%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC322-1 : 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 : n013.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 08:54:58 AM UTC 2026
% Result : Unsatisfiable 60.63s 13.18s
% Output : CNFRefutation 60.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of clauses : 81 ( 20 unt; 22 nHn; 81 RR)
% Number of literals : 183 ( 112 equ; 92 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
( app(X1,cons(X0,nil)) != sk4
| app(cons(X0,nil),X1) = sk3
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_8,negated_conjecture,
( nil != sk4
| nil = sk3 ) ).
cnf(co1_9,negated_conjecture,
( nil = sk2
| ssItem(sk5) ) ).
cnf(co1_10,negated_conjecture,
( nil != sk1
| ssItem(sk5) ) ).
cnf(co1_11,negated_conjecture,
( nil = sk2
| ssList(sk6) ) ).
cnf(co1_12,negated_conjecture,
( nil = sk2
| app(sk6,cons(sk5,nil)) = sk2 ) ).
cnf(co1_13,negated_conjecture,
( nil = sk2
| app(cons(sk5,nil),sk6) != sk1 ) ).
cnf(co1_14,negated_conjecture,
( nil != sk1
| ssList(sk6) ) ).
cnf(co1_15,negated_conjecture,
( nil != sk1
| app(sk6,cons(sk5,nil)) = sk2 ) ).
cnf(co1_16,negated_conjecture,
( nil != sk1
| app(cons(sk5,nil),sk6) != sk1 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ ssList(X0) ) ).
cnf(clause86,axiom,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause118,axiom,
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(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,
( app(X1,cons(X0,nil)) != sk4
| app(cons(X0,nil),X1) = sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
( nil != sk4
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
( nil = sk2
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
( nil != sk1
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( nil = sk2
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) != sk1 ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( nil != sk1
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c14,plain,
( nil != sk1
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c15,plain,
( nil != sk1
| app(cons(sk5,nil),sk6) != sk1 ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c23,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c89,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c101,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c133,plain,
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause118]) ).
cnf(c135,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)],[c7,c5]) ).
cnf(d1,plain,
( nil != sk2
| nil = sk1 ),
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ ssItem(X1)
| ~ ssList(X0)
| app(cons(X1,nil),X0) = sk3
| app(X0,cons(X1,nil)) != sk2 ),
inference(demodulation,[status(thm)],[c6,c4]) ).
cnf(d3,plain,
( ~ ssItem(X1)
| ~ ssList(X0)
| app(cons(X1,nil),X0) = sk1
| app(X0,cons(X1,nil)) != sk2 ),
inference(demodulation,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( nil = sk2
| ~ ssItem(sk5)
| ~ ssList(sk6)
| app(cons(sk5,nil),sk6) = sk1
| sk2 != sk2 ),
inference(superposition,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
( ssItem(sk5)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[c8,d1]) ).
cnf(d6,plain,
( ssItem(sk5)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ssItem(sk5)
| ssItem(sk5)
| nil != nil ),
inference(superposition,[status(thm)],[d6,c9]) ).
cnf(d8,plain,
ssItem(sk5),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ~ ssList(sk6)
| nil = sk2
| app(cons(sk5,nil),sk6) = sk1
| sk2 != sk2 ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( ssList(sk6)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[c10,d1]) ).
cnf(d11,plain,
( ssList(sk6)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ssList(sk6)
| ssList(sk6)
| nil != nil ),
inference(superposition,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
ssList(sk6),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk1
| sk2 != sk2 ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk1 ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( nil = sk2
| nil = sk2
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d15,c12]) ).
cnf(d17,plain,
nil = sk2,
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
nil = sk1,
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( nil != sk1
| app(sk6,cons(sk5,nil)) = nil ),
inference(demodulation,[status(thm)],[c14,d17]) ).
cnf(d20,plain,
( nil != nil
| app(sk6,cons(sk5,nil)) = nil ),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
app(sk6,cons(sk5,nil)) = nil,
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| nil = sk6
| nil != nil ),
inference(superposition,[status(thm)],[d21,c133]) ).
cnf(d23,plain,
( ~ ssList(cons(sk5,nil))
| nil = sk6
| nil != nil ),
inference(resolution,[status(thm)],[d13,d22]) ).
cnf(d24,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| nil = sk2
| cons(sk5,sk6) = sk1 ),
inference(superposition,[status(thm)],[c135,d15]) ).
cnf(d25,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| nil = sk2
| cons(sk5,sk6) = nil ),
inference(demodulation,[status(thm)],[d24,d18]) ).
cnf(d26,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| nil = nil
| cons(sk5,sk6) = nil ),
inference(demodulation,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
( ~ ssList(sk6)
| nil = nil
| cons(sk5,sk6) = nil ),
inference(resolution,[status(thm)],[d8,d26]) ).
cnf(d28,plain,
( nil = nil
| cons(sk5,sk6) = nil ),
inference(resolution,[status(thm)],[d13,d27]) ).
cnf(d29,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| nil != sk1
| cons(sk5,sk6) != sk1 ),
inference(superposition,[status(thm)],[c135,c15]) ).
cnf(d30,plain,
( ~ ssList(sk6)
| nil != sk1
| cons(sk5,sk6) != sk1 ),
inference(resolution,[status(thm)],[d8,d29]) ).
cnf(d31,plain,
( nil != sk1
| cons(sk5,sk6) != sk1 ),
inference(resolution,[status(thm)],[d13,d30]) ).
cnf(d32,plain,
cons(sk5,sk6) != sk1,
inference(resolution,[status(thm)],[d18,d31]) ).
cnf(d33,plain,
cons(sk5,sk6) != nil,
inference(demodulation,[status(thm)],[d32,d18]) ).
cnf(d34,plain,
nil = nil,
inference(resolution,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
( ~ ssList(cons(sk5,nil))
| nil = sk6 ),
inference(resolution,[status(thm)],[d34,d23]) ).
cnf(d36,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[d35,c101]) ).
cnf(d37,plain,
( ~ ssList(nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[d8,d36]) ).
cnf(d38,plain,
nil = sk6,
inference(resolution,[status(thm)],[c23,d37]) ).
cnf(d39,plain,
cons(sk5,nil) != nil,
inference(demodulation,[status(thm)],[d33,d38]) ).
cnf(d40,plain,
app(nil,cons(sk5,nil)) = nil,
inference(demodulation,[status(thm)],[d21,d38]) ).
cnf(d41,plain,
( ~ ssList(cons(sk5,nil))
| nil = cons(sk5,nil) ),
inference(superposition,[status(thm)],[d40,c89]) ).
cnf(d42,plain,
( ~ ssList(cons(sk5,nil))
| nil != nil ),
inference(superposition,[status(thm)],[d41,d39]) ).
cnf(d43,plain,
~ ssList(cons(sk5,nil)),
inference(resolution,[status(thm)],[d34,d42]) ).
cnf(d44,plain,
( ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d43,c101]) ).
cnf(d45,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d8,d44]) ).
cnf(d46,plain,
$false,
inference(resolution,[status(thm)],[c23,d45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC322-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n013.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sat Sep 26 12:47:41 UTC 2026
% 0.13/5.42 % CPUTime :
% 0.13/5.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 60.63/13.18 % SZS status Unsatisfiable for theBenchmark.p
% 60.63/13.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------