%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC219-1 : 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 : 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 08:54:39 AM UTC 2026
% Result : Unsatisfiable 46.66s 6.50s
% Output : CNFRefutation 46.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of clauses : 74 ( 20 unt; 13 nHn; 74 RR)
% Number of literals : 182 ( 73 equ; 100 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_1,negated_conjecture,
ssList(sk1) ).
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_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_14,negated_conjecture,
( nil = sk3
| ssItem(sk6) ) ).
cnf(co1_18,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause71,axiom,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ ssList(X0) ) ).
cnf(clause96,axiom,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause97,axiom,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause104,axiom,
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ) ).
cnf(clause120,axiom,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause149,axiom,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(c0,plain,
ssList(sk1),
inference(clausification,[status(esa)],[co1_1]) ).
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(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(c13,plain,
( nil = sk3
| ssItem(sk6) ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c17,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(clausification,[status(esa)],[co1_18]) ).
cnf(c27,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c90,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(clausification,[status(esa)],[clause71]) ).
cnf(c93,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c115,plain,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause96]) ).
cnf(c116,plain,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause97]) ).
cnf(c123,plain,
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause104]) ).
cnf(c139,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(c168,plain,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause149]) ).
cnf(d0,plain,
( cons(sk6,nil) = sk3
| nil = sk1 ),
inference(demodulation,[status(thm)],[c17,c5]) ).
cnf(d1,plain,
( cons(sk6,nil) = sk1
| nil = sk1 ),
inference(demodulation,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
cons(sk6,nil) = sk1,
inference(resolution,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
( memberP(X1,sk5(X1,X0,sk6))
| ~ ssItem(sk6)
| ~ ssList(X1)
| ~ ssList(X0)
| app(app(X0,sk1),X1) != sk1 ),
inference(superposition,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
( ssItem(sk6)
| nil = sk1 ),
inference(demodulation,[status(thm)],[c13,c5]) ).
cnf(d5,plain,
ssItem(sk6),
inference(resolution,[status(thm)],[c6,d4]) ).
cnf(d6,plain,
( memberP(X1,sk5(X1,X0,sk6))
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X0,sk1),X1) != sk1 ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ ssItem(sk6)
| ~ ssList(X0)
| app(sk1,X0) = cons(sk6,X0) ),
inference(superposition,[status(thm)],[d2,c139]) ).
cnf(d8,plain,
( ~ ssList(X0)
| app(sk1,X0) = cons(sk6,X0) ),
inference(resolution,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| app(X0,X1) = app(nil,app(X0,X1)) ),
inference(superposition,[status(thm)],[c93,c168]) ).
cnf(d10,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) = app(nil,app(X0,X1)) ),
inference(resolution,[status(thm)],[c27,d9]) ).
cnf(d11,plain,
( ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X0)
| app(sk1,X0) = app(nil,cons(sk6,X0)) ),
inference(superposition,[status(thm)],[d8,d10]) ).
cnf(d12,plain,
( ~ ssList(X0)
| app(sk1,X0) = app(nil,cons(sk6,X0)) ),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( ~ ssList(nil)
| app(sk1,nil) = app(nil,sk1) ),
inference(superposition,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
app(sk1,nil) = app(nil,sk1),
inference(resolution,[status(thm)],[c27,d13]) ).
cnf(d15,plain,
( ~ ssList(nil)
| app(nil,sk1) = cons(sk6,nil) ),
inference(superposition,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( ~ ssList(nil)
| app(nil,sk1) = sk1 ),
inference(demodulation,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c27,d16]) ).
cnf(d18,plain,
( memberP(X0,sk5(X0,nil,sk6))
| ~ ssList(nil)
| ~ ssList(X0)
| app(sk1,X0) != sk1 ),
inference(superposition,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
( memberP(X0,sk5(X0,nil,sk6))
| ~ ssList(X0)
| app(sk1,X0) != sk1 ),
inference(resolution,[status(thm)],[c27,d18]) ).
cnf(d20,plain,
app(sk1,nil) = sk1,
inference(demodulation,[status(thm)],[d14,d17]) ).
cnf(d21,plain,
( memberP(nil,sk5(nil,nil,sk6))
| ~ ssList(nil)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( memberP(nil,sk5(nil,nil,sk6))
| sk1 != sk1 ),
inference(resolution,[status(thm)],[c27,d21]) ).
cnf(d23,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| tl(sk1) = nil ),
inference(superposition,[status(thm)],[d2,c115]) ).
cnf(d24,plain,
( ~ ssItem(sk6)
| tl(sk1) = nil ),
inference(resolution,[status(thm)],[c27,d23]) ).
cnf(d25,plain,
tl(sk1) = nil,
inference(resolution,[status(thm)],[d5,d24]) ).
cnf(d26,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| hd(sk1) = sk6 ),
inference(superposition,[status(thm)],[d2,c116]) ).
cnf(d27,plain,
( ~ ssItem(sk6)
| hd(sk1) = sk6 ),
inference(resolution,[status(thm)],[c27,d26]) ).
cnf(d28,plain,
hd(sk1) = sk6,
inference(resolution,[status(thm)],[d5,d27]) ).
cnf(d29,plain,
( ~ ssList(sk1)
| nil = sk1
| cons(sk6,tl(sk1)) = sk1 ),
inference(superposition,[status(thm)],[d28,c123]) ).
cnf(d30,plain,
( ~ ssList(sk1)
| cons(sk6,nil) = sk1
| nil = sk1 ),
inference(demodulation,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( ~ ssList(sk1)
| sk1 = sk1
| nil = sk1 ),
inference(demodulation,[status(thm)],[d30,d2]) ).
cnf(d32,plain,
( sk1 = sk1
| nil = sk1 ),
inference(resolution,[status(thm)],[c0,d31]) ).
cnf(d33,plain,
sk1 = sk1,
inference(resolution,[status(thm)],[c6,d32]) ).
cnf(d34,plain,
memberP(nil,sk5(nil,nil,sk6)),
inference(resolution,[status(thm)],[d33,d22]) ).
cnf(d35,plain,
~ ssItem(sk5(nil,nil,sk6)),
inference(resolution,[status(thm)],[d34,c90]) ).
cnf(d36,plain,
( ssItem(sk5(X1,X0,sk6))
| ~ ssItem(sk6)
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X0,sk1),X1) != sk1 ),
inference(superposition,[status(thm)],[d2,c7]) ).
cnf(d37,plain,
( ssItem(sk5(X1,X0,sk6))
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X0,sk1),X1) != sk1 ),
inference(resolution,[status(thm)],[d5,d36]) ).
cnf(d38,plain,
( ssItem(sk5(X0,nil,sk6))
| ~ ssList(nil)
| ~ ssList(X0)
| app(sk1,X0) != sk1 ),
inference(superposition,[status(thm)],[d17,d37]) ).
cnf(d39,plain,
( ssItem(sk5(X0,nil,sk6))
| ~ ssList(X0)
| app(sk1,X0) != sk1 ),
inference(resolution,[status(thm)],[c27,d38]) ).
cnf(d40,plain,
( ssItem(sk5(nil,nil,sk6))
| ~ ssList(nil)
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d20,d39]) ).
cnf(d41,plain,
( ssItem(sk5(nil,nil,sk6))
| sk1 != sk1 ),
inference(resolution,[status(thm)],[c27,d40]) ).
cnf(d42,plain,
ssItem(sk5(nil,nil,sk6)),
inference(resolution,[status(thm)],[d33,d41]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC219-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 12:30:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.66/6.50 % SZS status Unsatisfiable for theBenchmark.p
% 46.66/6.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------