%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:54:15 AM UTC 2026
% Result : Unsatisfiable 95.22s 21.67s
% Output : CNFRefutation 95.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of clauses : 65 ( 10 unt; 31 nHn; 65 RR)
% Number of literals : 199 ( 102 equ; 106 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
( ~ memberP(sk2,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ) ).
cnf(co1_8,negated_conjecture,
( ~ memberP(sk2,X0)
| memberP(sk2,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ) ).
cnf(co1_9,negated_conjecture,
( ~ memberP(sk2,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ) ).
cnf(co1_10,negated_conjecture,
( ~ memberP(sk2,X0)
| X0 != sk5(X0)
| cons(X0,nil) != sk1
| ~ ssItem(X0) ) ).
cnf(co1_11,negated_conjecture,
( nil != sk1
| nil != sk2 ) ).
cnf(co1_12,negated_conjecture,
( nil = sk4
| ssItem(sk6) ) ).
cnf(co1_13,negated_conjecture,
( nil = sk3
| ssItem(sk6) ) ).
cnf(co1_14,negated_conjecture,
( nil = sk4
| cons(sk6,nil) = sk3 ) ).
cnf(co1_15,negated_conjecture,
( nil = sk4
| memberP(sk4,sk6) ) ).
cnf(co1_16,negated_conjecture,
( nil = sk4
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ) ).
cnf(co1_18,negated_conjecture,
( nil = sk3
| memberP(sk4,sk6) ) ).
cnf(clause71,axiom,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ).
cnf(c4,plain,
sk2 = sk4,
inference(clausification,[status(esa)],[co1_5]) ).
cnf(c5,plain,
sk1 = sk3,
inference(clausification,[status(esa)],[co1_6]) ).
cnf(c6,plain,
( ~ memberP(sk2,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
( ~ memberP(sk2,X0)
| memberP(sk2,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
( ~ memberP(sk2,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
( ~ memberP(sk2,X0)
| X0 != sk5(X0)
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( nil != sk1
| nil != sk2 ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( nil = sk4
| ssItem(sk6) ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( nil = sk3
| ssItem(sk6) ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( nil = sk4
| cons(sk6,nil) = sk3 ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c14,plain,
( nil = sk4
| memberP(sk4,sk6) ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c15,plain,
( ~ memberP(sk4,X0)
| nil = sk4
| ~ ssItem(X0)
| sk6 = X0
| ~ leq(sk6,X0) ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c17,plain,
( nil = sk3
| memberP(sk4,sk6) ),
inference(clausification,[status(esa)],[co1_18]) ).
cnf(c89,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(clausification,[status(esa)],[clause71]) ).
cnf(d0,plain,
( ~ memberP(sk2,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3
| X0 != sk5(X0) ),
inference(demodulation,[status(thm)],[c9,c5]) ).
cnf(d1,plain,
( ~ memberP(sk4,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3
| X0 != sk5(X0) ),
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( nil = sk4
| ~ memberP(sk4,sk6)
| ~ ssItem(sk6)
| sk6 != sk5(sk6)
| sk3 != sk3 ),
inference(superposition,[status(thm)],[c13,d1]) ).
cnf(d3,plain,
( ~ memberP(sk4,sk6)
| sk6 != sk5(sk6)
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c11,d2]) ).
cnf(d4,plain,
( sk6 != sk5(sk6)
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c14,d3]) ).
cnf(d5,plain,
( leq(X0,sk5(X0))
| ~ memberP(sk2,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[c8,c5]) ).
cnf(d6,plain,
( leq(X0,sk5(X0))
| ~ memberP(sk4,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( nil = sk4
| leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ ssItem(sk6)
| sk3 != sk3 ),
inference(superposition,[status(thm)],[c13,d6]) ).
cnf(d8,plain,
( leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk6)
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c11,d7]) ).
cnf(d9,plain,
( leq(sk6,sk5(sk6))
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c14,d8]) ).
cnf(d10,plain,
( leq(sk6,sk5(sk6))
| nil = sk4 ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( ~ memberP(sk4,sk5(sk6))
| ~ ssItem(sk5(sk6))
| sk6 = sk5(sk6)
| nil = sk4
| nil = sk4 ),
inference(resolution,[status(thm)],[d10,c15]) ).
cnf(d12,plain,
( ~ memberP(sk2,X0)
| ssItem(sk5(X0))
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[c6,c5]) ).
cnf(d13,plain,
( ~ memberP(sk4,X0)
| ssItem(sk5(X0))
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
( nil = sk4
| ~ memberP(sk4,sk6)
| ssItem(sk5(sk6))
| ~ ssItem(sk6)
| sk3 != sk3 ),
inference(superposition,[status(thm)],[c13,d13]) ).
cnf(d15,plain,
( ~ memberP(sk4,sk6)
| ssItem(sk5(sk6))
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c11,d14]) ).
cnf(d16,plain,
( ssItem(sk5(sk6))
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c14,d15]) ).
cnf(d17,plain,
( ssItem(sk5(sk6))
| nil = sk4 ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ memberP(sk4,sk5(sk6))
| sk6 = sk5(sk6)
| nil = sk4
| nil = sk4 ),
inference(resolution,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
( memberP(sk2,sk5(X0))
| ~ memberP(sk2,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[c7,c5]) ).
cnf(d20,plain,
( memberP(sk2,sk5(X0))
| ~ memberP(sk4,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[d19,c4]) ).
cnf(d21,plain,
( memberP(sk4,sk5(X0))
| ~ memberP(sk4,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3 ),
inference(demodulation,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
( nil = sk4
| memberP(sk4,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ ssItem(sk6)
| sk3 != sk3 ),
inference(superposition,[status(thm)],[c13,d21]) ).
cnf(d23,plain,
( ~ memberP(sk4,sk6)
| memberP(sk4,sk5(sk6))
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c11,d22]) ).
cnf(d24,plain,
( memberP(sk4,sk5(sk6))
| nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[c14,d23]) ).
cnf(d25,plain,
( memberP(sk4,sk5(sk6))
| nil = sk4 ),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
( sk6 = sk5(sk6)
| nil = sk4
| nil = sk4 ),
inference(resolution,[status(thm)],[d25,d18]) ).
cnf(d27,plain,
( nil = sk4
| sk3 != sk3
| nil = sk4 ),
inference(resolution,[status(thm)],[d26,d4]) ).
cnf(d28,plain,
nil = sk4,
inference(equality_resolution,[status(thm)],[d27]) ).
cnf(d29,plain,
( memberP(nil,sk6)
| nil = sk3 ),
inference(demodulation,[status(thm)],[c17,d28]) ).
cnf(d30,plain,
( nil != sk2
| nil != sk3 ),
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d31,plain,
( nil != sk4
| nil != sk3 ),
inference(demodulation,[status(thm)],[d30,c4]) ).
cnf(d32,plain,
nil != sk3,
inference(resolution,[status(thm)],[d28,d31]) ).
cnf(d33,plain,
memberP(nil,sk6),
inference(resolution,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
~ ssItem(sk6),
inference(resolution,[status(thm)],[d33,c89]) ).
cnf(d35,plain,
ssItem(sk6),
inference(resolution,[status(thm)],[d32,c12]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:18:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.22/21.67 % SZS status Unsatisfiable for theBenchmark.p
% 95.22/21.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------