TSTP Solution File: COL100-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL100-1 : TPTP v3.4.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 11:34:28 EDT 2009
% Result : Unsatisfiable 144.4s
% Output : Refutation 144.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 33 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 42 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(diamond_trancl_2h4,plain,
! [A] :
( ~ member(pair(y,A),trancl(r))
| member(pair(ya,sk1(A)),trancl(r)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155150976,plain,
( ~ member(pair(y,A),trancl(r))
| member(pair(ya,sk1(A)),trancl(r)) ),
inference(rewrite,[status(thm)],[diamond_trancl_2h4]),
[] ).
fof(diamond_trancl_2c1,plain,
member(pair(y,yp),trancl(r)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155162864,plain,
member(pair(y,yp),trancl(r)),
inference(rewrite,[status(thm)],[diamond_trancl_2c1]),
[] ).
cnf(167099576,plain,
member(pair(ya,sk1(yp)),trancl(r)),
inference(resolution,[status(thm)],[155150976,155162864]),
[] ).
fof(diamond_trancl_2c2,plain,
! [A] :
( ~ member(pair(z,A),trancl(r))
| ~ member(pair(yp,A),trancl(r)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155168480,plain,
( ~ member(pair(z,A),trancl(r))
| ~ member(pair(yp,A),trancl(r)) ),
inference(rewrite,[status(thm)],[diamond_trancl_2c2]),
[] ).
fof(diamond_trancl_2h1,plain,
diamond(r),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155131840,plain,
diamond(r),
inference(rewrite,[status(thm)],[diamond_trancl_2h1]),
[] ).
fof(diamond_strip_lemmaD1,plain,
! [A,B,C,D] :
( ~ diamond(A)
| ~ member(pair(B,C),trancl(A))
| ~ member(pair(B,D),A)
| member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155097272,plain,
( ~ diamond(A)
| ~ member(pair(B,C),trancl(A))
| ~ member(pair(B,D),A)
| member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A)) ),
inference(rewrite,[status(thm)],[diamond_strip_lemmaD1]),
[] ).
fof(diamond_trancl_2h3,plain,
member(pair(ya,z),r),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155145248,plain,
member(pair(ya,z),r),
inference(rewrite,[status(thm)],[diamond_trancl_2h3]),
[] ).
cnf(165823144,plain,
( ~ member(pair(ya,A),trancl(r))
| member(pair(z,diamond_strip_lemmad_sk1(ya,A,z,r)),trancl(r)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155097272,155145248]),
[] ).
cnf(170753944,plain,
member(pair(z,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolution,[status(thm)],[165823144,167099576]),
[] ).
cnf(284290032,plain,
~ member(pair(yp,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolution,[status(thm)],[155168480,170753944]),
[] ).
fof(diamond_strip_lemmaD2,plain,
! [A,B,C,D] :
( ~ diamond(A)
| ~ member(pair(B,C),trancl(A))
| ~ member(pair(B,D),A)
| member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155123376,plain,
( ~ diamond(A)
| ~ member(pair(B,C),trancl(A))
| ~ member(pair(B,D),A)
| member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A) ),
inference(rewrite,[status(thm)],[diamond_strip_lemmaD2]),
[] ).
cnf(165806648,plain,
( ~ member(pair(ya,A),trancl(r))
| member(pair(A,diamond_strip_lemmad_sk1(ya,A,z,r)),r) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155123376,155145248]),
[] ).
fof(trans_trancl,plain,
! [A] : trans(trancl(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155051216,plain,
trans(trancl(A)),
inference(rewrite,[status(thm)],[trans_trancl]),
[] ).
fof(transD,plain,
! [A,B,C,D] :
( ~ trans(A)
| ~ member(pair(B,C),A)
| ~ member(pair(C,D),A)
| member(pair(B,D),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155061560,plain,
( ~ trans(A)
| ~ member(pair(B,C),A)
| ~ member(pair(C,D),A)
| member(pair(B,D),A) ),
inference(rewrite,[status(thm)],[transD]),
[] ).
fof(diamond_trancl_2h5,plain,
! [A] :
( ~ member(pair(y,A),trancl(r))
| member(pair(A,sk1(A)),trancl(r)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155159248,plain,
( ~ member(pair(y,A),trancl(r))
| member(pair(A,sk1(A)),trancl(r)) ),
inference(rewrite,[status(thm)],[diamond_trancl_2h5]),
[] ).
cnf(167246976,plain,
member(pair(yp,sk1(yp)),trancl(r)),
inference(resolution,[status(thm)],[155159248,155162864]),
[] ).
cnf(170847592,plain,
( ~ member(pair(sk1(yp),A),trancl(r))
| member(pair(yp,A),trancl(r)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[155051216,155061560,167246976]),
[] ).
fof(r_into_trancl,plain,
! [A,B,C] :
( ~ member(pair(A,B),C)
| member(pair(A,B),trancl(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),
[] ).
cnf(155042024,plain,
( ~ member(pair(A,B),C)
| member(pair(A,B),trancl(C)) ),
inference(rewrite,[status(thm)],[r_into_trancl]),
[] ).
cnf(199901488,plain,
( member(pair(yp,A),trancl(r))
| ~ member(pair(sk1(yp),A),r) ),
inference(resolution,[status(thm)],[170847592,155042024]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[167099576,284290032,165806648,199901488]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 143 seconds
% START OF PROOF SEQUENCE
% fof(diamond_trancl_2h4,plain,(~member(pair(y,A),trancl(r))|member(pair(ya,sk1(A)),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155150976,plain,(~member(pair(y,A),trancl(r))|member(pair(ya,sk1(A)),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2h4]),[]).
%
% fof(diamond_trancl_2c1,plain,(member(pair(y,yp),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155162864,plain,(member(pair(y,yp),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2c1]),[]).
%
% cnf(167099576,plain,(member(pair(ya,sk1(yp)),trancl(r))),inference(resolution,[status(thm)],[155150976,155162864]),[]).
%
% fof(diamond_trancl_2c2,plain,(~member(pair(z,A),trancl(r))|~member(pair(yp,A),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155168480,plain,(~member(pair(z,A),trancl(r))|~member(pair(yp,A),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2c2]),[]).
%
% fof(diamond_trancl_2h1,plain,(diamond(r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155131840,plain,(diamond(r)),inference(rewrite,[status(thm)],[diamond_trancl_2h1]),[]).
%
% fof(diamond_strip_lemmaD1,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155097272,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(D,diamond_strip_lemmad_sk1(B,C,D,A)),trancl(A))),inference(rewrite,[status(thm)],[diamond_strip_lemmaD1]),[]).
%
% fof(diamond_trancl_2h3,plain,(member(pair(ya,z),r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155145248,plain,(member(pair(ya,z),r)),inference(rewrite,[status(thm)],[diamond_trancl_2h3]),[]).
%
% cnf(165823144,plain,(~member(pair(ya,A),trancl(r))|member(pair(z,diamond_strip_lemmad_sk1(ya,A,z,r)),trancl(r))),inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155097272,155145248]),[]).
%
% cnf(170753944,plain,(member(pair(z,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r))),inference(resolution,[status(thm)],[165823144,167099576]),[]).
%
% cnf(284290032,plain,(~member(pair(yp,diamond_strip_lemmad_sk1(ya,sk1(yp),z,r)),trancl(r))),inference(resolution,[status(thm)],[155168480,170753944]),[]).
%
% fof(diamond_strip_lemmaD2,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155123376,plain,(~diamond(A)|~member(pair(B,C),trancl(A))|~member(pair(B,D),A)|member(pair(C,diamond_strip_lemmad_sk1(B,C,D,A)),A)),inference(rewrite,[status(thm)],[diamond_strip_lemmaD2]),[]).
%
% cnf(165806648,plain,(~member(pair(ya,A),trancl(r))|member(pair(A,diamond_strip_lemmad_sk1(ya,A,z,r)),r)),inference(forward_subsumption_resolution__resolution,[status(thm)],[155131840,155123376,155145248]),[]).
%
% fof(trans_trancl,plain,(trans(trancl(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155051216,plain,(trans(trancl(A))),inference(rewrite,[status(thm)],[trans_trancl]),[]).
%
% fof(transD,plain,(~trans(A)|~member(pair(B,C),A)|~member(pair(C,D),A)|member(pair(B,D),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155061560,plain,(~trans(A)|~member(pair(B,C),A)|~member(pair(C,D),A)|member(pair(B,D),A)),inference(rewrite,[status(thm)],[transD]),[]).
%
% fof(diamond_trancl_2h5,plain,(~member(pair(y,A),trancl(r))|member(pair(A,sk1(A)),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155159248,plain,(~member(pair(y,A),trancl(r))|member(pair(A,sk1(A)),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_2h5]),[]).
%
% cnf(167246976,plain,(member(pair(yp,sk1(yp)),trancl(r))),inference(resolution,[status(thm)],[155159248,155162864]),[]).
%
% cnf(170847592,plain,(~member(pair(sk1(yp),A),trancl(r))|member(pair(yp,A),trancl(r))),inference(forward_subsumption_resolution__resolution,[status(thm)],[155051216,155061560,167246976]),[]).
%
% fof(r_into_trancl,plain,(~member(pair(A,B),C)|member(pair(A,B),trancl(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL100-1.tptp',unknown),[]).
%
% cnf(155042024,plain,(~member(pair(A,B),C)|member(pair(A,B),trancl(C))),inference(rewrite,[status(thm)],[r_into_trancl]),[]).
%
% cnf(199901488,plain,(member(pair(yp,A),trancl(r))|~member(pair(sk1(yp),A),r)),inference(resolution,[status(thm)],[170847592,155042024]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[167099576,284290032,165806648,199901488]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------