%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC316-1 : 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 : 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 08:54:57 AM UTC 2026
% Result : Unsatisfiable 112.90s 27.15s
% Output : CNFRefutation 113.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 20
% Syntax : Number of clauses : 106 ( 25 unt; 9 nHn; 92 RR)
% Number of literals : 337 ( 104 equ; 253 neg)
% Maximal clause size : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 101 ( 11 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_14,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ) ).
cnf(co1_15,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ) ).
cnf(co1_16,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ) ).
cnf(co1_17,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ) ).
cnf(co1_18,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| hd(sk1) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sk1) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause72,axiom,
( ssItem(X1)
| duplicatefreeP(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(clause96,axiom,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause97,axiom,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause98,axiom,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ) ).
cnf(clause102,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ).
cnf(clause120,axiom,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(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(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(c13,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c14,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c15,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c16,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(clausification,[status(esa)],[co1_17]) ).
cnf(c17,plain,
( app(X1,X3) != X0
| ~ ssList(X3)
| ~ ssItem(X2)
| cons(X2,nil) != X3
| tl(sk1) != X1
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| sk2 != X0
| ~ neq(sk4,nil)
| hd(sk1) != X2
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_18]) ).
cnf(c25,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c89,plain,
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause72]) ).
cnf(c102,plain,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause85]) ).
cnf(c103,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c113,plain,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause96]) ).
cnf(c114,plain,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause97]) ).
cnf(c115,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause98]) ).
cnf(c119,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause102]) ).
cnf(c137,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(c196,plain,
( ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X2,cons(X3,X4)),cons(X3,X0)) != X1
| ~ duplicatefreeP(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause179]) ).
cnf(d0,plain,
( duplicatefreeP(app(X1,X0))
| ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c102,c89]) ).
cnf(d1,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(demodulation,[status(thm)],[c16,c4]) ).
cnf(d2,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(demodulation,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
app(sk6,cons(sk5,nil)) = sk2,
inference(resolution,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk2,cons(sk5,X0)) != X1 ),
inference(superposition,[status(thm)],[d3,c196]) ).
cnf(d5,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk2,cons(sk5,X0)) != X1 ),
inference(resolution,[status(thm)],[c25,d4]) ).
cnf(d6,plain,
( ssItem(sk5)
| ~ neq(sk2,nil) ),
inference(demodulation,[status(thm)],[c13,c4]) ).
cnf(d7,plain,
ssItem(sk5),
inference(resolution,[status(thm)],[c6,d6]) ).
cnf(d8,plain,
( ~ duplicatefreeP(X1)
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk2,cons(sk5,X0)) != X1 ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(demodulation,[status(thm)],[c14,c4]) ).
cnf(d10,plain,
ssList(sk6),
inference(resolution,[status(thm)],[c6,d9]) ).
cnf(d11,plain,
( ~ duplicatefreeP(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk2,cons(sk5,X0)) != X1 ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk1 ),
inference(demodulation,[status(thm)],[c15,c5]) ).
cnf(d13,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) = sk1 ),
inference(demodulation,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
app(cons(sk5,nil),sk6) = sk1,
inference(resolution,[status(thm)],[c6,d13]) ).
cnf(d15,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| cons(sk5,sk6) = sk1 ),
inference(superposition,[status(thm)],[c137,d14]) ).
cnf(d16,plain,
( ~ ssList(sk6)
| cons(sk5,sk6) = sk1 ),
inference(resolution,[status(thm)],[d7,d15]) ).
cnf(d17,plain,
cons(sk5,sk6) = sk1,
inference(resolution,[status(thm)],[d10,d16]) ).
cnf(d18,plain,
( ~ duplicatefreeP(X0)
| ~ ssList(sk6)
| ~ ssList(X0)
| app(sk2,sk1) != X0 ),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
( ~ duplicatefreeP(X0)
| ~ ssList(X0)
| app(sk2,sk1) != X0 ),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
( ~ duplicatefreeP(app(sk2,sk1))
| ~ ssList(app(sk2,sk1)) ),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
( ssItem(X0)
| ~ ssList(sk1)
| ~ ssList(sk2)
| ~ ssList(app(sk2,sk1)) ),
inference(resolution,[status(thm)],[d20,d0]) ).
cnf(d22,plain,
( ssItem(X0)
| ~ ssList(app(sk2,sk1))
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c0,d21]) ).
cnf(d23,plain,
( ssItem(X0)
| ~ ssList(app(sk2,sk1)) ),
inference(resolution,[status(thm)],[c1,d22]) ).
cnf(d24,plain,
( ~ ssList(sk2)
| ~ ssList(sk1)
| ssItem(X0) ),
inference(resolution,[status(thm)],[d23,c102]) ).
cnf(d25,plain,
( ssItem(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c0,d24]) ).
cnf(d26,plain,
ssItem(X0),
inference(resolution,[status(thm)],[c1,d25]) ).
cnf(d27,plain,
( ~ ssItem(X0)
| neq(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d26,c119]) ).
cnf(d28,plain,
( neq(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d26,d27]) ).
cnf(d29,plain,
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[d26,c103]) ).
cnf(d30,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| hd(sk1) = sk5 ),
inference(superposition,[status(thm)],[d17,c114]) ).
cnf(d31,plain,
( ~ ssList(sk6)
| hd(sk1) = sk5 ),
inference(resolution,[status(thm)],[d7,d30]) ).
cnf(d32,plain,
hd(sk1) = sk5,
inference(resolution,[status(thm)],[d10,d31]) ).
cnf(d33,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| tl(sk1) = sk6 ),
inference(superposition,[status(thm)],[d17,c113]) ).
cnf(d34,plain,
( ~ ssList(sk6)
| tl(sk1) = sk6 ),
inference(resolution,[status(thm)],[d7,d33]) ).
cnf(d35,plain,
tl(sk1) = sk6,
inference(resolution,[status(thm)],[d10,d34]) ).
cnf(d36,plain,
( ~ ssItem(X3)
| ~ neq(nil,sk1)
| ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| hd(sk1) != X3
| tl(sk1) != X1
| cons(X3,nil) != X2
| app(X1,X2) != X0
| sk2 != X0 ),
inference(demodulation,[status(thm)],[c17,c4]) ).
cnf(d37,plain,
( ~ ssItem(X3)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| hd(sk1) != X3
| tl(sk1) != X1
| cons(X3,nil) != X2
| app(X1,X2) != X0
| sk2 != X0 ),
inference(resolution,[status(thm)],[c6,d36]) ).
cnf(d38,plain,
( ~ ssItem(X2)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil))
| hd(sk1) != X2
| tl(sk1) != X1
| app(X1,cons(X2,nil)) != X0
| sk2 != X0 ),
inference(equality_resolution,[status(thm)],[d37]) ).
cnf(d39,plain,
( ~ ssItem(X2)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(X2,nil))
| ~ ssList(X0)
| ~ ssList(X1)
| hd(sk1) != X2
| sk6 != X1
| app(X1,cons(X2,nil)) != X0
| sk2 != X0 ),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
( ~ ssItem(X2)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(X2,nil))
| ~ ssList(X0)
| ~ ssList(X1)
| sk5 != X2
| sk6 != X1
| app(X1,cons(X2,nil)) != X0
| sk2 != X0 ),
inference(demodulation,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
( ~ ssItem(sk5)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| ~ ssList(sk6)
| sk5 != sk5
| sk6 != sk6
| sk2 != X0
| sk2 != X0 ),
inference(superposition,[status(thm)],[d3,d40]) ).
cnf(d42,plain,
( ~ ssItem(sk5)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk6 != sk6
| sk5 != sk5
| sk2 != X0 ),
inference(resolution,[status(thm)],[d10,d41]) ).
cnf(d43,plain,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk6 != sk6
| sk5 != sk5
| sk2 != X0 ),
inference(resolution,[status(thm)],[d26,d42]) ).
cnf(d44,plain,
( ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[d26,c113]) ).
cnf(d45,plain,
( ~ ssList(sk6)
| tl(sk1) = sk6 ),
inference(superposition,[status(thm)],[d17,d44]) ).
cnf(d46,plain,
( ~ ssList(sk6)
| sk6 = sk6 ),
inference(demodulation,[status(thm)],[d45,d35]) ).
cnf(d47,plain,
sk6 = sk6,
inference(resolution,[status(thm)],[d10,d46]) ).
cnf(d48,plain,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk5 != sk5
| sk2 != X0 ),
inference(resolution,[status(thm)],[d47,d43]) ).
cnf(d49,plain,
( ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
inference(resolution,[status(thm)],[d26,c114]) ).
cnf(d50,plain,
( ~ ssList(sk6)
| hd(sk1) = sk5 ),
inference(superposition,[status(thm)],[d17,d49]) ).
cnf(d51,plain,
( ~ ssList(sk6)
| sk5 = sk5 ),
inference(demodulation,[status(thm)],[d50,d32]) ).
cnf(d52,plain,
sk5 = sk5,
inference(resolution,[status(thm)],[d10,d51]) ).
cnf(d53,plain,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| sk2 != X0 ),
inference(resolution,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk2) ),
inference(equality_resolution,[status(thm)],[d53]) ).
cnf(d55,plain,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c1,d54]) ).
cnf(d56,plain,
( ~ ssList(nil)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil) ),
inference(resolution,[status(thm)],[d55,d29]) ).
cnf(d57,plain,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil) ),
inference(resolution,[status(thm)],[c25,d56]) ).
cnf(d58,plain,
( nil = sk1
| ~ neq(sk1,nil) ),
inference(resolution,[status(thm)],[d57,d28]) ).
cnf(d59,plain,
( sk1 = nil
| nil = sk1 ),
inference(resolution,[status(thm)],[d58,d28]) ).
cnf(d60,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| sk1 != nil ),
inference(superposition,[status(thm)],[d17,c115]) ).
cnf(d61,plain,
( ~ ssList(sk6)
| sk1 != nil ),
inference(resolution,[status(thm)],[d7,d60]) ).
cnf(d62,plain,
sk1 != nil,
inference(resolution,[status(thm)],[d10,d61]) ).
cnf(d63,plain,
nil = sk1,
inference(resolution,[status(thm)],[d62,d59]) ).
cnf(d64,plain,
nil != nil,
inference(demodulation,[status(thm)],[d62,d63]) ).
cnf(d65,plain,
$false,
inference(equality_resolution,[status(thm)],[d64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC316-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 12:47:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 112.90/27.15 % SZS status Unsatisfiable for theBenchmark.p
% 112.90/27.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------