%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC003-1 : 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 : n018.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 08:53:54 AM UTC 2026
% Result : Unsatisfiable 37.29s 9.99s
% Output : CNFRefutation 37.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 54 ( 18 unt; 3 nHn; 54 RR)
% Number of literals : 139 ( 34 equ; 98 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ) ).
cnf(co1_16,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(X1,nil)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(co1_17,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ) ).
cnf(co1_18,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ) ).
cnf(co1_19,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ) ).
cnf(co1_20,negated_conjecture,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) ).
cnf(co1_21,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause11,axiom,
~ singletonP(nil) ).
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(c4,plain,
sk2 = sk4,
inference(clausification,[status(esa)],[co1_5]) ).
cnf(c5,plain,
sk1 = sk3,
inference(clausification,[status(esa)],[co1_6]) ).
cnf(c6,plain,
neq(sk2,nil),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c15,plain,
( app(app(X0,X2),X1) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil)
| app(X0,X1) != sk1
| ~ neq(sk4,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c16,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_17]) ).
cnf(c17,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_18]) ).
cnf(c18,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(clausification,[status(esa)],[co1_19]) ).
cnf(c19,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(clausification,[status(esa)],[co1_20]) ).
cnf(c20,plain,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
inference(clausification,[status(esa)],[co1_21]) ).
cnf(c29,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c32,plain,
~ singletonP(nil),
inference(clausification,[status(esa)],[clause11]) ).
cnf(c107,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c121,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c137,plain,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(clausification,[status(esa)],[clause116]) ).
cnf(d0,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(equality_resolution,[status(thm)],[c137]) ).
cnf(d1,plain,
( ~ ssItem(X0)
| ~ ssList(nil)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d0,c107]) ).
cnf(d2,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c29,d1]) ).
cnf(d3,plain,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk1 ),
inference(demodulation,[status(thm)],[c20,c5]) ).
cnf(d4,plain,
neq(sk4,nil),
inference(demodulation,[status(thm)],[c6,c4]) ).
cnf(d5,plain,
app(sk6,sk7) = sk1,
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ neq(sk4,nil)
| ~ neq(X2,nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X0,X2),X1) != sk4
| app(X0,X1) != sk1 ),
inference(demodulation,[status(thm)],[c15,c4]) ).
cnf(d7,plain,
( ~ neq(X2,nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X0,X2),X1) != sk4
| app(X0,X1) != sk1 ),
inference(resolution,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk4,
inference(resolution,[status(thm)],[d4,c19]) ).
cnf(d9,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| app(sk6,sk7) != sk1
| sk4 != sk4 ),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk6)
| sk1 != sk1
| sk4 != sk4 ),
inference(demodulation,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
ssList(sk6),
inference(resolution,[status(thm)],[d4,c17]) ).
cnf(d12,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| sk1 != sk1
| sk4 != sk4 ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
ssList(sk7),
inference(resolution,[status(thm)],[d4,c18]) ).
cnf(d14,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil))
| sk4 != sk4
| sk1 != sk1 ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil))
| sk1 != sk1 ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil)) ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| cons(sk5,nil) = nil
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[d16,c121]) ).
cnf(d18,plain,
( ~ ssList(cons(sk5,nil))
| cons(sk5,nil) = nil ),
inference(resolution,[status(thm)],[c29,d17]) ).
cnf(d19,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| singletonP(nil) ),
inference(superposition,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
( ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c32,d19]) ).
cnf(d21,plain,
ssItem(sk5),
inference(resolution,[status(thm)],[d4,c16]) ).
cnf(d22,plain,
~ ssList(cons(sk5,nil)),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d22,c107]) ).
cnf(d24,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c29,d23]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d21,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC003-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 12:04:52 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.29/9.99 % SZS status Unsatisfiable for theBenchmark.p
% 37.29/9.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------