%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC392-1 : 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 : 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 08:57:41 AM UTC 2026
% Result : Unsatisfiable 42.67s 6.60s
% Output : CNFRefutation 42.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 75 ( 30 unt; 0 def)
% Number of atoms : 191 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 221 ( 105 ~; 116 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 72 ( 13 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause179,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ ssList(VAR_4)
| ~ duplicatefreeP(VAR_4)
| ~ ssItem(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_3)
| app(app(VAR_0,cons(VAR_1,VAR_2)),cons(VAR_1,VAR_3)) != VAR_4 ),
file('theBenchmark.p',clause179) ).
cnf(c_7,plain,
( ~ ssList(E)
| ~ duplicatefreeP(E)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ ssList(D)
| app(app(A,cons(B,C)),cons(B,D)) != E ),
inference(clausify,[status(thm)],[clause179]) ).
fof(clause72,axiom,
! [VAR_0,VAR_1] :
( ssItem(VAR_1)
| duplicatefreeP(VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause72) ).
cnf(c_8,plain,
( ssItem(B)
| duplicatefreeP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause72]) ).
cnf(c_43,plain,
( ~ ssList(A)
| ~ ssItem(D)
| ~ ssList(C)
| ~ ssList(E)
| ~ ssList(F)
| app(app(C,cons(D,E)),cons(D,F)) != A
| ssItem(B)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_44,plain,
( ~ ssItem(D)
| ~ ssList(C)
| ~ ssList(E)
| ~ ssList(F)
| app(app(C,cons(D,E)),cons(D,F)) != A
| ssItem(B)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_43]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_49,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause71,axiom,
! [VAR_0] :
( ~ ssItem(VAR_0)
| ~ memberP(nil,VAR_0) ),
file('theBenchmark.p',clause71) ).
cnf(c_107,plain,
( ~ ssItem(A)
| ~ memberP(nil,A) ),
inference(clausify,[status(thm)],[clause71]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_109,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause85,axiom,
! [VAR_0,VAR_1] :
( ssList(app(VAR_1,VAR_0))
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause85) ).
cnf(c_118,plain,
( ssList(app(B,A))
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause85]) ).
fof(clause98,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause98) ).
cnf(c_124,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != nil ),
inference(clausify,[status(thm)],[clause98]) ).
fof(clause161,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_0
| memberP(VAR_1,VAR_2)
| ~ ssItem(VAR_2)
| ~ ssItem(VAR_0)
| ~ ssList(VAR_1)
| ~ memberP(cons(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',clause161) ).
cnf(c_182,plain,
( C = A
| memberP(B,C)
| ~ ssItem(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(cons(A,B),C) ),
inference(clausify,[status(thm)],[clause161]) ).
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,
ssItem(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
ssItem(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
memberP(sk1,sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_205,plain,
memberP(sk1,sk5),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_206,plain,
memberP(sk3,sk5),
inference(paramod,[status(thm)],[c_203,c_205]) ).
fof(co1_9,axiom,
~ memberP(sk2,sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_207,plain,
~ memberP(sk2,sk5),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_208,plain,
~ memberP(sk4,sk5),
inference(paramod,[status(thm)],[c_202,c_207]) ).
fof(co1_11,axiom,
( nil = sk3
| ssItem(sk6) ),
file('theBenchmark.p',co1_11) ).
cnf(c_211,plain,
( nil = sk3
| ssItem(sk6) ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_212,plain,
( sk3 = nil
| ssItem(sk6) ),
inference(copy,[status(thm)],[c_211]) ).
fof(co1_15,axiom,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('theBenchmark.p',co1_15) ).
cnf(c_219,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_220,plain,
( sk3 = nil
| cons(sk6,nil) = sk3 ),
inference(copy,[status(thm)],[c_219]) ).
fof(co1_16,axiom,
( nil = sk3
| memberP(sk4,sk6) ),
file('theBenchmark.p',co1_16) ).
cnf(c_221,plain,
( nil = sk3
| memberP(sk4,sk6) ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_222,plain,
( sk3 = nil
| memberP(sk4,sk6) ),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_309,plain,
( ssList(app(A,A))
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_118]) ).
cnf(c_825,plain,
( ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ ssList(D)
| ssItem(E)
| ~ ssList(app(app(A,cons(B,C)),cons(B,D))) ),
inference(xxres,[status(thm)],[c_44]) ).
cnf(c_826,plain,
( ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ssItem(D)
| ~ ssList(app(app(A,cons(B,C)),cons(B,C))) ),
inference(factor,[status(thm)],[c_825]) ).
cnf(c_829,plain,
( ~ ssItem(B)
| ~ ssList(A)
| ssItem(C)
| ~ ssList(app(app(A,cons(B,A)),cons(B,A))) ),
inference(factor,[status(thm)],[c_826]) ).
cnf(c_1657,plain,
( ~ ssItem(A)
| cons(A,nil) != nil ),
inference(resolve,[status(thm)],[c_124,c_49]) ).
cnf(c_7078,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_200,c_109]) ).
cnf(c_7383,plain,
~ memberP(nil,sk5),
inference(resolve,[status(thm)],[c_204,c_107]) ).
cnf(c_16723,plain,
( memberP(nil,sk5)
| ssItem(sk6) ),
inference(paramod,[status(thm)],[c_212,c_206]) ).
cnf(c_7600,plain,
ssItem(sk6),
inference(resolve,[status(thm)],[c_7383,c_16723]) ).
cnf(c_16724,plain,
( A = sk6
| memberP(nil,A)
| ~ ssItem(A)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(paramod,[status(thm)],[c_220,c_182]) ).
cnf(c_16725,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(copy,[status(thm)],[c_16724]) ).
cnf(c_16726,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ ssItem(sk6)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_49,c_16725]) ).
cnf(c_7714,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_7600,c_16726]) ).
cnf(c_16727,plain,
( memberP(nil,sk5)
| cons(sk6,nil) = sk3 ),
inference(paramod,[status(thm)],[c_220,c_206]) ).
cnf(c_7721,plain,
cons(sk6,nil) = sk3,
inference(resolve,[status(thm)],[c_7383,c_16727]) ).
cnf(c_16728,plain,
( memberP(nil,sk5)
| memberP(sk4,sk6) ),
inference(paramod,[status(thm)],[c_222,c_206]) ).
cnf(c_7755,plain,
memberP(sk4,sk6),
inference(resolve,[status(thm)],[c_7383,c_16728]) ).
cnf(c_8673,plain,
ssList(app(sk3,sk3)),
inference(resolve,[status(thm)],[c_309,c_200]) ).
cnf(c_16729,plain,
cons(sk6,nil) != nil,
inference(resolve,[status(thm)],[c_1657,c_7600]) ).
cnf(c_11663,plain,
sk3 != nil,
inference(paramod,[status(thm)],[c_7721,c_16729]) ).
cnf(c_11714,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ memberP(sk3,A) ),
inference(resolve,[status(thm)],[c_11663,c_7714]) ).
cnf(c_16730,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(A)
| ~ ssList(app(app(nil,sk3),cons(sk6,nil))) ),
inference(paramod,[status(thm)],[c_7721,c_829]) ).
cnf(c_16731,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(A)
| ~ ssList(app(sk3,cons(sk6,nil))) ),
inference(paramod,[status(thm)],[c_7078,c_16730]) ).
cnf(c_16732,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(A)
| ~ ssList(app(sk3,sk3)) ),
inference(paramod,[status(thm)],[c_7721,c_16731]) ).
cnf(c_16733,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(A) ),
inference(resolve,[status(thm)],[c_8673,c_16732]) ).
cnf(c_16734,plain,
( ~ ssItem(sk6)
| ssItem(A) ),
inference(resolve,[status(thm)],[c_49,c_16733]) ).
cnf(c_12604,plain,
ssItem(A),
inference(resolve,[status(thm)],[c_7600,c_16734]) ).
cnf(c_12799,plain,
( sk6 = A
| memberP(nil,A)
| ~ memberP(sk3,A) ),
inference(resolve,[status(thm)],[c_12604,c_11714]) ).
cnf(c_16389,plain,
~ memberP(nil,A),
inference(resolve,[status(thm)],[c_12604,c_107]) ).
cnf(c_16426,plain,
( sk6 = A
| ~ memberP(sk3,A) ),
inference(resolve,[status(thm)],[c_16389,c_12799]) ).
cnf(c_16735,plain,
sk6 = sk5,
inference(resolve,[status(thm)],[c_16426,c_206]) ).
cnf(c_16694,plain,
sk5 = sk6,
inference(copy,[status(thm)],[c_16735]) ).
cnf(c_16736,plain,
~ memberP(sk4,sk6),
inference(paramod,[status(thm)],[c_16694,c_208]) ).
cnf(c_16722,plain,
$false,
inference(resolve,[status(thm)],[c_7755,c_16736]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC392-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:57:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3722789 was started by sandbox2 on n008,
% 0.09/0.37 % Sat Sep 26 12:57:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 42.67/6.60
% 42.67/6.60 % given #500 (I,wt=72): 564 app(A,cons(app(skaf80(B),cons(skaf78(B),cons(skaf79(B),skaf81(B)))),cons(B,B))) != B | -ssList(B) | -ssList(A) | -ssItem(B) | -ssItem(app(skaf80(B),cons(skaf78(B),cons(skaf79(B),skaf81(B))))) | app(skaf80(B),cons(skaf78(B),cons(skaf79(B),skaf81(B)))) = B. [factor(375,f,g)].
% 42.67/6.60
% 42.67/6.60 % given #1000 (T,wt=8): 7073 sk3 != nil | rearsegP(nil,sk3). [resolve(200,a,114,b),flip(a)].
% 42.67/6.60
% 42.67/6.60 % SZS status Unsatisfiable for theBenchmark
% 42.67/6.60
% 42.67/6.60 % Proof 1 at 4.66 (+ 1.39) seconds.
% 42.67/6.60 % Length of proof is 44.
% 42.67/6.60 % Level of proof is 10.
% 42.67/6.60 % Maximum clause weight is 33.000.
% 42.67/6.60 % Given clauses 1321.
% 42.67/6.60
% 42.67/6.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------