%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC029-1 : 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 08:54:00 AM UTC 2026
% Result : Unsatisfiable 40.80s 9.60s
% Output : CNFRefutation 40.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 20
% Syntax : Number of clauses : 103 ( 18 unt; 27 nHn; 101 RR)
% Number of literals : 274 ( 113 equ; 150 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 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 : 36 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
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,
( 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,
( nil = sk1
| nil = sk2 ) ).
cnf(co1_15,negated_conjecture,
( nil != sk2
| nil != sk1 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause47,axiom,
ssItem(skaf44(X0)) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ 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(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause101,axiom,
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ) ).
cnf(clause116,axiom,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ) ).
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(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,
( 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,
( nil = sk1
| nil = sk2 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c14,plain,
( nil != sk2
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c22,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c61,plain,
ssItem(skaf44(X0)),
inference(clausification,[status(esa)],[clause47]) ).
cnf(c88,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c100,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c110,plain,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause96]) ).
cnf(c114,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c115,plain,
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(clausification,[status(esa)],[clause101]) ).
cnf(c130,plain,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(clausification,[status(esa)],[clause116]) ).
cnf(c132,plain,
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause118]) ).
cnf(c134,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(d0,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(equality_resolution,[status(thm)],[c130]) ).
cnf(d1,plain,
( ~ ssItem(X0)
| ~ ssList(nil)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d0,c100]) ).
cnf(d2,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c22,d1]) ).
cnf(d3,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ neq(sk4,nil)
| cons(sk5,sk6) = sk4 ),
inference(superposition,[status(thm)],[c134,c9]) ).
cnf(d4,plain,
( nil != sk4
| nil != sk1 ),
inference(demodulation,[status(thm)],[c14,c4]) ).
cnf(d5,plain,
( nil != sk4
| nil = sk1 ),
inference(demodulation,[status(thm)],[c6,c5]) ).
cnf(d6,plain,
( nil = sk4
| nil = sk1 ),
inference(demodulation,[status(thm)],[c11,c4]) ).
cnf(d7,plain,
( nil = sk1
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
nil = sk1,
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
nil != sk4,
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(sk4)
| sk4 = nil ),
inference(resolution,[status(thm)],[c114,c7]) ).
cnf(d11,plain,
( ssItem(sk5)
| ~ ssList(nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d10]) ).
cnf(d12,plain,
( ssItem(sk5)
| sk4 = nil ),
inference(resolution,[status(thm)],[c22,d11]) ).
cnf(d13,plain,
( ssItem(sk5)
| nil != nil ),
inference(superposition,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
ssItem(sk5),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( ~ neq(sk4,nil)
| ~ ssList(sk6)
| cons(sk5,sk6) = sk4 ),
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
( ssList(sk6)
| ~ ssList(nil)
| ~ ssList(sk4)
| sk4 = nil ),
inference(resolution,[status(thm)],[c114,c8]) ).
cnf(d17,plain,
( ssList(sk6)
| ~ ssList(nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d16]) ).
cnf(d18,plain,
( ssList(sk6)
| sk4 = nil ),
inference(resolution,[status(thm)],[c22,d17]) ).
cnf(d19,plain,
( ssList(sk6)
| nil != nil ),
inference(superposition,[status(thm)],[d18,d9]) ).
cnf(d20,plain,
ssList(sk6),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
( ~ neq(sk4,nil)
| cons(sk5,sk6) = sk4 ),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d23,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = nil ),
inference(demodulation,[status(thm)],[d22,d8]) ).
cnf(d24,plain,
( ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| nil = sk6
| nil != nil ),
inference(superposition,[status(thm)],[d23,c132]) ).
cnf(d25,plain,
( ~ neq(sk4,nil)
| ~ ssList(cons(sk5,nil))
| nil = sk6
| nil != nil ),
inference(resolution,[status(thm)],[d20,d24]) ).
cnf(d26,plain,
( ~ neq(sk4,nil)
| ~ ssList(cons(sk5,nil))
| nil = sk6 ),
inference(equality_resolution,[status(thm)],[d25]) ).
cnf(d27,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ neq(sk4,nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[d26,c100]) ).
cnf(d28,plain,
( ~ ssItem(sk5)
| ~ neq(sk4,nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[c22,d27]) ).
cnf(d29,plain,
( ~ neq(sk4,nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[d14,d28]) ).
cnf(d30,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| sk4 = nil
| nil = sk6 ),
inference(resolution,[status(thm)],[d29,c114]) ).
cnf(d31,plain,
( ~ ssList(nil)
| nil = sk6
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d30]) ).
cnf(d32,plain,
( nil = sk6
| sk4 = nil ),
inference(resolution,[status(thm)],[c22,d31]) ).
cnf(d33,plain,
( sk4 = nil
| ~ neq(sk4,nil)
| cons(sk5,nil) = sk4 ),
inference(superposition,[status(thm)],[d32,d21]) ).
cnf(d34,plain,
( ~ neq(sk4,nil)
| sk4 = nil
| ~ ssItem(sk5)
| singletonP(sk4) ),
inference(superposition,[status(thm)],[d33,d2]) ).
cnf(d35,plain,
( singletonP(sk4)
| ~ neq(sk4,nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[d14,d34]) ).
cnf(d36,plain,
( ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| tl(sk4) = sk6 ),
inference(superposition,[status(thm)],[d21,c110]) ).
cnf(d37,plain,
( ~ neq(sk4,nil)
| ~ ssList(sk6)
| tl(sk4) = sk6 ),
inference(resolution,[status(thm)],[d14,d36]) ).
cnf(d38,plain,
( ~ neq(sk4,nil)
| tl(sk4) = sk6 ),
inference(resolution,[status(thm)],[d20,d37]) ).
cnf(d39,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| ~ ssItem(skaf44(X0))
| ~ ssList(nil)
| tl(X0) = nil ),
inference(superposition,[status(thm)],[c115,c110]) ).
cnf(d40,plain,
( ~ singletonP(X0)
| ~ ssItem(skaf44(X0))
| ~ ssList(X0)
| tl(X0) = nil ),
inference(resolution,[status(thm)],[c22,d39]) ).
cnf(d41,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| tl(X0) = nil ),
inference(resolution,[status(thm)],[c61,d40]) ).
cnf(d42,plain,
( ~ singletonP(sk4)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| nil = sk6 ),
inference(superposition,[status(thm)],[d41,d38]) ).
cnf(d43,plain,
( ~ singletonP(sk4)
| ~ neq(sk4,nil)
| nil = sk6 ),
inference(resolution,[status(thm)],[c3,d42]) ).
cnf(d44,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| sk4 = nil
| ~ singletonP(sk4)
| nil = sk6 ),
inference(resolution,[status(thm)],[d43,c114]) ).
cnf(d45,plain,
( ~ singletonP(sk4)
| ~ ssList(nil)
| nil = sk6
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d44]) ).
cnf(d46,plain,
( ~ singletonP(sk4)
| nil = sk6
| sk4 = nil ),
inference(resolution,[status(thm)],[c22,d45]) ).
cnf(d47,plain,
( ~ singletonP(sk4)
| sk4 = nil
| ~ neq(sk4,nil)
| cons(sk5,nil) = sk4 ),
inference(superposition,[status(thm)],[d46,d21]) ).
cnf(d48,plain,
( ~ singletonP(sk4)
| ~ neq(sk4,nil)
| sk4 = nil
| ~ neq(sk4,nil)
| app(sk6,sk4) = nil ),
inference(superposition,[status(thm)],[d47,d23]) ).
cnf(d49,plain,
( ~ singletonP(sk4)
| sk4 = nil
| ~ singletonP(sk4)
| ~ neq(sk4,nil)
| sk4 = nil
| app(nil,sk4) = nil ),
inference(superposition,[status(thm)],[d46,d48]) ).
cnf(d50,plain,
( ~ ssList(sk4)
| ~ singletonP(sk4)
| ~ neq(sk4,nil)
| sk4 = nil
| sk4 = nil ),
inference(superposition,[status(thm)],[c88,d49]) ).
cnf(d51,plain,
( ~ singletonP(sk4)
| ~ neq(sk4,nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d50]) ).
cnf(d52,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| sk4 = nil
| ~ singletonP(sk4)
| sk4 = nil ),
inference(resolution,[status(thm)],[d51,c114]) ).
cnf(d53,plain,
( ~ singletonP(sk4)
| ~ ssList(nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d52]) ).
cnf(d54,plain,
( ~ singletonP(sk4)
| sk4 = nil ),
inference(resolution,[status(thm)],[c22,d53]) ).
cnf(d55,plain,
( ~ singletonP(sk4)
| nil != nil ),
inference(superposition,[status(thm)],[d54,d9]) ).
cnf(d56,plain,
~ singletonP(sk4),
inference(equality_resolution,[status(thm)],[d55]) ).
cnf(d57,plain,
( ~ neq(sk4,nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[d56,d35]) ).
cnf(d58,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| sk4 = nil
| sk4 = nil ),
inference(resolution,[status(thm)],[d57,c114]) ).
cnf(d59,plain,
( ~ ssList(nil)
| sk4 = nil ),
inference(resolution,[status(thm)],[c3,d58]) ).
cnf(d60,plain,
sk4 = nil,
inference(resolution,[status(thm)],[c22,d59]) ).
cnf(d61,plain,
nil != nil,
inference(demodulation,[status(thm)],[d9,d60]) ).
cnf(d62,plain,
$false,
inference(equality_resolution,[status(thm)],[d61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC029-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n010.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 12:06:30 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.80/9.60 % SZS status Unsatisfiable for theBenchmark.p
% 40.80/9.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------