%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC419-1 : 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 : n008.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 08:55:20 AM UTC 2026
% Result : Unsatisfiable 94.58s 29.56s
% Output : CNFRefutation 94.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of clauses : 83 ( 23 unt; 3 nHn; 73 RR)
% Number of literals : 226 ( 59 equ; 163 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 75 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_3,negated_conjecture,
ssList(sk3) ).
cnf(co1_4,negated_conjecture,
ssList(sk4) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil) ).
cnf(co1_8,negated_conjecture,
( app(app(X2,cons(X0,nil)),X1) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(co1_10,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ) ).
cnf(co1_13,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause72,axiom,
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ) ).
cnf(clause73,axiom,
( app(X0,nil) = X0
| ~ ssList(X0) ) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ ssList(X0) ) ).
cnf(clause85,axiom,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause86,axiom,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause120,axiom,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause149,axiom,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause179,axiom,
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ) ).
cnf(c2,plain,
ssList(sk3),
inference(clausification,[status(esa)],[co1_3]) ).
cnf(c3,plain,
ssList(sk4),
inference(clausification,[status(esa)],[co1_4]) ).
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(c7,plain,
( ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X0) != sk2
| ~ ssItem(X1)
| app(app(X0,cons(X1,nil)),X2) != sk1
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c9,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c20,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c84,plain,
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause72]) ).
cnf(c85,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause73]) ).
cnf(c86,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c97,plain,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause85]) ).
cnf(c98,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c132,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(c161,plain,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause149]) ).
cnf(c191,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| app(app(X2,cons(X3,X4)),cons(X3,X1)) != X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ duplicatefreeP(X0) ),
inference(clausification,[status(esa)],[clause179]) ).
cnf(d0,plain,
( duplicatefreeP(app(X0,X1))
| ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c97,c84]) ).
cnf(d1,plain,
neq(sk4,nil),
inference(demodulation,[status(thm)],[c6,c4]) ).
cnf(d2,plain,
app(sk6,cons(sk5,nil)) = sk3,
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(sk5)
| ~ ssList(X1)
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ ssList(X0)
| app(sk3,cons(sk5,X0)) != X1 ),
inference(superposition,[status(thm)],[d2,c191]) ).
cnf(d4,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk3,cons(sk5,X0)) != X1 ),
inference(resolution,[status(thm)],[c20,d3]) ).
cnf(d5,plain,
ssItem(sk5),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d6,plain,
( ~ duplicatefreeP(X1)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk3,cons(sk5,X0)) != X1 ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
ssList(sk6),
inference(resolution,[status(thm)],[d1,c10]) ).
cnf(d8,plain,
( ~ duplicatefreeP(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk3,cons(sk5,X0)) != X1 ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
app(cons(sk5,nil),sk6) = sk4,
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d10,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| cons(sk5,sk6) = sk4 ),
inference(superposition,[status(thm)],[c132,d9]) ).
cnf(d11,plain,
( ~ ssList(sk6)
| cons(sk5,sk6) = sk4 ),
inference(resolution,[status(thm)],[d5,d10]) ).
cnf(d12,plain,
cons(sk5,sk6) = sk4,
inference(resolution,[status(thm)],[d7,d11]) ).
cnf(d13,plain,
( ~ duplicatefreeP(X0)
| ~ ssList(sk6)
| ~ ssList(X0)
| app(sk3,sk4) != X0 ),
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ duplicatefreeP(X0)
| ~ ssList(X0)
| app(sk3,sk4) != X0 ),
inference(resolution,[status(thm)],[d7,d13]) ).
cnf(d15,plain,
( ~ duplicatefreeP(app(sk3,sk4))
| ~ ssList(app(sk3,sk4)) ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(app(sk3,sk4)) ),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( ssItem(X0)
| ~ ssList(app(sk3,sk4))
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[c2,d16]) ).
cnf(d18,plain,
( ssItem(X0)
| ~ ssList(app(sk3,sk4)) ),
inference(resolution,[status(thm)],[c3,d17]) ).
cnf(d19,plain,
( ~ ssList(sk4)
| ~ ssList(sk3)
| ssItem(X0) ),
inference(resolution,[status(thm)],[d18,c97]) ).
cnf(d20,plain,
( ssItem(X0)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[c2,d19]) ).
cnf(d21,plain,
ssItem(X0),
inference(resolution,[status(thm)],[c3,d20]) ).
cnf(d22,plain,
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[d21,c98]) ).
cnf(d23,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| app(app(X2,cons(X1,nil)),X0) != sk1
| app(app(X0,cons(X1,nil)),X2) != sk4 ),
inference(demodulation,[status(thm)],[c7,c4]) ).
cnf(d24,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| app(app(X2,cons(X1,nil)),X0) != sk3
| app(app(X0,cons(X1,nil)),X2) != sk4 ),
inference(demodulation,[status(thm)],[d23,c5]) ).
cnf(d25,plain,
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| app(app(X1,cons(X0,nil)),nil) != sk3
| app(cons(X0,nil),X1) != sk4 ),
inference(superposition,[status(thm)],[c86,d24]) ).
cnf(d26,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X0)
| app(cons(X1,nil),X0) != sk4
| app(app(X0,cons(X1,nil)),nil) != sk3 ),
inference(resolution,[status(thm)],[c20,d25]) ).
cnf(d27,plain,
( ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| app(cons(sk5,nil),sk6) != sk4
| app(sk3,nil) != sk3 ),
inference(superposition,[status(thm)],[d2,d26]) ).
cnf(d28,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| sk4 != sk4
| app(sk3,nil) != sk3 ),
inference(demodulation,[status(thm)],[d27,d9]) ).
cnf(d29,plain,
( ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| sk4 != sk4
| app(sk3,nil) != sk3 ),
inference(resolution,[status(thm)],[d7,d28]) ).
cnf(d30,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| sk4 = cons(sk5,sk6) ),
inference(superposition,[status(thm)],[d9,c132]) ).
cnf(d31,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| sk4 = sk4 ),
inference(demodulation,[status(thm)],[d30,d12]) ).
cnf(d32,plain,
( ~ ssList(sk6)
| sk4 = sk4 ),
inference(resolution,[status(thm)],[d5,d31]) ).
cnf(d33,plain,
sk4 = sk4,
inference(resolution,[status(thm)],[d7,d32]) ).
cnf(d34,plain,
( ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| app(sk3,nil) != sk3 ),
inference(resolution,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
( ~ ssList(cons(sk5,nil))
| app(sk3,nil) != sk3 ),
inference(resolution,[status(thm)],[d21,d34]) ).
cnf(d36,plain,
( ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(cons(sk5,nil))
| app(sk3,X0) = app(sk6,app(cons(sk5,nil),X0)) ),
inference(superposition,[status(thm)],[d2,c161]) ).
cnf(d37,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| app(sk3,X0) = app(sk6,app(cons(sk5,nil),X0)) ),
inference(resolution,[status(thm)],[d7,d36]) ).
cnf(d38,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| app(sk3,nil) = app(sk6,cons(sk5,nil)) ),
inference(superposition,[status(thm)],[c85,d37]) ).
cnf(d39,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| app(sk3,nil) = sk3 ),
inference(demodulation,[status(thm)],[d38,d2]) ).
cnf(d40,plain,
( ~ ssList(cons(sk5,nil))
| app(sk3,nil) = sk3 ),
inference(resolution,[status(thm)],[c20,d39]) ).
cnf(d41,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| sk3 != sk3 ),
inference(superposition,[status(thm)],[d40,d35]) ).
cnf(d42,plain,
~ ssList(cons(sk5,nil)),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d42,d22]) ).
cnf(d44,plain,
$false,
inference(resolution,[status(thm)],[c20,d43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC419-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n008.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.06/0.41 % CPULimit : 300
% 0.06/0.41 % WCLimit : 300
% 0.06/0.41 % DateTime : Sat Sep 26 13:01:39 UTC 2026
% 0.06/0.41 % CPUTime :
% 0.06/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 94.58/29.56 % SZS status Unsatisfiable for theBenchmark.p
% 94.58/29.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------