%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC182-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:57:05 AM UTC 2026
% Result : Unsatisfiable 36.85s 8.41s
% Output : CNFRefutation 36.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 22 unt; 0 def)
% Number of atoms : 74 ( 20 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 76 ( 40 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 20 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_49,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause80,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ segmentP(nil,VAR_0) ),
file('theBenchmark.p',clause80) ).
cnf(c_113,plain,
( nil = A
| ~ ssList(A)
| ~ segmentP(nil,A) ),
inference(clausify,[status(thm)],[clause80]) ).
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_119,plain,
( ssList(cons(A,B))
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause86]) ).
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(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_190,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(co1_5,axiom,
nil = sk3,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
nil = sk3,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_203,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_202]) ).
fof(co1_7,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_207,plain,
sk1 = nil,
inference(paramod,[status(thm)],[c_203,c_206]) ).
fof(co1_8,axiom,
ssItem(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_208,plain,
ssItem(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_9,axiom,
ssList(sk6),
file('theBenchmark.p',co1_9) ).
cnf(c_209,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_10,axiom,
ssList(sk7),
file('theBenchmark.p',co1_10) ).
cnf(c_210,plain,
ssList(sk7),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_11,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('theBenchmark.p',co1_11) ).
cnf(c_211,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_212,plain,
app(app(sk6,cons(sk5,nil)),sk7) = nil,
inference(paramod,[status(thm)],[c_207,c_211]) ).
cnf(c_1457,plain,
( ssList(cons(A,nil))
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_119,c_49]) ).
cnf(c_1646,plain,
( ~ ssItem(A)
| cons(A,nil) != nil ),
inference(resolve,[status(thm)],[c_124,c_49]) ).
cnf(c_13151,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_212,c_190]) ).
cnf(c_13152,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_210,c_13151]) ).
cnf(c_13153,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil)) ),
inference(resolve,[status(thm)],[c_209,c_13152]) ).
cnf(c_7566,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(resolve,[status(thm)],[c_49,c_13153]) ).
cnf(c_11244,plain,
cons(sk5,nil) != nil,
inference(resolve,[status(thm)],[c_1646,c_208]) ).
cnf(c_13020,plain,
ssList(cons(sk5,nil)),
inference(resolve,[status(thm)],[c_1457,c_208]) ).
cnf(c_13040,plain,
segmentP(nil,cons(sk5,nil)),
inference(resolve,[status(thm)],[c_13020,c_7566]) ).
cnf(c_13154,plain,
( nil = cons(sk5,nil)
| ~ segmentP(nil,cons(sk5,nil)) ),
inference(resolve,[status(thm)],[c_13020,c_113]) ).
cnf(c_13155,plain,
( cons(sk5,nil) = nil
| ~ segmentP(nil,cons(sk5,nil)) ),
inference(copy,[status(thm)],[c_13154]) ).
cnf(c_13156,plain,
cons(sk5,nil) = nil,
inference(resolve,[status(thm)],[c_13040,c_13155]) ).
cnf(c_13150,plain,
$false,
inference(resolve,[status(thm)],[c_11244,c_13156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC182-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:29:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 441195 was started by sandbox on n018,
% 0.10/0.37 % Sat Sep 26 12:29:21 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 36.85/8.41
% 36.85/8.41 % given #500 (I,wt=40): 559 app(A,cons(B,cons(C,cons(C,nil)))) != cons(C,nil) | -ssList(cons(C,nil)) | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C. [factor(371,d,g)].
% 36.85/8.41
% 36.85/8.41 % given #1000 (F,wt=9): 11097 cons(skac2,nil) != nil. [resolve(1617,b,49,a)].
% 36.85/8.41
% 36.85/8.41 % SZS status Unsatisfiable for theBenchmark
% 36.85/8.41
% 36.85/8.41 % Proof 1 at 4.11 (+ 1.20) seconds.
% 36.85/8.41 % Length of proof is 21.
% 36.85/8.41 % Level of proof is 6.
% 36.85/8.41 % Maximum clause weight is 26.000.
% 36.85/8.41 % Given clauses 1304.
% 36.85/8.41
% 36.85/8.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------