%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL099-1 : 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 11:34:26 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/COL099-1.tptp',unknown),
[] ).
cnf(142922776,plain,
( ~ member(pair(A,B),C)
| member(pair(A,B),trancl(C)) ),
inference(rewrite,[status(thm)],[r_into_trancl]),
[] ).
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/COL099-1.tptp',unknown),
[] ).
cnf(143003872,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]),
[] ).
fof(diamond_trancl_1h1,plain,
diamond(r),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),
[] ).
cnf(143008216,plain,
diamond(r),
inference(rewrite,[status(thm)],[diamond_trancl_1h1]),
[] ).
cnf(153509920,plain,
( ~ member(pair(A,B),trancl(r))
| ~ member(pair(A,C),r)
| member(pair(B,diamond_strip_lemmad_sk1(A,B,C,r)),r) ),
inference(resolution,[status(thm)],[143003872,143008216]),
[] ).
fof(diamond_trancl_1h2,plain,
member(pair(y,ya),r),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),
[] ).
cnf(143013128,plain,
member(pair(y,ya),r),
inference(rewrite,[status(thm)],[diamond_trancl_1h2]),
[] ).
cnf(153711800,plain,
( ~ member(pair(y,A),trancl(r))
| member(pair(A,diamond_strip_lemmad_sk1(y,A,ya,r)),r) ),
inference(resolution,[status(thm)],[153509920,143013128]),
[] ).
fof(diamond_trancl_1c1,plain,
member(pair(y,yp),trancl(r)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),
[] ).
cnf(143021480,plain,
member(pair(y,yp),trancl(r)),
inference(rewrite,[status(thm)],[diamond_trancl_1c1]),
[] ).
cnf(153859264,plain,
member(pair(yp,diamond_strip_lemmad_sk1(y,yp,ya,r)),r),
inference(resolution,[status(thm)],[153711800,143021480]),
[] ).
cnf(157845592,plain,
member(pair(yp,diamond_strip_lemmad_sk1(y,yp,ya,r)),trancl(r)),
inference(resolution,[status(thm)],[142922776,153859264]),
[] ).
fof(diamond_trancl_1c2,plain,
! [A] :
( ~ member(pair(ya,A),trancl(r))
| ~ member(pair(yp,A),trancl(r)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),
[] ).
cnf(143027160,plain,
( ~ member(pair(ya,A),trancl(r))
| ~ member(pair(yp,A),trancl(r)) ),
inference(rewrite,[status(thm)],[diamond_trancl_1c2]),
[] ).
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/COL099-1.tptp',unknown),
[] ).
cnf(142977832,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]),
[] ).
cnf(153534064,plain,
( ~ member(pair(A,B),trancl(r))
| ~ member(pair(A,C),r)
| member(pair(C,diamond_strip_lemmad_sk1(A,B,C,r)),trancl(r)) ),
inference(resolution,[status(thm)],[142977832,143008216]),
[] ).
cnf(153731592,plain,
( ~ member(pair(y,A),trancl(r))
| member(pair(ya,diamond_strip_lemmad_sk1(y,A,ya,r)),trancl(r)) ),
inference(resolution,[status(thm)],[153534064,143013128]),
[] ).
cnf(153877928,plain,
member(pair(ya,diamond_strip_lemmad_sk1(y,yp,ya,r)),trancl(r)),
inference(resolution,[status(thm)],[153731592,143021480]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[157845592,143027160,153877928]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/COL099-1.tptp',unknown),[]).
%
% cnf(142922776,plain,(~member(pair(A,B),C)|member(pair(A,B),trancl(C))),inference(rewrite,[status(thm)],[r_into_trancl]),[]).
%
% 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/COL099-1.tptp',unknown),[]).
%
% cnf(143003872,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]),[]).
%
% fof(diamond_trancl_1h1,plain,(diamond(r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),[]).
%
% cnf(143008216,plain,(diamond(r)),inference(rewrite,[status(thm)],[diamond_trancl_1h1]),[]).
%
% cnf(153509920,plain,(~member(pair(A,B),trancl(r))|~member(pair(A,C),r)|member(pair(B,diamond_strip_lemmad_sk1(A,B,C,r)),r)),inference(resolution,[status(thm)],[143003872,143008216]),[]).
%
% fof(diamond_trancl_1h2,plain,(member(pair(y,ya),r)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),[]).
%
% cnf(143013128,plain,(member(pair(y,ya),r)),inference(rewrite,[status(thm)],[diamond_trancl_1h2]),[]).
%
% cnf(153711800,plain,(~member(pair(y,A),trancl(r))|member(pair(A,diamond_strip_lemmad_sk1(y,A,ya,r)),r)),inference(resolution,[status(thm)],[153509920,143013128]),[]).
%
% fof(diamond_trancl_1c1,plain,(member(pair(y,yp),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),[]).
%
% cnf(143021480,plain,(member(pair(y,yp),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_1c1]),[]).
%
% cnf(153859264,plain,(member(pair(yp,diamond_strip_lemmad_sk1(y,yp,ya,r)),r)),inference(resolution,[status(thm)],[153711800,143021480]),[]).
%
% cnf(157845592,plain,(member(pair(yp,diamond_strip_lemmad_sk1(y,yp,ya,r)),trancl(r))),inference(resolution,[status(thm)],[142922776,153859264]),[]).
%
% fof(diamond_trancl_1c2,plain,(~member(pair(ya,A),trancl(r))|~member(pair(yp,A),trancl(r))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL099-1.tptp',unknown),[]).
%
% cnf(143027160,plain,(~member(pair(ya,A),trancl(r))|~member(pair(yp,A),trancl(r))),inference(rewrite,[status(thm)],[diamond_trancl_1c2]),[]).
%
% 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/COL099-1.tptp',unknown),[]).
%
% cnf(142977832,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]),[]).
%
% cnf(153534064,plain,(~member(pair(A,B),trancl(r))|~member(pair(A,C),r)|member(pair(C,diamond_strip_lemmad_sk1(A,B,C,r)),trancl(r))),inference(resolution,[status(thm)],[142977832,143008216]),[]).
%
% cnf(153731592,plain,(~member(pair(y,A),trancl(r))|member(pair(ya,diamond_strip_lemmad_sk1(y,A,ya,r)),trancl(r))),inference(resolution,[status(thm)],[153534064,143013128]),[]).
%
% cnf(153877928,plain,(member(pair(ya,diamond_strip_lemmad_sk1(y,yp,ya,r)),trancl(r))),inference(resolution,[status(thm)],[153731592,143021480]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[157845592,143027160,153877928]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------