%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC204-1 : 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 : n005.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 08:54:36 AM UTC 2026
% Result : Unsatisfiable 156.39s 26.38s
% Output : CNFRefutation 156.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of clauses : 87 ( 22 unt; 13 nHn; 83 RR)
% Number of literals : 263 ( 85 equ; 169 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_1,negated_conjecture,
ssList(sk1) ).
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)
| neq(sk2,nil) ) ).
cnf(co1_11,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ) ).
cnf(co1_12,negated_conjecture,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause12,axiom,
ssItem(skaf83(X0)) ).
cnf(clause13,axiom,
ssList(skaf82(X0)) ).
cnf(clause73,axiom,
( app(X0,nil) = X0
| ~ ssList(X0) ) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ ssList(X0) ) ).
cnf(clause75,axiom,
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ) ).
cnf(clause85,axiom,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause96,axiom,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause99,axiom,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ) ).
cnf(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause109,axiom,
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ) ).
cnf(clause149,axiom,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(c0,plain,
ssList(sk1),
inference(clausification,[status(esa)],[co1_1]) ).
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(c10,plain,
( ~ neq(nil,sk4)
| ~ ssList(X1)
| sk4 = X0
| app(sk3,X1) != X0
| ~ neq(sk4,nil)
| tl(sk4) != X1
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c19,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c23,plain,
ssItem(skaf83(X0)),
inference(clausification,[status(esa)],[clause12]) ).
cnf(c24,plain,
ssList(skaf82(X0)),
inference(clausification,[status(esa)],[clause13]) ).
cnf(c84,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause73]) ).
cnf(c85,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c86,plain,
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause75]) ).
cnf(c96,plain,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause85]) ).
cnf(c107,plain,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause96]) ).
cnf(c110,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(clausification,[status(esa)],[clause99]) ).
cnf(c111,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c120,plain,
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause109]) ).
cnf(c160,plain,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause149]) ).
cnf(d0,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssItem(skaf83(X0))
| ~ ssList(skaf82(X0))
| X0 != skaf82(X0) ),
inference(superposition,[status(thm)],[c120,c110]) ).
cnf(d1,plain,
( ~ ssList(skaf82(X0))
| ~ ssList(X0)
| nil = X0
| X0 != skaf82(X0) ),
inference(resolution,[status(thm)],[c23,d0]) ).
cnf(d2,plain,
( ~ ssList(X0)
| nil = X0
| X0 != skaf82(X0) ),
inference(resolution,[status(thm)],[c24,d1]) ).
cnf(d3,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssItem(skaf83(X0))
| ~ ssList(skaf82(X0))
| tl(X0) = skaf82(X0) ),
inference(superposition,[status(thm)],[c120,c107]) ).
cnf(d4,plain,
( ~ ssList(skaf82(X0))
| ~ ssList(X0)
| tl(X0) = skaf82(X0)
| nil = X0 ),
inference(resolution,[status(thm)],[c23,d3]) ).
cnf(d5,plain,
( ~ ssList(X0)
| tl(X0) = skaf82(X0)
| nil = X0 ),
inference(resolution,[status(thm)],[c24,d4]) ).
cnf(d6,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(X0)
| nil = X0
| X0 != tl(X0) ),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| app(X0,X1) = app(nil,app(X0,X1)) ),
inference(superposition,[status(thm)],[c85,c160]) ).
cnf(d8,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) = app(nil,app(X0,X1)) ),
inference(resolution,[status(thm)],[c19,d7]) ).
cnf(d9,plain,
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) = app(X0,app(nil,X1)) ),
inference(superposition,[status(thm)],[c84,c160]) ).
cnf(d10,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) = app(X0,app(nil,X1)) ),
inference(resolution,[status(thm)],[c19,d9]) ).
cnf(d11,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(nil,X1))
| app(X0,app(nil,X1)) = app(nil,app(X0,X1)) ),
inference(superposition,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ ssList(app(nil,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(nil,X1))
| ssList(app(nil,app(X0,X1))) ),
inference(superposition,[status(thm)],[d11,c96]) ).
cnf(d13,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| app(X0,nil) = app(nil,X0) ),
inference(superposition,[status(thm)],[c84,d8]) ).
cnf(d14,plain,
( ~ ssList(X0)
| app(X0,nil) = app(nil,X0) ),
inference(resolution,[status(thm)],[c19,d13]) ).
cnf(d15,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| app(X0,nil) = app(nil,app(nil,X0)) ),
inference(superposition,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( ~ ssList(X0)
| app(X0,nil) = app(nil,app(nil,X0)) ),
inference(resolution,[status(thm)],[c19,d15]) ).
cnf(d17,plain,
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0)
| app(nil,X0) = app(X0,nil) ),
inference(superposition,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
( ~ ssList(X0)
| app(nil,X0) = app(X0,nil) ),
inference(resolution,[status(thm)],[c19,d17]) ).
cnf(d19,plain,
( ~ ssList(X0)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ssList(app(nil,app(X0,nil))) ),
inference(superposition,[status(thm)],[d18,d12]) ).
cnf(d20,plain,
( ssList(app(nil,app(X0,nil)))
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c19,d19]) ).
cnf(d21,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| app(X0,nil) = app(nil,app(X0,nil)) ),
inference(superposition,[status(thm)],[d14,d16]) ).
cnf(d22,plain,
( ~ ssList(X0)
| ~ ssList(app(nil,X0))
| ~ ssList(X0)
| ssList(app(X0,nil)) ),
inference(superposition,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( ~ ssList(X0)
| ssList(app(X0,nil))
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c85,d22]) ).
cnf(d24,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ssList(app(nil,X0)) ),
inference(superposition,[status(thm)],[d14,d23]) ).
cnf(d25,plain,
neq(sk4,nil),
inference(demodulation,[status(thm)],[c6,c4]) ).
cnf(d26,plain,
~ neq(sk1,nil),
inference(resolution,[status(thm)],[d25,c11]) ).
cnf(d27,plain,
( ~ ssList(sk1)
| ~ ssList(nil)
| sk1 = nil ),
inference(resolution,[status(thm)],[c111,d26]) ).
cnf(d28,plain,
( ~ ssList(nil)
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d27]) ).
cnf(d29,plain,
sk1 = nil,
inference(resolution,[status(thm)],[c19,d28]) ).
cnf(d30,plain,
( ~ neq(nil,sk4)
| ~ neq(sk4,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| app(sk1,X1) != X0
| tl(sk4) != X1
| sk4 = X0 ),
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d31,plain,
( ~ neq(nil,sk4)
| ~ ssList(X1)
| ~ ssList(X0)
| app(sk1,X1) != X0
| tl(sk4) != X1
| sk4 = X0 ),
inference(resolution,[status(thm)],[d25,d30]) ).
cnf(d32,plain,
( ~ neq(nil,sk4)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0)
| tl(sk4) != X0
| sk4 = app(sk1,X0) ),
inference(equality_resolution,[status(thm)],[d31]) ).
cnf(d33,plain,
( ~ neq(nil,sk4)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0)
| tl(sk4) != X0
| sk4 = app(nil,X0) ),
inference(demodulation,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
( ~ neq(nil,sk4)
| ~ ssList(app(nil,X0))
| ~ ssList(X0)
| tl(sk4) != X0
| sk4 = app(nil,X0) ),
inference(demodulation,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
( ~ neq(nil,sk4)
| ~ ssList(app(nil,tl(sk4)))
| ~ ssList(tl(sk4))
| sk4 = app(nil,tl(sk4)) ),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
( ~ neq(nil,sk4)
| ~ ssList(app(nil,tl(sk4)))
| ~ ssList(tl(sk4))
| ~ ssList(tl(sk4))
| sk4 = tl(sk4) ),
inference(superposition,[status(thm)],[d35,c85]) ).
cnf(d37,plain,
( ~ ssList(tl(sk4))
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| sk4 = tl(sk4) ),
inference(resolution,[status(thm)],[d36,d24]) ).
cnf(d38,plain,
( ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ~ ssList(sk4)
| nil = sk4
| sk4 != sk4 ),
inference(superposition,[status(thm)],[d37,d6]) ).
cnf(d39,plain,
( ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| nil = sk4
| sk4 != sk4 ),
inference(resolution,[status(thm)],[c3,d38]) ).
cnf(d40,plain,
( ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| nil = sk4 ),
inference(equality_resolution,[status(thm)],[d39]) ).
cnf(d41,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil = sk4
| ~ ssList(tl(sk4))
| nil = sk4 ),
inference(resolution,[status(thm)],[d40,c111]) ).
cnf(d42,plain,
( ~ ssList(tl(sk4))
| ~ ssList(nil)
| nil = sk4 ),
inference(resolution,[status(thm)],[c3,d41]) ).
cnf(d43,plain,
( ~ ssList(tl(sk4))
| nil = sk4 ),
inference(resolution,[status(thm)],[c19,d42]) ).
cnf(d44,plain,
( ~ ssList(sk4)
| nil = sk4
| nil = sk4 ),
inference(resolution,[status(thm)],[d43,c86]) ).
cnf(d45,plain,
nil = sk4,
inference(resolution,[status(thm)],[c3,d44]) ).
cnf(d46,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[d25,d45]) ).
cnf(d47,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm)],[d26,d29]) ).
cnf(d48,plain,
$false,
inference(resolution,[status(thm)],[d47,d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC204-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n005.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 12:30:32 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 156.39/26.38 % SZS status Unsatisfiable for theBenchmark.p
% 156.39/26.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------