%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC218-1 : 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 08:57:12 AM UTC 2026
% Result : Unsatisfiable 208.63s 28.02s
% Output : CNFRefutation 208.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 23 unt; 0 def)
% Number of atoms : 90 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 49 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 6 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
~ neq(sk1,nil),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
~ neq(sk1,nil),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
ssItem(sk7),
file('theBenchmark.p',co1_10) ).
cnf(c_53,plain,
ssItem(sk7),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_8,axiom,
ssList(sk6),
file('theBenchmark.p',co1_8) ).
cnf(c_55,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_57,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_60,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_70,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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_138,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause99,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,VAR_1) != VAR_1 ),
file('theBenchmark.p',clause99) ).
cnf(c_139,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != B ),
inference(clausify,[status(thm)],[clause99]) ).
fof(clause86,axiom,
! [VAR_0,VAR_1] :
( ssList(cons(VAR_0,VAR_1))
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',clause86) ).
cnf(c_145,plain,
( ssList(cons(A,B))
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause86]) ).
fof(clause80,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ segmentP(nil,VAR_0) ),
file('theBenchmark.p',clause80) ).
cnf(c_151,plain,
( nil = A
| ~ ssList(A)
| ~ segmentP(nil,A) ),
inference(clausify,[status(thm)],[clause80]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_215,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_319,plain,
~ neq(sk3,nil),
inference(paramod,[status(thm)],[c_57,c_51]) ).
cnf(c_11162,plain,
( segmentP(sk3,cons(sk7,nil))
| ~ ssList(sk3)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_70,c_52]) ).
cnf(c_11163,plain,
( segmentP(sk3,cons(sk7,nil))
| ~ ssList(sk3)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_55,c_11162]) ).
cnf(c_11164,plain,
( segmentP(sk3,cons(sk7,nil))
| ~ ssList(sk3)
| ~ ssList(cons(sk7,nil)) ),
inference(resolve,[status(thm)],[c_56,c_11163]) ).
cnf(c_877,plain,
( segmentP(sk3,cons(sk7,nil))
| ~ ssList(cons(sk7,nil)) ),
inference(resolve,[status(thm)],[c_60,c_11164]) ).
cnf(c_1312,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_138,c_60]) ).
cnf(c_1316,plain,
( ~ ssList(A)
| cons(sk7,A) != A ),
inference(resolve,[status(thm)],[c_139,c_53]) ).
cnf(c_1344,plain,
( ssList(cons(sk7,A))
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_145,c_53]) ).
cnf(c_11165,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1312,c_215]) ).
cnf(c_7287,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_319,c_11165]) ).
cnf(c_7463,plain,
( segmentP(nil,cons(sk7,nil))
| ~ ssList(cons(sk7,nil)) ),
inference(paramod,[status(thm)],[c_7287,c_877]) ).
cnf(c_9125,plain,
cons(sk7,nil) != nil,
inference(resolve,[status(thm)],[c_1316,c_215]) ).
cnf(c_11060,plain,
ssList(cons(sk7,nil)),
inference(resolve,[status(thm)],[c_1344,c_215]) ).
cnf(c_11091,plain,
segmentP(nil,cons(sk7,nil)),
inference(resolve,[status(thm)],[c_11060,c_7463]) ).
cnf(c_11166,plain,
( nil = cons(sk7,nil)
| ~ segmentP(nil,cons(sk7,nil)) ),
inference(resolve,[status(thm)],[c_11060,c_151]) ).
cnf(c_11167,plain,
( cons(sk7,nil) = nil
| ~ segmentP(nil,cons(sk7,nil)) ),
inference(copy,[status(thm)],[c_11166]) ).
cnf(c_11168,plain,
cons(sk7,nil) = nil,
inference(resolve,[status(thm)],[c_11091,c_11167]) ).
cnf(c_11161,plain,
$false,
inference(resolve,[status(thm)],[c_9125,c_11168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC218-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 12:33:40 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3664206 was started by sandbox2 on n008,
% 0.17/0.43 % Sat Sep 26 12:33:40 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 208.63/28.02
% 208.63/28.02 % given #500 (I,wt=49): 551 app(app(A,cons(B,C)),cons(B,A)) != D | -ssList(A) | -ssList(C) | -ssItem(B) | -ssList(D) | lt(B,B) | -lt(skaf59(D),skaf60(D)). [factor(291,d,e),merge(g)].
% 208.63/28.02
% 208.63/28.02 % given #1000 (F,wt=14): 2344 -memberP(nil,skaf55(A)). [resolve(183,a,157,b)].
% 208.63/28.02
% 208.63/28.02 % given #1500 (W,wt=15): 4485 geq(skaf83(A),skaf83(A)). [resolve(211,a,168,a)].
% 208.63/28.02
% 208.63/28.02 % SZS status Unsatisfiable for theBenchmark
% 208.63/28.02
% 208.63/28.02 % Proof 1 at 2.33 (+ 0.95) seconds.
% 208.63/28.02 % Length of proof is 24.
% 208.63/28.02 % Level of proof is 5.
% 208.63/28.02 % Maximum clause weight is 35.000.
% 208.63/28.02 % Given clauses 1610.
% 208.63/28.02
% 208.63/28.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------