm)],[lg_27_1690]),[]).
%
% cnf(174688040,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),H))),equivalent(D,equivalent(equivalent(C,B),H))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[166839952,166845096]),[]).
%
% cnf(174668080,plain,(~is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))))|is_a_theorem(equivalent(C,equivalent(equivalent(B,A),G)))),inference(resolution,[status(thm)],[166839952,166845096]),[]).
%
% cnf(177427088,plain,(is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),D)),equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B))),D)))),inference(resolution,[status(thm)],[174668080,166845096]),[]).
%
% cnf(177549128,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)),equivalent(equivalent(B,A),D)))),inference(resolution,[status(thm)],[174668080,177427088]),[]).
%
% cnf(177572376,plain,(~is_a_theorem(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)))|is_a_theorem(equivalent(equivalent(B,A),D))),inference(resolution,[status(thm)],[166839952,177549128]),[]).
%
% cnf(177744920,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A),A))),inference(resolution,[status(thm)],[177572376,177549128]),[]).
%
% cnf(177879312,plain,(is_a_theorem(equivalent(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))),equivalent(equivalent(B,A),D)))),inference(resolution,[status(thm)],[174688040,177744920]),[]).
%
% cnf(178283136,plain,(~is_a_theorem(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))))|is_a_theorem(equivalent(equivalent(B,A),D))),inference(resolution,[status(thm)],[166839952,177879312]),[]).
%
% cnf(178455384,plain,(is_a_theorem(equivalent(equivalent(equivalent(E,equivalent(B,C)),A),equivalent(equivalent(E,equivalent(equivalent(D,B),equivalent(D,C))),A)))),inference(resolution,[status(thm)],[178283136,177427088]),[]).
%
% cnf(178571280,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(F,equivalent(C,D)),B),equivalent(equivalent(F,equivalent(equivalent(E,C),equivalent(E,D))),B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[166839952,178455384]),[]).
%
% cnf(178989520,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),D),equivalent(equivalent(equivalent(C,A),equivalent(equivalent(E,C),equivalent(E,B))),D)))),inference(resolution,[status(thm)],[178571280,177549128]),[]).
%
% cnf(179046368,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),E),equivalent(equivalent(equivalent(D,B),equivalent(equivalent(F,D),equivalent(F,C))),E)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[166839952,178989520]),[]).
%
% cnf(177762296,plain,(~is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[166839952,177744920]),[]).
%
% cnf(177927472,plain,(is_a_theorem(equivalent(equivalent(equivalent(D,equivalent(C,A)),equivalent(equivalent(F,equivalent(E,D)),equivalent(F,equivalent(E,equivalent(C,B))))),equivalent(A,B)))),inference(resolution,[status(thm)],[177762296,177744920]),[]).
%
% cnf(179775832,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,C),equivalent(equivalent(C,A),D)),D))),inference(resolution,[status(thm)],[179046368,177927472]),[]).
%
% cnf(179899568,plain,(~is_a_theorem(equivalent(equivalent(B,D),equivalent(equivalent(D,B),A)))|is_a_theorem(A)),inference(resolution,[status(thm)],[166839952,179775832]),[]).
%
% cnf(179935576,plain,(is_a_theorem(equivalent(B,B))),inference(resolution,[status(thm)],[179899568,178455384]),[]).
%
% cnf(180143216,plain,(~is_a_theorem(equivalent(equivalent(C,C),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[166839952,179935576]),[]).
%
% cnf(180165016,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(D,C),equivalent(D,B)),E),equivalent(equivalent(C,B),E)))),inference(resolution,[status(thm)],[180143216,166845096]),[]).
%
% cnf(181392952,plain,(~is_a_theorem(equivalent(equivalent(equivalent(D,C),equivalent(D,B)),E))|is_a_theorem(equivalent(equivalent(C,B),E))),inference(resolution,[status(thm)],[166839952,180165016]),[]).
%
% cnf(181525368,plain,(is_a_theorem(equivalent(equivalent(equivalent(F,D),B),equivalent(equivalent(E,D),equivalent(equivalent(F,E),B))))),inference(resolution,[status(thm)],[181392952,180165016]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[166853664,181525368]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------