%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC217-1 : 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 08:57:11 AM UTC 2026
% Result : Unsatisfiable 30.12s 4.27s
% Output : CNFRefutation 30.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 25 unt; 0 def)
% Number of atoms : 74 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 37 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_11,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_8,axiom,
~ neq(sk1,nil),
file('theBenchmark.p',co1_8) ).
cnf(c_56,plain,
~ neq(sk1,nil),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_57,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_58,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_59,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_61,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_63,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause119,axiom,
! [VAR_0,VAR_1] :
( nil = VAR_1
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause119) ).
cnf(c_120,plain,
( nil = B
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause119]) ).
fof(clause100,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| neq(VAR_1,VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause100) ).
cnf(c_139,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
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_141,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != nil ),
inference(clausify,[status(thm)],[clause98]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_156,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_216,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_828,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_59,c_57]) ).
cnf(c_829,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_828,c_53]) ).
cnf(c_830,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_828,c_52]) ).
cnf(c_15098,plain,
( nil = sk3
| ~ ssList(A)
| app(A,sk3) != nil ),
inference(resolve,[status(thm)],[c_120,c_61]) ).
cnf(c_1022,plain,
( sk3 = nil
| ~ ssList(A)
| app(A,sk3) != nil ),
inference(copy,[status(thm)],[c_15098]) ).
cnf(c_1055,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_63]) ).
cnf(c_1084,plain,
app(nil,sk1) = sk1,
inference(resolve,[status(thm)],[c_156,c_63]) ).
cnf(c_4858,plain,
( ~ ssList(A)
| cons(sk5,A) != nil ),
inference(resolve,[status(thm)],[c_829,c_141]) ).
cnf(c_9115,plain,
cons(sk5,nil) != nil,
inference(resolve,[status(thm)],[c_4858,c_216]) ).
cnf(c_9147,plain,
sk3 != nil,
inference(paramod,[status(thm)],[c_830,c_9115]) ).
cnf(c_9161,plain,
( ~ ssList(A)
| app(A,sk3) != nil ),
inference(resolve,[status(thm)],[c_9147,c_1022]) ).
cnf(c_9959,plain,
app(nil,sk3) != nil,
inference(resolve,[status(thm)],[c_9161,c_216]) ).
cnf(c_11209,plain,
app(nil,sk3) = sk1,
inference(paramod,[status(thm)],[c_58,c_1084]) ).
cnf(c_13417,plain,
sk1 != nil,
inference(paramod,[status(thm)],[c_11209,c_9959]) ).
cnf(c_15099,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1055,c_216]) ).
cnf(c_15100,plain,
sk1 = nil,
inference(resolve,[status(thm)],[c_56,c_15099]) ).
cnf(c_15097,plain,
$false,
inference(resolve,[status(thm)],[c_13417,c_15100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC217-1 : 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 : n017.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 12:27:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 707229 was started by sandbox2 on n017,
% 0.09/0.37 % Sat Sep 26 12:27:48 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).
% 30.12/4.27
% 30.12/4.27 % given #500 (I,wt=35): 556 app(app(A,cons(B,C)),cons(B,D)) != C | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(C),skaf60(C)). [factor(295,e,f),merge(g)].
% 30.12/4.27
% 30.12/4.27 % given #1000 (F,wt=11): 9160 app(sk3,A) != nil | -ssList(A). [back_unit_del(1034),unit_del(c,9147)].
% 30.12/4.27
% 30.12/4.27 % given #1500 (W,wt=9): 11254 app(sk4,nil) = sk2. [para(59(a,1),1089(a,1,1))].
% 30.12/4.27
% 30.12/4.27 % SZS status Unsatisfiable for theBenchmark
% 30.12/4.27
% 30.12/4.27 % Proof 1 at 2.91 (+ 0.91) seconds.
% 30.12/4.27 % Length of proof is 27.
% 30.12/4.27 % Level of proof is 9.
% 30.12/4.27 % Maximum clause weight is 16.000.
% 30.12/4.27 % Given clauses 1619.
% 30.12/4.27
% 30.12/4.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------