%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC013-1 : 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 : n009.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 08:53:56 AM UTC 2026
% Result : Unsatisfiable 77.14s 17.80s
% Output : CNFRefutation 77.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 13 unt; 6 nHn; 44 RR)
% Number of literals : 159 ( 55 equ; 122 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_11,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk1 != X0
| ~ ssList(X0) ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause76,axiom,
( nil = X0
| ssItem(hd(X0))
| ~ 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(clause115,axiom,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ) ).
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(c10,plain,
( ~ ssItem(X0)
| cons(X0,nil) != X1
| ~ neq(nil,sk4)
| sk3 = X1
| ~ ssList(X1)
| ~ neq(sk4,nil)
| hd(sk4) != X0 ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( cons(X0,nil) != X1
| ~ ssItem(X0)
| ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssList(X1)
| sk1 != X1
| hd(sk2) != X0 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c19,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c87,plain,
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause76]) ).
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(c126,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(clausification,[status(esa)],[clause115]) ).
cnf(d0,plain,
( ~ neq(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[c126]) ).
cnf(d1,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ neq(sk2,nil)
| ~ ssList(X0)
| hd(sk2) != X1
| cons(X1,nil) != X0
| sk1 != X0 ),
inference(demodulation,[status(thm)],[c11,c4]) ).
cnf(d2,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ ssList(X0)
| hd(sk2) != X1
| cons(X1,nil) != X0
| sk1 != X0 ),
inference(resolution,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
( ~ ssItem(X0)
| ~ neq(nil,sk2)
| ~ ssList(cons(X0,nil))
| hd(sk2) != X0
| sk1 != cons(X0,nil) ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil)
| ~ ssList(X0)
| hd(sk4) != X1
| cons(X1,nil) != X0
| sk1 = X0 ),
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d5,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil)
| ~ ssList(X0)
| hd(sk2) != X1
| cons(X1,nil) != X0
| sk1 = X0 ),
inference(demodulation,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk4)
| ~ neq(sk2,nil)
| ~ ssList(X0)
| hd(sk2) != X1
| cons(X1,nil) != X0
| sk1 = X0 ),
inference(demodulation,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ neq(sk2,nil)
| ~ ssList(X0)
| hd(sk2) != X1
| cons(X1,nil) != X0
| sk1 = X0 ),
inference(demodulation,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( ~ ssItem(X1)
| ~ neq(nil,sk2)
| ~ ssList(X0)
| hd(sk2) != X1
| cons(X1,nil) != X0
| sk1 = X0 ),
inference(resolution,[status(thm)],[c6,d7]) ).
cnf(d9,plain,
( ~ ssItem(X0)
| ~ neq(nil,sk2)
| ~ ssList(cons(X0,nil))
| hd(sk2) != X0
| sk1 = cons(X0,nil) ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( ~ ssItem(X0)
| ~ neq(nil,sk2)
| ~ ssList(cons(X0,nil))
| hd(sk2) != X0
| ~ ssItem(X0)
| ~ neq(nil,sk2)
| ~ ssList(cons(X0,nil))
| hd(sk2) != X0 ),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
( ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ~ ssList(cons(hd(sk2),nil)) ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssItem(hd(sk2))
| ~ neq(nil,sk2) ),
inference(resolution,[status(thm)],[d11,c97]) ).
cnf(d13,plain,
( ~ ssItem(hd(sk2))
| ~ neq(nil,sk2) ),
inference(resolution,[status(thm)],[c19,d12]) ).
cnf(d14,plain,
( ~ ssList(sk2)
| nil = sk2
| ~ neq(nil,sk2) ),
inference(resolution,[status(thm)],[d13,c87]) ).
cnf(d15,plain,
( ~ neq(nil,sk2)
| nil = sk2 ),
inference(resolution,[status(thm)],[c1,d14]) ).
cnf(d16,plain,
( ~ ssList(nil)
| ~ ssList(sk2)
| nil = sk2
| nil = sk2 ),
inference(resolution,[status(thm)],[d15,c111]) ).
cnf(d17,plain,
( ~ ssList(nil)
| nil = sk2 ),
inference(resolution,[status(thm)],[c1,d16]) ).
cnf(d18,plain,
nil = sk2,
inference(resolution,[status(thm)],[c19,d17]) ).
cnf(d19,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[c6,d18]) ).
cnf(d20,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[c19,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC013-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n009.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 12:03:59 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.14/17.80 % SZS status Unsatisfiable for theBenchmark.p
% 77.14/17.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------