%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:22:05 AM UTC 2026
% Result : Unsatisfiable 9.79s 7.64s
% Output : CNFRefutation 9.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 17 unt; 0 nHn; 25 RR)
% Number of literals : 47 ( 0 equ; 29 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_of_borders,axiom,
( borders(X1,X0)
| ~ borders(X0,X1) ) ).
cnf(indian,negated_conjecture,
ocean(indian) ).
cnf(western_australia,negated_conjecture,
state('western$uaustralia') ).
cnf(northern_territory,negated_conjecture,
state('northern$uterritory') ).
cnf(wa_nt,negated_conjecture,
borders('western$uaustralia','northern$uterritory') ).
cnf(indian_wa,negated_conjecture,
borders(indian,'western$uaustralia') ).
cnf(indian_nt,negated_conjecture,
borders(indian,'northern$uterritory') ).
cnf(prove_borders,negated_conjecture,
( ~ ocean(X2)
| ~ borders(X1,X2)
| ~ borders(X0,X2)
| ~ borders(X0,X1)
| ~ state(X1)
| ~ state(X0) ) ).
cnf(c0,plain,
( borders(X1,X0)
| ~ borders(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_borders]) ).
cnf(c2,plain,
ocean(indian),
inference(clausification,[status(esa)],[indian]) ).
cnf(c5,plain,
state('western$uaustralia'),
inference(clausification,[status(esa)],[western_australia]) ).
cnf(c6,plain,
state('northern$uterritory'),
inference(clausification,[status(esa)],[northern_territory]) ).
cnf(c12,plain,
borders('western$uaustralia','northern$uterritory'),
inference(clausification,[status(esa)],[wa_nt]) ).
cnf(c21,plain,
borders(indian,'western$uaustralia'),
inference(clausification,[status(esa)],[indian_wa]) ).
cnf(c22,plain,
borders(indian,'northern$uterritory'),
inference(clausification,[status(esa)],[indian_nt]) ).
cnf(c32,plain,
( ~ borders(X2,X1)
| ~ borders(X0,X1)
| ~ state(X2)
| ~ borders(X0,X2)
| ~ ocean(X1)
| ~ state(X0) ),
inference(clausification,[status(esa)],[prove_borders]) ).
cnf(d0,plain,
borders('northern$uterritory','western$uaustralia'),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d1,plain,
borders('western$uaustralia',indian),
inference(resolution,[status(thm)],[c21,c0]) ).
cnf(d2,plain,
( ~ state('western$uaustralia')
| ~ state(X0)
| ~ ocean(indian)
| ~ borders(X0,indian)
| ~ borders(X0,'western$uaustralia') ),
inference(resolution,[status(thm)],[d1,c32]) ).
cnf(d3,plain,
( ~ state('western$uaustralia')
| ~ state(X0)
| ~ borders(X0,'western$uaustralia')
| ~ borders(X0,indian) ),
inference(resolution,[status(thm)],[c2,d2]) ).
cnf(d4,plain,
( ~ state(X0)
| ~ borders(X0,'western$uaustralia')
| ~ borders(X0,indian) ),
inference(resolution,[status(thm)],[c5,d3]) ).
cnf(d5,plain,
( ~ state('northern$uterritory')
| ~ borders('northern$uterritory',indian) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
~ borders('northern$uterritory',indian),
inference(resolution,[status(thm)],[c6,d5]) ).
cnf(d7,plain,
borders('northern$uterritory',indian),
inference(resolution,[status(thm)],[c22,c0]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n007.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sat Sep 26 05:03:14 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.79/7.64 % SZS status Unsatisfiable for theBenchmark.p
% 9.79/7.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------