%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC218-1 : 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 : n020.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 71.98s 9.72s
% Output : CNFRefutation 71.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 20
% Syntax : Number of clauses : 87 ( 32 unt; 2 nHn; 87 RR)
% Number of literals : 202 ( 66 equ; 121 neg)
% Maximal clause size : 5 ( 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; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_1,negated_conjecture,
ssList(sk1) ).
cnf(co1_4,negated_conjecture,
ssList(sk4) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
ssList(sk5) ).
cnf(co1_8,negated_conjecture,
ssList(sk6) ).
cnf(co1_9,negated_conjecture,
app(sk5,sk6) = sk4 ).
cnf(co1_10,negated_conjecture,
ssItem(sk7) ).
cnf(co1_11,negated_conjecture,
app(app(sk5,cons(sk7,nil)),sk6) = sk3 ).
cnf(co1_12,negated_conjecture,
~ neq(sk1,nil) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause11,axiom,
~ singletonP(nil) ).
cnf(clause73,axiom,
( app(X0,nil) = X0
| ~ ssList(X0) ) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ ssList(X0) ) ).
cnf(clause85,axiom,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause86,axiom,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause116,axiom,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ) ).
cnf(clause118,axiom,
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ) ).
cnf(clause119,axiom,
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ) ).
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(c3,plain,
ssList(sk4),
inference(clausification,[status(esa)],[co1_4]) ).
cnf(c5,plain,
sk1 = sk3,
inference(clausification,[status(esa)],[co1_6]) ).
cnf(c6,plain,
ssList(sk5),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
ssList(sk6),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
app(sk5,sk6) = sk4,
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
ssItem(sk7),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
~ neq(sk1,nil),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c19,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c22,plain,
~ singletonP(nil),
inference(clausification,[status(esa)],[clause11]) ).
cnf(c84,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause73]) ).
cnf(c85,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c96,plain,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause85]) ).
cnf(c97,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c111,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c127,plain,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(clausification,[status(esa)],[clause116]) ).
cnf(c129,plain,
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause118]) ).
cnf(c130,plain,
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause119]) ).
cnf(c160,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,
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(equality_resolution,[status(thm)],[c127]) ).
cnf(d1,plain,
( ~ ssItem(X0)
| ~ ssList(nil)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d0,c97]) ).
cnf(d2,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c19,d1]) ).
cnf(d3,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| app(X0,X1) = app(nil,app(X0,X1)) ),
inference(superposition,[status(thm)],[c85,c160]) ).
cnf(d4,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) = app(nil,app(X0,X1)) ),
inference(resolution,[status(thm)],[c19,d3]) ).
cnf(d5,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| app(X0,nil) = app(nil,X0) ),
inference(superposition,[status(thm)],[c84,d4]) ).
cnf(d6,plain,
( ~ ssList(X0)
| app(X0,nil) = app(nil,X0) ),
inference(resolution,[status(thm)],[c19,d5]) ).
cnf(d7,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| X0 = app(nil,X0) ),
inference(superposition,[status(thm)],[c84,d6]) ).
cnf(d8,plain,
( ~ ssList(nil)
| ~ ssList(sk1)
| sk1 = nil ),
inference(resolution,[status(thm)],[c111,c11]) ).
cnf(d9,plain,
( ~ ssList(nil)
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
sk1 = nil,
inference(resolution,[status(thm)],[c19,d9]) ).
cnf(d11,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk1,
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d12,plain,
app(app(sk5,cons(sk7,nil)),sk6) = nil,
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| nil = sk6
| nil != nil ),
inference(superposition,[status(thm)],[d12,c130]) ).
cnf(d14,plain,
( ~ ssList(app(sk5,cons(sk7,nil)))
| nil != nil
| nil = sk6 ),
inference(resolution,[status(thm)],[c7,d13]) ).
cnf(d15,plain,
( ~ ssList(app(sk5,cons(sk7,nil)))
| nil = sk6 ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| nil = sk6 ),
inference(resolution,[status(thm)],[d15,c96]) ).
cnf(d17,plain,
( ~ ssList(cons(sk7,nil))
| nil = sk6 ),
inference(resolution,[status(thm)],[c6,d16]) ).
cnf(d18,plain,
( ~ ssItem(sk7)
| ~ ssList(nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[d17,c97]) ).
cnf(d19,plain,
( ~ ssList(nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[c9,d18]) ).
cnf(d20,plain,
nil = sk6,
inference(resolution,[status(thm)],[c19,d19]) ).
cnf(d21,plain,
app(sk5,nil) = sk4,
inference(demodulation,[status(thm)],[c8,d20]) ).
cnf(d22,plain,
( ~ ssList(sk5)
| sk4 = sk5 ),
inference(superposition,[status(thm)],[d21,c84]) ).
cnf(d23,plain,
sk4 = sk5,
inference(resolution,[status(thm)],[c6,d22]) ).
cnf(d24,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ~ ssList(sk6)
| app(sk5,app(cons(sk7,nil),sk6)) = nil ),
inference(superposition,[status(thm)],[c160,d12]) ).
cnf(d25,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(sk6)
| ~ ssList(sk5)
| app(sk4,app(cons(sk7,nil),sk6)) = nil ),
inference(demodulation,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(sk6)
| ~ ssList(sk5)
| app(sk4,app(cons(sk7,nil),nil)) = nil ),
inference(demodulation,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(sk6)
| ~ ssList(sk4)
| app(sk4,app(cons(sk7,nil),nil)) = nil ),
inference(demodulation,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk4)
| app(sk4,app(cons(sk7,nil),nil)) = nil ),
inference(demodulation,[status(thm)],[d27,d20]) ).
cnf(d29,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(nil)
| app(sk4,app(cons(sk7,nil),nil)) = nil ),
inference(resolution,[status(thm)],[c3,d28]) ).
cnf(d30,plain,
( ~ ssList(cons(sk7,nil))
| app(sk4,app(cons(sk7,nil),nil)) = nil ),
inference(resolution,[status(thm)],[c19,d29]) ).
cnf(d31,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| X0 = app(X0,nil) ),
inference(superposition,[status(thm)],[d6,d7]) ).
cnf(d32,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(cons(sk7,nil))
| app(sk4,cons(sk7,nil)) = nil ),
inference(superposition,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(sk4)
| ~ ssList(cons(sk7,nil))
| nil = sk4
| nil != nil ),
inference(superposition,[status(thm)],[d32,c129]) ).
cnf(d34,plain,
( ~ ssList(cons(sk7,nil))
| nil != nil
| nil = sk4 ),
inference(resolution,[status(thm)],[c3,d33]) ).
cnf(d35,plain,
( ~ ssList(cons(sk7,nil))
| nil = sk4 ),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
( ~ ssItem(sk7)
| ~ ssList(nil)
| nil = sk4 ),
inference(resolution,[status(thm)],[d35,c97]) ).
cnf(d37,plain,
( ~ ssList(nil)
| nil = sk4 ),
inference(resolution,[status(thm)],[c9,d36]) ).
cnf(d38,plain,
nil = sk4,
inference(resolution,[status(thm)],[c19,d37]) ).
cnf(d39,plain,
( ~ ssList(cons(sk7,nil))
| app(nil,cons(sk7,nil)) = nil ),
inference(demodulation,[status(thm)],[d32,d38]) ).
cnf(d40,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(cons(sk7,nil))
| cons(sk7,nil) = nil ),
inference(superposition,[status(thm)],[d39,d7]) ).
cnf(d41,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssItem(sk7)
| singletonP(nil) ),
inference(superposition,[status(thm)],[d40,d2]) ).
cnf(d42,plain,
( ~ ssItem(sk7)
| ~ ssList(cons(sk7,nil)) ),
inference(resolution,[status(thm)],[c22,d41]) ).
cnf(d43,plain,
~ ssList(cons(sk7,nil)),
inference(resolution,[status(thm)],[c9,d42]) ).
cnf(d44,plain,
( ~ ssItem(sk7)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d43,c97]) ).
cnf(d45,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c9,d44]) ).
cnf(d46,plain,
$false,
inference(resolution,[status(thm)],[c19,d45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC218-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 12:33:34 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.98/9.72 % SZS status Unsatisfiable for theBenchmark.p
% 71.98/9.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------