%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW409-1 : TPTP v9.3.1. Released v5.2.0.
% 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 09:11:49 AM UTC 2026
% Result : Unsatisfiable 20.06s 4.28s
% Output : CNFRefutation 20.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 12 unt; 5 nHn; 17 RR)
% Number of literals : 32 ( 10 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(premise_3,hypothesis,
x1 != x3 ).
cnf(premise_5,hypothesis,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))) ).
cnf(conclusion_1,negated_conjecture,
~ heap(sep(lseg(x2,nil),emp)) ).
cnf(associative_commutative,axiom,
sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)) ).
cnf(unfolding_2,axiom,
( heap(sep(lseg(X0,X2),X3))
| X0 = X1
| ~ heap(sep(next(X0,X1),sep(lseg(X1,X2),X3))) ) ).
cnf(unfolding_3,axiom,
( heap(sep(lseg(X0,nil),X2))
| ~ heap(sep(lseg(X0,X1),sep(lseg(X1,nil),X2))) ) ).
cnf(c2,plain,
x1 != x3,
inference(clausification,[status(esa)],[premise_3]) ).
cnf(c4,plain,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))),
inference(clausification,[status(esa)],[premise_5]) ).
cnf(c5,plain,
~ heap(sep(lseg(x2,nil),emp)),
inference(clausification,[status(esa)],[conclusion_1]) ).
cnf(c6,plain,
sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)),
inference(clausification,[status(esa)],[associative_commutative]) ).
cnf(c13,plain,
( heap(sep(lseg(X0,X2),X3))
| X0 = X1
| ~ heap(sep(next(X0,X1),sep(lseg(X1,X2),X3))) ),
inference(clausification,[status(esa)],[unfolding_2]) ).
cnf(c14,plain,
( heap(sep(lseg(X0,nil),X2))
| ~ heap(sep(lseg(X0,X1),sep(lseg(X1,nil),X2))) ),
inference(clausification,[status(esa)],[unfolding_3]) ).
cnf(d0,plain,
( heap(sep(lseg(X0,nil),X2))
| ~ heap(sep(lseg(X1,nil),sep(lseg(X0,X1),X2))) ),
inference(superposition,[status(thm)],[c6,c14]) ).
cnf(d1,plain,
( heap(sep(lseg(X0,X2),X3))
| X0 = X1
| ~ heap(sep(lseg(X1,X2),sep(next(X0,X1),X3))) ),
inference(superposition,[status(thm)],[c6,c13]) ).
cnf(d2,plain,
sep(X0,sep(X3,sep(X1,X2))) = sep(X3,sep(X1,sep(X0,X2))),
inference(superposition,[status(thm)],[c6,c6]) ).
cnf(d3,plain,
( heap(sep(lseg(X2,X1),sep(X3,X4)))
| X2 = X0
| ~ heap(sep(X3,sep(lseg(X0,X1),sep(next(X2,X0),X4)))) ),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp)))
| x1 = x3 ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp))),
inference(resolution,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
heap(sep(lseg(x2,nil),emp)),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c5,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW409-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 15:49:34 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.06/4.28 % SZS status Unsatisfiable for theBenchmark.p
% 20.06/4.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------