%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC220-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:54:39 AM UTC 2026
% Result : Unsatisfiable 39.22s 10.06s
% Output : CNFRefutation 39.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 65 ( 15 unt; 16 nHn; 65 RR)
% Number of literals : 193 ( 55 equ; 123 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
nil != sk1 ).
cnf(co1_8,negated_conjecture,
( ssItem(sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_9,negated_conjecture,
( memberP(X1,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_10,negated_conjecture,
( memberP(X2,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_11,negated_conjecture,
( leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_12,negated_conjecture,
( ~ leq(sk5(X2,X1,X0),X0)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_13,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ) ).
cnf(co1_14,negated_conjecture,
( ssList(sk7)
| nil = sk3 ) ).
cnf(co1_15,negated_conjecture,
( ssList(sk8)
| nil = sk3 ) ).
cnf(co1_16,negated_conjecture,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ) ).
cnf(co1_17,negated_conjecture,
( ~ leq(sk6,X0)
| ~ memberP(sk8,X0)
| ~ memberP(sk7,X0)
| leq(X0,sk6)
| ~ ssItem(X0)
| nil = sk3 ) ).
cnf(c5,plain,
sk1 = sk3,
inference(clausification,[status(esa)],[co1_6]) ).
cnf(c6,plain,
nil != sk1,
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
( ~ ssItem(X2)
| app(app(X1,cons(X2,nil)),X0) != sk1
| ssItem(sk5(X0,X1,X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
( app(app(X2,cons(X1,nil)),X0) != sk1
| memberP(X2,sk5(X0,X2,X1))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
( memberP(X1,sk5(X1,X0,X2))
| app(app(X0,cons(X2,nil)),X1) != sk1
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( leq(X0,sk5(X2,X1,X0))
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( ~ leq(sk5(X1,X2,X0),X0)
| app(app(X2,cons(X0,nil)),X1) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( ssItem(sk6)
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( ssList(sk7)
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c14,plain,
( ssList(sk8)
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c15,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c16,plain,
( ~ ssItem(X0)
| ~ memberP(sk7,X0)
| ~ memberP(sk8,X0)
| nil = sk3
| ~ leq(sk6,X0)
| leq(X0,sk6) ),
inference(clausification,[status(esa)],[co1_17]) ).
cnf(d0,plain,
( ~ leq(sk6,X0)
| leq(X0,sk6)
| ~ memberP(sk8,X0)
| ~ memberP(sk7,X0)
| ~ ssItem(X0)
| nil = sk1 ),
inference(demodulation,[status(thm)],[c16,c5]) ).
cnf(d1,plain,
( ~ leq(sk6,X0)
| leq(X0,sk6)
| ~ memberP(sk8,X0)
| ~ memberP(sk7,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk1 ),
inference(demodulation,[status(thm)],[c15,c5]) ).
cnf(d3,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk1
| nil = sk1 ),
inference(demodulation,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk1,
inference(resolution,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( ssItem(sk6)
| nil = sk1 ),
inference(demodulation,[status(thm)],[c12,c5]) ).
cnf(d7,plain,
ssItem(sk6),
inference(resolution,[status(thm)],[c6,d6]) ).
cnf(d8,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ssList(sk7)
| nil = sk1 ),
inference(demodulation,[status(thm)],[c13,c5]) ).
cnf(d10,plain,
ssList(sk7),
inference(resolution,[status(thm)],[c6,d9]) ).
cnf(d11,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ssList(sk8)
| nil = sk1 ),
inference(demodulation,[status(thm)],[c14,c5]) ).
cnf(d13,plain,
ssList(sk8),
inference(resolution,[status(thm)],[c6,d12]) ).
cnf(d14,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( leq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6)) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d4,c7]) ).
cnf(d18,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d7,d17]) ).
cnf(d19,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
( ssItem(sk5(sk8,sk7,sk6))
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d13,d19]) ).
cnf(d21,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
( leq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d4,c11]) ).
cnf(d24,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d7,d23]) ).
cnf(d25,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d10,d24]) ).
cnf(d26,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d13,d25]) ).
cnf(d27,plain,
~ leq(sk5(sk8,sk7,sk6),sk6),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(resolution,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d4,c9]) ).
cnf(d30,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d7,d29]) ).
cnf(d31,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d10,d30]) ).
cnf(d32,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d13,d31]) ).
cnf(d33,plain,
memberP(sk8,sk5(sk8,sk7,sk6)),
inference(equality_resolution,[status(thm)],[d32]) ).
cnf(d34,plain,
~ memberP(sk7,sk5(sk8,sk7,sk6)),
inference(resolution,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d4,c8]) ).
cnf(d36,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d7,d35]) ).
cnf(d37,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d10,d36]) ).
cnf(d38,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d13,d37]) ).
cnf(d39,plain,
memberP(sk7,sk5(sk8,sk7,sk6)),
inference(equality_resolution,[status(thm)],[d38]) ).
cnf(d40,plain,
$false,
inference(resolution,[status(thm)],[d39,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC220-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 12:32:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.22/10.06 % SZS status Unsatisfiable for theBenchmark.p
% 39.22/10.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------