%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC312-1 : 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 : n017.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 08:54:56 AM UTC 2026
% Result : Unsatisfiable 44.18s 10.26s
% Output : CNFRefutation 44.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 65 ( 8 unt; 15 nHn; 65 RR)
% Number of literals : 155 ( 73 equ; 84 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
( nil != sk4
| nil = sk3 ) ).
cnf(co1_8,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ) ).
cnf(co1_9,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ) ).
cnf(co1_10,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ) ).
cnf(co1_12,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ) ).
cnf(co1_13,negated_conjecture,
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk2 ) ).
cnf(co1_14,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ) ).
cnf(clause98,axiom,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ) ).
cnf(clause120,axiom,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
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,
( nil != sk4
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( ~ ssItem(X1)
| app(cons(X1,nil),X0) != sk2
| nil = sk2
| app(X0,cons(X1,nil)) != sk1
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c112,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause98]) ).
cnf(c134,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(d0,plain,
( nil != sk4
| nil = sk1 ),
inference(demodulation,[status(thm)],[c6,c5]) ).
cnf(d1,plain,
( nil != sk2
| nil = sk1 ),
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(demodulation,[status(thm)],[c9,c4]) ).
cnf(d3,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(demodulation,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| app(sk6,cons(sk5,nil)) != sk1
| nil = sk2
| sk2 != sk2 ),
inference(superposition,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
( ssItem(sk5)
| ~ neq(sk2,nil) ),
inference(demodulation,[status(thm)],[c7,c4]) ).
cnf(d6,plain,
( ssItem(sk5)
| nil = sk2 ),
inference(resolution,[status(thm)],[c11,d5]) ).
cnf(d7,plain,
( ssItem(sk5)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ssItem(sk5)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ssItem(sk5)
| neq(sk2,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d8,c13]) ).
cnf(d10,plain,
( ssItem(sk5)
| neq(sk2,nil) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( ssItem(sk5)
| ssItem(sk5) ),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
( ~ neq(sk2,nil)
| ~ ssList(sk6)
| app(sk6,cons(sk5,nil)) != sk1
| nil = sk2
| sk2 != sk2 ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(demodulation,[status(thm)],[c8,c4]) ).
cnf(d14,plain,
( ssList(sk6)
| nil = sk2 ),
inference(resolution,[status(thm)],[c11,d13]) ).
cnf(d15,plain,
( ssList(sk6)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( ssList(sk6)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ssList(sk6)
| neq(sk2,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d16,c13]) ).
cnf(d18,plain,
( neq(sk2,nil)
| ssList(sk6) ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( ssList(sk6)
| ssList(sk6) ),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) != sk1
| nil = sk2
| sk2 != sk2 ),
inference(resolution,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d22,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(demodulation,[status(thm)],[d21,c4]) ).
cnf(d23,plain,
( ~ neq(sk2,nil)
| ~ neq(sk2,nil)
| nil = sk2
| sk2 != sk2
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( ~ neq(sk2,nil)
| nil = sk2
| sk1 != sk1 ),
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
( ~ neq(sk2,nil)
| nil = sk2 ),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
( nil = sk2
| nil = sk2 ),
inference(resolution,[status(thm)],[d25,c11]) ).
cnf(d27,plain,
nil = sk1,
inference(resolution,[status(thm)],[d26,d1]) ).
cnf(d28,plain,
( neq(nil,nil)
| nil != sk1 ),
inference(demodulation,[status(thm)],[c13,d26]) ).
cnf(d29,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ neq(sk2,nil)
| cons(sk5,sk6) = sk2 ),
inference(superposition,[status(thm)],[c134,d3]) ).
cnf(d31,plain,
( ~ neq(sk2,nil)
| ~ ssList(sk6)
| cons(sk5,sk6) = sk2 ),
inference(resolution,[status(thm)],[d11,d30]) ).
cnf(d32,plain,
( ~ neq(sk2,nil)
| cons(sk5,sk6) = sk2 ),
inference(resolution,[status(thm)],[d19,d31]) ).
cnf(d33,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk2 != nil ),
inference(superposition,[status(thm)],[d32,c112]) ).
cnf(d34,plain,
( ~ neq(sk2,nil)
| ~ ssList(sk6)
| sk2 != nil ),
inference(resolution,[status(thm)],[d11,d33]) ).
cnf(d35,plain,
( ~ neq(sk2,nil)
| sk2 != nil ),
inference(resolution,[status(thm)],[d19,d34]) ).
cnf(d36,plain,
( ~ neq(sk2,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d35,d26]) ).
cnf(d37,plain,
( ~ neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d36,d26]) ).
cnf(d38,plain,
~ neq(nil,nil),
inference(equality_resolution,[status(thm)],[d37]) ).
cnf(d39,plain,
nil != nil,
inference(resolution,[status(thm)],[d38,d29]) ).
cnf(d40,plain,
$false,
inference(equality_resolution,[status(thm)],[d39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC312-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n017.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:41:48 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.18/10.26 % SZS status Unsatisfiable for theBenchmark.p
% 44.18/10.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------