%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC198-1 : 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 08:57:08 AM UTC 2026
% Result : Unsatisfiable 43.84s 6.16s
% Output : CNFRefutation 43.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 74 ( 24 unt; 0 def)
% Number of atoms : 198 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 235 ( 111 ~; 124 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 17 sgn 19 !; 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(clause10,axiom,
ssItem(skac2),
file('theBenchmark.p',clause10) ).
cnf(c_51,plain,
ssItem(skac2),
inference(clausify,[status(thm)],[clause10]) ).
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_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] :
( ssItem(sk5(VAR_0))
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
( ssItem(sk5(A))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
! [VAR_0] :
( memberP(sk1,sk5(VAR_0))
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_205,plain,
( memberP(sk1,sk5(A))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_206,plain,
( memberP(sk3,sk5(A))
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_203,c_205]) ).
fof(co1_9,axiom,
! [VAR_0] :
( VAR_0 != sk5(VAR_0)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_9) ).
cnf(c_207,plain,
( A != sk5(A)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_208,plain,
( sk5(A) != A
| ~ ssItem(A) ),
inference(copy,[status(thm)],[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]) ).
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_7329,plain,
ssItem(sk5(skac2)),
inference(resolve,[status(thm)],[c_204,c_51]) ).
cnf(c_7346,plain,
memberP(sk3,sk5(skac2)),
inference(resolve,[status(thm)],[c_206,c_51]) ).
cnf(c_16387,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_16388,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(copy,[status(thm)],[c_16387]) ).
cnf(c_7674,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ ssItem(sk6)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_49,c_16388]) ).
cnf(c_8562,plain,
ssList(app(sk3,sk3)),
inference(resolve,[status(thm)],[c_309,c_200]) ).
cnf(c_16389,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(A)
| ~ ssList(app(app(nil,cons(sk6,nil)),sk3))
| sk3 = nil ),
inference(paramod,[status(thm)],[c_220,c_829]) ).
cnf(c_10125,plain,
( ~ ssItem(sk6)
| ssItem(A)
| ~ ssList(app(app(nil,cons(sk6,nil)),sk3))
| sk3 = nil ),
inference(resolve,[status(thm)],[c_49,c_16389]) ).
cnf(c_10262,plain,
~ memberP(nil,sk5(skac2)),
inference(resolve,[status(thm)],[c_7329,c_107]) ).
cnf(c_16390,plain,
( memberP(nil,sk5(skac2))
| ssItem(sk6) ),
inference(paramod,[status(thm)],[c_212,c_7346]) ).
cnf(c_11894,plain,
ssItem(sk6),
inference(resolve,[status(thm)],[c_10262,c_16390]) ).
cnf(c_16391,plain,
( memberP(nil,sk5(skac2))
| cons(sk6,nil) = sk3 ),
inference(paramod,[status(thm)],[c_220,c_7346]) ).
cnf(c_11895,plain,
cons(sk6,nil) = sk3,
inference(resolve,[status(thm)],[c_10262,c_16391]) ).
cnf(c_16392,plain,
( ~ ssItem(sk6)
| ssItem(A)
| ~ ssList(app(app(nil,sk3),sk3))
| sk3 = nil ),
inference(paramod,[status(thm)],[c_11895,c_10125]) ).
cnf(c_16393,plain,
( ~ ssItem(sk6)
| ssItem(A)
| ~ ssList(app(sk3,sk3))
| sk3 = nil ),
inference(paramod,[status(thm)],[c_7078,c_16392]) ).
cnf(c_16394,plain,
( ~ ssItem(sk6)
| ssItem(A)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_8562,c_16393]) ).
cnf(c_11897,plain,
( ssItem(A)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_11894,c_16394]) ).
cnf(c_11946,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ memberP(sk3,A)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_11894,c_7674]) ).
cnf(c_16395,plain,
cons(sk6,nil) != nil,
inference(resolve,[status(thm)],[c_11894,c_1657]) ).
cnf(c_12016,plain,
sk3 != nil,
inference(paramod,[status(thm)],[c_11895,c_16395]) ).
cnf(c_12159,plain,
( sk6 = A
| memberP(nil,A)
| ~ ssItem(A)
| ~ memberP(sk3,A) ),
inference(resolve,[status(thm)],[c_12016,c_11946]) ).
cnf(c_12188,plain,
ssItem(A),
inference(resolve,[status(thm)],[c_12016,c_11897]) ).
cnf(c_12304,plain,
( sk6 = A
| memberP(nil,A)
| ~ memberP(sk3,A) ),
inference(resolve,[status(thm)],[c_12188,c_12159]) ).
cnf(c_15743,plain,
sk5(A) != A,
inference(resolve,[status(thm)],[c_12188,c_208]) ).
cnf(c_15744,plain,
memberP(sk3,sk5(A)),
inference(resolve,[status(thm)],[c_12188,c_206]) ).
cnf(c_15790,plain,
~ memberP(nil,A),
inference(resolve,[status(thm)],[c_12188,c_107]) ).
cnf(c_15810,plain,
( sk6 = A
| ~ memberP(sk3,A) ),
inference(resolve,[status(thm)],[c_15790,c_12304]) ).
cnf(c_16396,plain,
sk6 = sk5(A),
inference(resolve,[status(thm)],[c_15810,c_15744]) ).
cnf(c_16385,plain,
sk5(A) = sk6,
inference(copy,[status(thm)],[c_16396]) ).
cnf(c_16386,plain,
$false,
inference(resolve,[status(thm)],[c_16385,c_15743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC198-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n008.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
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 12:30:39 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 3658274 was started by sandbox2 on n008,
% 0.12/0.39 % Sat Sep 26 12:30:39 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 43.84/6.16
% 43.84/6.16 % 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)].
% 43.84/6.16
% 43.84/6.16 % given #1000 (T,wt=4): 11894 ssItem(sk6). [para(212(b,1),7346(a,1)),unit_del(b,10262)].
% 43.84/6.16
% 43.84/6.16 % SZS status Unsatisfiable for theBenchmark
% 43.84/6.16
% 43.84/6.16 % Proof 1 at 4.44 (+ 1.22) seconds.
% 43.84/6.16 % Length of proof is 48.
% 43.84/6.16 % Level of proof is 12.
% 43.84/6.16 % Maximum clause weight is 33.000.
% 43.84/6.16 % Given clauses 1210.
% 43.84/6.16
% 43.84/6.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------