%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:56:56 AM UTC 2026
% Result : Unsatisfiable 17.36s 3.34s
% Output : CNFRefutation 17.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 16 unt; 0 nHn; 34 RR)
% Number of literals : 71 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 1 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 : 44 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(r_into_trancl,axiom,
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ) ).
cnf(trans_trancl,axiom,
trans(trancl(X0)) ).
cnf(transD,axiom,
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ) ).
cnf(diamond_strip_lemmaD1,axiom,
( member(pair(X3,'diamond$ustrip$ulemmaD$usk1'(X1,X2,X3,X0)),trancl(X0))
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ) ).
cnf(diamond_strip_lemmaD2,axiom,
( member(pair(X2,'diamond$ustrip$ulemmaD$usk1'(X1,X2,X3,X0)),X0)
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ) ).
cnf(diamond_trancl_2h1,hypothesis,
diamond(r) ).
cnf(diamond_trancl_2h3,hypothesis,
member(pair(ya,z),r) ).
cnf(diamond_trancl_2h4,hypothesis,
( member(pair(ya,sk1(X0)),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ) ).
cnf(diamond_trancl_2h5,hypothesis,
( member(pair(X0,sk1(X0)),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ) ).
cnf(diamond_trancl_2c1,negated_conjecture,
member(pair(y,yp),trancl(r)) ).
cnf(diamond_trancl_2c2,negated_conjecture,
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(z,X0),trancl(r)) ) ).
cnf(c6,plain,
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
inference(clausification,[status(esa)],[r_into_trancl]) ).
cnf(c7,plain,
trans(trancl(X0)),
inference(clausification,[status(esa)],[trans_trancl]) ).
cnf(c8,plain,
( member(pair(X3,X1),X2)
| ~ member(pair(X3,X0),X2)
| ~ trans(X2)
| ~ member(pair(X0,X1),X2) ),
inference(clausification,[status(esa)],[transD]) ).
cnf(c9,plain,
( member(pair(X1,'diamond$ustrip$ulemmaD$usk1'(X0,X3,X1,X2)),trancl(X2))
| ~ member(pair(X0,X3),trancl(X2))
| ~ diamond(X2)
| ~ member(pair(X0,X1),X2) ),
inference(clausification,[status(esa)],[diamond_strip_lemmaD1]) ).
cnf(c10,plain,
( member(pair(X3,'diamond$ustrip$ulemmaD$usk1'(X0,X3,X1,X2)),X2)
| ~ member(pair(X0,X3),trancl(X2))
| ~ diamond(X2)
| ~ member(pair(X0,X1),X2) ),
inference(clausification,[status(esa)],[diamond_strip_lemmaD2]) ).
cnf(c11,plain,
diamond(r),
inference(clausification,[status(esa)],[diamond_trancl_2h1]) ).
cnf(c13,plain,
member(pair(ya,z),r),
inference(clausification,[status(esa)],[diamond_trancl_2h3]) ).
cnf(c14,plain,
( member(pair(ya,sk1(X0)),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ),
inference(clausification,[status(esa)],[diamond_trancl_2h4]) ).
cnf(c15,plain,
( member(pair(X0,sk1(X0)),trancl(r))
| ~ member(pair(y,X0),trancl(r)) ),
inference(clausification,[status(esa)],[diamond_trancl_2h5]) ).
cnf(c16,plain,
member(pair(y,yp),trancl(r)),
inference(clausification,[status(esa)],[diamond_trancl_2c1]) ).
cnf(c17,plain,
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(z,X0),trancl(r)) ),
inference(clausification,[status(esa)],[diamond_trancl_2c2]) ).
cnf(d0,plain,
member(pair(yp,sk1(yp)),trancl(r)),
inference(resolution,[status(thm)],[c15,c16]) ).
cnf(d1,plain,
member(pair(ya,sk1(yp)),trancl(r)),
inference(resolution,[status(thm)],[c14,c16]) ).
cnf(d2,plain,
( ~ diamond(r)
| ~ member(pair(ya,X0),trancl(r))
| member(pair(X0,'diamond$ustrip$ulemmaD$usk1'(ya,X0,z,r)),r) ),
inference(resolution,[status(thm)],[c10,c13]) ).
cnf(d3,plain,
( ~ member(pair(ya,X0),trancl(r))
| member(pair(X0,'diamond$ustrip$ulemmaD$usk1'(ya,X0,z,r)),r) ),
inference(resolution,[status(thm)],[c11,d2]) ).
cnf(d4,plain,
member(pair(sk1(yp),'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),r),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
member(pair(sk1(yp),'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),trancl(r)),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
( ~ trans(trancl(r))
| ~ member(pair(X0,sk1(yp)),trancl(r))
| member(pair(X0,'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),trancl(r)) ),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( ~ member(pair(X0,sk1(yp)),trancl(r))
| member(pair(X0,'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),trancl(r)) ),
inference(resolution,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
member(pair(yp,'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),trancl(r)),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( ~ diamond(r)
| ~ member(pair(ya,X0),trancl(r))
| member(pair(z,'diamond$ustrip$ulemmaD$usk1'(ya,X0,z,r)),trancl(r)) ),
inference(resolution,[status(thm)],[c9,c13]) ).
cnf(d10,plain,
( member(pair(z,'diamond$ustrip$ulemmaD$usk1'(ya,X0,z,r)),trancl(r))
| ~ member(pair(ya,X0),trancl(r)) ),
inference(resolution,[status(thm)],[c11,d9]) ).
cnf(d11,plain,
member(pair(z,'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),trancl(r)),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
~ member(pair(yp,'diamond$ustrip$ulemmaD$usk1'(ya,sk1(yp),z,r)),trancl(r)),
inference(resolution,[status(thm)],[d11,c17]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sat Sep 26 23:14:35 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.36/3.34 % SZS status Unsatisfiable for theBenchmark.p
% 17.36/3.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------