%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC416-1 : 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 : n010.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 08:55:19 AM UTC 2026
% Result : Unsatisfiable 161.87s 23.84s
% Output : CNFRefutation 161.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of clauses : 64 ( 21 unt; 3 nHn; 64 RR)
% Number of literals : 178 ( 55 equ; 128 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_1,negated_conjecture,
ssList(sk1) ).
cnf(co1_2,negated_conjecture,
ssList(sk2) ).
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_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk1) != X0
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ) ).
cnf(co1_13,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ) ).
cnf(co1_14,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause71,axiom,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ).
cnf(clause86,axiom,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause97,axiom,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause120,axiom,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause138,axiom,
( memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1 ) ).
cnf(c0,plain,
ssList(sk1),
inference(clausification,[status(esa)],[co1_1]) ).
cnf(c1,plain,
ssList(sk2),
inference(clausification,[status(esa)],[co1_2]) ).
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(c11,plain,
( app(X2,sk1) != X0
| ~ neq(nil,sk2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X0)
| ~ ssList(X2)
| hd(sk2) != X1
| ~ neq(sk4,nil)
| sk2 != X0 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c21,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c84,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(clausification,[status(esa)],[clause71]) ).
cnf(c99,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c110,plain,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause97]) ).
cnf(c113,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c133,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(c151,plain,
( X2 != X0
| memberP(cons(X0,X1),X2)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause138]) ).
cnf(d0,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk1) = sk4 ),
inference(demodulation,[status(thm)],[c13,c5]) ).
cnf(d1,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk1) = sk2 ),
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk1) = sk2 ),
inference(demodulation,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
app(cons(sk5,nil),sk1) = sk2,
inference(resolution,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
( ~ ssItem(sk5)
| ~ ssList(sk1)
| cons(sk5,sk1) = sk2 ),
inference(superposition,[status(thm)],[c133,d3]) ).
cnf(d5,plain,
( ~ ssItem(sk5)
| cons(sk5,sk1) = sk2 ),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
( ssItem(sk5)
| ~ neq(sk2,nil) ),
inference(demodulation,[status(thm)],[c12,c4]) ).
cnf(d7,plain,
ssItem(sk5),
inference(resolution,[status(thm)],[c6,d6]) ).
cnf(d8,plain,
cons(sk5,sk1) = sk2,
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ ssItem(sk5)
| ~ ssList(sk1)
| hd(sk2) = sk5 ),
inference(superposition,[status(thm)],[d8,c110]) ).
cnf(d10,plain,
( ~ ssItem(sk5)
| hd(sk2) = sk5 ),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
hd(sk2) = sk5,
inference(resolution,[status(thm)],[d7,d10]) ).
cnf(d12,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ neq(sk2,nil)
| ~ ssList(X2)
| ~ ssList(X0)
| hd(sk2) != X1
| app(X2,sk1) != X0
| cons(X1,nil) != X2
| sk2 != X0 ),
inference(demodulation,[status(thm)],[c11,c4]) ).
cnf(d13,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ ssList(X2)
| ~ ssList(X0)
| hd(sk2) != X1
| app(X2,sk1) != X0
| cons(X1,nil) != X2
| sk2 != X0 ),
inference(resolution,[status(thm)],[c6,d12]) ).
cnf(d14,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ ssList(X0)
| ~ ssList(cons(sk5,nil))
| hd(sk2) != X1
| cons(X1,nil) != cons(sk5,nil)
| sk2 != X0
| sk2 != X0 ),
inference(superposition,[status(thm)],[d3,d13]) ).
cnf(d15,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk5 != X1
| cons(X1,nil) != cons(sk5,nil)
| sk2 != X0 ),
inference(demodulation,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ~ ssItem(sk5)
| ~ neq(nil,sk2)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk5 != sk5
| sk2 != X0 ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ neq(nil,sk2)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk5 != sk5
| sk2 != X0 ),
inference(resolution,[status(thm)],[d7,d16]) ).
cnf(d18,plain,
( ~ neq(nil,sk2)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk2 != X0 ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( ~ neq(nil,sk2)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk2) ),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
( ~ neq(nil,sk2)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c1,d19]) ).
cnf(d21,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ neq(nil,sk2) ),
inference(resolution,[status(thm)],[d20,c99]) ).
cnf(d22,plain,
( ~ ssItem(sk5)
| ~ neq(nil,sk2) ),
inference(resolution,[status(thm)],[c21,d21]) ).
cnf(d23,plain,
~ neq(nil,sk2),
inference(resolution,[status(thm)],[d7,d22]) ).
cnf(d24,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| nil = sk2 ),
inference(resolution,[status(thm)],[d23,c113]) ).
cnf(d25,plain,
( ~ ssList(nil)
| nil = sk2 ),
inference(resolution,[status(thm)],[c1,d24]) ).
cnf(d26,plain,
nil = sk2,
inference(resolution,[status(thm)],[c21,d25]) ).
cnf(d27,plain,
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[c151]) ).
cnf(d28,plain,
( ~ ssItem(sk5)
| ~ ssList(sk1)
| memberP(sk2,sk5) ),
inference(superposition,[status(thm)],[d8,d27]) ).
cnf(d29,plain,
( memberP(sk2,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c0,d28]) ).
cnf(d30,plain,
memberP(sk2,sk5),
inference(resolution,[status(thm)],[d7,d29]) ).
cnf(d31,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[d31,c84]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d7,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC416-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43 % Computer : n010.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Sat Sep 26 13:01:15 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 161.87/23.84 % SZS status Unsatisfiable for theBenchmark.p
% 161.87/23.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------