%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:56:49 AM UTC 2026
% Result : Unsatisfiable 33.95s 10.31s
% Output : CNFRefutation 33.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 91 ( 19 unt; 0 def)
% Number of atoms : 231 ( 97 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 267 ( 127 ~; 140 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_52,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause116,axiom,
! [VAR_0,VAR_1] :
( singletonP(VAR_1)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,nil) != VAR_1 ),
file('theBenchmark.p',clause116) ).
cnf(c_139,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_200,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_203,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| ssItem(sk5(VAR_0))
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
( ~ memberP(sk2,A)
| ssItem(sk5(A))
| cons(A,nil) != sk1
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_10564,plain,
( ~ memberP(sk2,A)
| ssItem(sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_203,c_204]) ).
cnf(c_205,plain,
( ~ memberP(sk4,A)
| ssItem(sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_202,c_10564]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| memberP(sk2,sk5(VAR_0))
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_206,plain,
( ~ memberP(sk2,A)
| memberP(sk2,sk5(A))
| cons(A,nil) != sk1
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_10565,plain,
( ~ memberP(sk2,A)
| memberP(sk2,sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_203,c_206]) ).
cnf(c_10566,plain,
( ~ memberP(sk2,A)
| memberP(sk4,sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_202,c_10565]) ).
cnf(c_207,plain,
( ~ memberP(sk4,A)
| memberP(sk4,sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_202,c_10566]) ).
fof(co1_9,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| leq(VAR_0,sk5(VAR_0))
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_9) ).
cnf(c_208,plain,
( ~ memberP(sk2,A)
| leq(A,sk5(A))
| cons(A,nil) != sk1
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_10567,plain,
( ~ memberP(sk2,A)
| leq(A,sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_203,c_208]) ).
cnf(c_209,plain,
( ~ memberP(sk4,A)
| leq(A,sk5(A))
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_202,c_10567]) ).
fof(co1_10,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| VAR_0 != sk5(VAR_0)
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_10) ).
cnf(c_210,plain,
( ~ memberP(sk2,A)
| A != sk5(A)
| cons(A,nil) != sk1
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_10568,plain,
( ~ memberP(sk2,A)
| A != sk5(A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_203,c_210]) ).
cnf(c_10569,plain,
( ~ memberP(sk4,A)
| A != sk5(A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_202,c_10568]) ).
cnf(c_211,plain,
( ~ memberP(sk4,A)
| sk5(A) != A
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(copy,[status(thm)],[c_10569]) ).
fof(co1_11,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_11) ).
cnf(c_212,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_10570,plain,
( nil != sk1
| nil != sk4 ),
inference(paramod,[status(thm)],[c_202,c_212]) ).
cnf(c_10571,plain,
( nil != sk3
| nil != sk4 ),
inference(paramod,[status(thm)],[c_203,c_10570]) ).
cnf(c_10572,plain,
( nil != sk3
| sk4 != nil ),
inference(copy,[status(thm)],[c_10571]) ).
cnf(c_213,plain,
( sk3 != nil
| sk4 != nil ),
inference(copy,[status(thm)],[c_10572]) ).
fof(co1_12,axiom,
( nil = sk4
| ssItem(sk6) ),
file('theBenchmark.p',co1_12) ).
cnf(c_214,plain,
( nil = sk4
| ssItem(sk6) ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_215,plain,
( sk4 = nil
| ssItem(sk6) ),
inference(copy,[status(thm)],[c_214]) ).
fof(co1_13,axiom,
( nil = sk3
| ssItem(sk6) ),
file('theBenchmark.p',co1_13) ).
cnf(c_216,plain,
( nil = sk3
| ssItem(sk6) ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_217,plain,
( sk3 = nil
| ssItem(sk6) ),
inference(copy,[status(thm)],[c_216]) ).
fof(co1_14,axiom,
( nil = sk4
| cons(sk6,nil) = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_218,plain,
( nil = sk4
| cons(sk6,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_219,plain,
( sk4 = nil
| cons(sk6,nil) = sk3 ),
inference(copy,[status(thm)],[c_218]) ).
fof(co1_17,axiom,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('theBenchmark.p',co1_17) ).
cnf(c_224,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_225,plain,
( sk3 = nil
| cons(sk6,nil) = sk3 ),
inference(copy,[status(thm)],[c_224]) ).
fof(co1_18,axiom,
( nil = sk3
| memberP(sk4,sk6) ),
file('theBenchmark.p',co1_18) ).
cnf(c_226,plain,
( nil = sk3
| memberP(sk4,sk6) ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_227,plain,
( sk3 = nil
| memberP(sk4,sk6) ),
inference(copy,[status(thm)],[c_226]) ).
fof(co1_19,axiom,
! [VAR_0] :
( nil = sk3
| ~ leq(sk6,VAR_0)
| ~ memberP(sk4,VAR_0)
| sk6 = VAR_0
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_19) ).
cnf(c_228,plain,
( nil = sk3
| ~ leq(sk6,A)
| ~ memberP(sk4,A)
| sk6 = A
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_19]) ).
cnf(c_229,plain,
( sk3 = nil
| ~ leq(sk6,A)
| ~ memberP(sk4,A)
| sk6 = A
| ~ ssItem(A) ),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_7466,plain,
( sk3 != nil
| ssItem(sk6) ),
inference(resolve,[status(thm)],[c_215,c_213]) ).
cnf(c_10573,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk6)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_219,c_139]) ).
cnf(c_7612,plain,
( singletonP(sk3)
| ~ ssItem(sk6)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_200,c_10573]) ).
cnf(c_10574,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk6)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_225,c_139]) ).
cnf(c_7695,plain,
( singletonP(sk3)
| ~ ssItem(sk6)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_200,c_10574]) ).
cnf(c_10575,plain,
( ssItem(sk6)
| ssItem(sk6) ),
inference(resolve,[status(thm)],[c_7466,c_217]) ).
cnf(c_10147,plain,
ssItem(sk6),
inference(copy,[status(thm)],[c_10575]) ).
cnf(c_10227,plain,
( singletonP(sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_10147,c_7695]) ).
cnf(c_10253,plain,
( singletonP(sk3)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_10147,c_7612]) ).
cnf(c_10292,plain,
( ~ memberP(sk4,sk6)
| sk5(sk6) != sk6
| cons(sk6,nil) != sk3 ),
inference(resolve,[status(thm)],[c_10147,c_211]) ).
cnf(c_10293,plain,
( ~ memberP(sk4,sk6)
| leq(sk6,sk5(sk6))
| cons(sk6,nil) != sk3 ),
inference(resolve,[status(thm)],[c_10147,c_209]) ).
cnf(c_10294,plain,
( ~ memberP(sk4,sk6)
| memberP(sk4,sk5(sk6))
| cons(sk6,nil) != sk3 ),
inference(resolve,[status(thm)],[c_10147,c_207]) ).
cnf(c_10295,plain,
( ~ memberP(sk4,sk6)
| ssItem(sk5(sk6))
| cons(sk6,nil) != sk3 ),
inference(resolve,[status(thm)],[c_10147,c_205]) ).
cnf(c_10374,plain,
( sk4 != nil
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_10227,c_213]) ).
cnf(c_10576,plain,
( singletonP(sk3)
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_10374,c_10253]) ).
cnf(c_10409,plain,
singletonP(sk3),
inference(copy,[status(thm)],[c_10576]) ).
cnf(c_10577,plain,
( singletonP(nil)
| cons(sk6,nil) = sk3 ),
inference(paramod,[status(thm)],[c_225,c_10409]) ).
cnf(c_10411,plain,
cons(sk6,nil) = sk3,
inference(resolve,[status(thm)],[c_52,c_10577]) ).
cnf(c_10578,plain,
( singletonP(nil)
| memberP(sk4,sk6) ),
inference(paramod,[status(thm)],[c_227,c_10409]) ).
cnf(c_10412,plain,
memberP(sk4,sk6),
inference(resolve,[status(thm)],[c_52,c_10578]) ).
cnf(c_10579,plain,
( ~ memberP(sk4,sk6)
| ssItem(sk5(sk6))
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_10411,c_10295]) ).
cnf(c_10580,plain,
( ~ memberP(sk4,sk6)
| ssItem(sk5(sk6)) ),
inference(copy,[status(thm)],[c_10579]) ).
cnf(c_10417,plain,
ssItem(sk5(sk6)),
inference(resolve,[status(thm)],[c_10412,c_10580]) ).
cnf(c_10581,plain,
( ~ memberP(sk4,sk6)
| memberP(sk4,sk5(sk6))
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_10411,c_10294]) ).
cnf(c_10582,plain,
( ~ memberP(sk4,sk6)
| memberP(sk4,sk5(sk6)) ),
inference(copy,[status(thm)],[c_10581]) ).
cnf(c_10418,plain,
memberP(sk4,sk5(sk6)),
inference(resolve,[status(thm)],[c_10412,c_10582]) ).
cnf(c_10583,plain,
( ~ memberP(sk4,sk6)
| leq(sk6,sk5(sk6))
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_10411,c_10293]) ).
cnf(c_10584,plain,
( ~ memberP(sk4,sk6)
| leq(sk6,sk5(sk6)) ),
inference(copy,[status(thm)],[c_10583]) ).
cnf(c_10419,plain,
leq(sk6,sk5(sk6)),
inference(resolve,[status(thm)],[c_10412,c_10584]) ).
cnf(c_10585,plain,
( ~ memberP(sk4,sk6)
| sk5(sk6) != sk6
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_10411,c_10292]) ).
cnf(c_10586,plain,
( ~ memberP(sk4,sk6)
| sk5(sk6) != sk6 ),
inference(copy,[status(thm)],[c_10585]) ).
cnf(c_10420,plain,
sk5(sk6) != sk6,
inference(resolve,[status(thm)],[c_10412,c_10586]) ).
cnf(c_10587,plain,
( sk3 = nil
| ~ leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk5(sk6))
| sk6 = sk5(sk6) ),
inference(resolve,[status(thm)],[c_10417,c_229]) ).
cnf(c_10588,plain,
( sk3 = nil
| ~ leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk5(sk6))
| sk5(sk6) = sk6 ),
inference(copy,[status(thm)],[c_10587]) ).
cnf(c_10589,plain,
( sk3 = nil
| ~ leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk5(sk6)) ),
inference(resolve,[status(thm)],[c_10420,c_10588]) ).
cnf(c_10590,plain,
( sk3 = nil
| ~ leq(sk6,sk5(sk6)) ),
inference(resolve,[status(thm)],[c_10418,c_10589]) ).
cnf(c_10479,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_10419,c_10590]) ).
cnf(c_10591,plain,
singletonP(nil),
inference(paramod,[status(thm)],[c_10479,c_10409]) ).
cnf(c_10563,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_10591]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.42 % Computer : n017.cluster.edu
% 0.17/5.42 % Model : x86_64 x86_64
% 0.17/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.42 % Memory : 8046.5625MB
% 0.17/5.42 % OS : Linux 6.8.0-71-generic
% 0.17/5.42 % CPULimit : 300
% 0.17/5.42 % WCLimit : 300
% 0.17/5.42 % DateTime : Sat Sep 26 12:10:25 UTC 2026
% 0.17/5.42 % CPUTime :
% 0.17/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.42 % Process 674672 was started by sandbox2 on n017,
% 0.17/5.42 % Sat Sep 26 12:10:25 2026
% 0.17/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.43
% 0.17/5.43 % From the command line: assign(max_seconds, 300).
% 33.95/10.31
% 33.95/10.31 % given #500 (I,wt=45): 567 app(A,cons(B,cons(C,A))) != A | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C | app(skaf80(A),cons(skaf78(A),cons(skaf79(A),skaf81(A)))) = A. [factor(379,b,e)].
% 33.95/10.31
% 33.95/10.31 % SZS status Unsatisfiable for theBenchmark
% 33.95/10.31
% 33.95/10.31 % Proof 1 at 3.75 (+ 1.07) seconds.
% 33.95/10.31 % Length of proof is 47.
% 33.95/10.31 % Level of proof is 10.
% 33.95/10.31 % Maximum clause weight is 18.000.
% 33.95/10.31 % Given clauses 869.
% 33.95/10.31
% 33.95/10.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------