%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV030-2 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:34:24 AM UTC 2026
% Result : Unsatisfiable 1.52s 21.09s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 19 unt; 0 def)
% Number of atoms : 39 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quest_3,axiom,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0),
file('theBenchmark.p',quest_3) ).
cnf(c_9,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0),
inference(clausify,[status(thm)],[quest_3]) ).
fof(quest_2,axiom,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))),
file('theBenchmark.p',quest_2) ).
cnf(c_10,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('theBenchmark.p',quest_1) ).
cnf(c_11,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(clausify,[status(thm)],[quest_1]) ).
fof(axiom_80,axiom,
f__length_(f__empty_) = n0,
file('theBenchmark.p',axiom_80) ).
cnf(c_77,plain,
f__length_(f__empty_) = n0,
inference(clausify,[status(thm)],[axiom_80]) ).
cnf(c_78,plain,
n0 = f__length_(f__empty_),
inference(copy,[status(thm)],[c_77]) ).
fof(axiom_75,axiom,
! [VAR_0] : p_LES_EQU_(VAR_0,VAR_0),
file('theBenchmark.p',axiom_75) ).
cnf(c_86,plain,
p_LES_EQU_(A,A),
inference(clausify,[status(thm)],[axiom_75]) ).
fof(axiom_69,axiom,
! [VAR_0,VAR_1] :
( p_LES_EQU_(f_ADD_(VAR_0,n1),VAR_1)
| VAR_0 = VAR_1
| ~ p_LES_EQU_(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_69) ).
cnf(c_94,plain,
( p_LES_EQU_(f_ADD_(A,n1),B)
| A = B
| ~ p_LES_EQU_(A,B) ),
inference(clausify,[status(thm)],[axiom_69]) ).
fof(axiom_60,axiom,
! [VAR_0] : ~ p_LES_EQU_(f_ADD_(VAR_0,n1),n0),
file('theBenchmark.p',axiom_60) ).
cnf(c_100,plain,
~ p_LES_EQU_(f_ADD_(A,n1),n0),
inference(clausify,[status(thm)],[axiom_60]) ).
cnf(c_101,plain,
~ p_LES_EQU_(f_ADD_(A,n1),f__length_(f__empty_)),
inference(paramod,[status(thm)],[c_78,c_100]) ).
fof(axiom_11,axiom,
! [VAR_0] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(VAR_0))
| fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(VAR_0,n1)) = n0 ),
file('theBenchmark.p',axiom_11) ).
cnf(c_180,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(A,n1)) = n0 ),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_181,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(A,n1)) = f__length_(f__empty_) ),
inference(paramod,[status(thm)],[c_78,c_180]) ).
cnf(c_209,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_)),
inference(paramod,[status(thm)],[c_78,c_9]) ).
cnf(c_1341,plain,
( p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n1),fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)))
| fwork_DOTfifo_DOTrtl_DOTfifo__length_ = fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) ),
inference(resolve,[status(thm)],[c_94,c_10]) ).
cnf(c_650,plain,
( p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n1),fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)))
| fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ),
inference(copy,[status(thm)],[c_1341]) ).
cnf(c_1040,plain,
fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_),
inference(resolve,[status(thm)],[c_181,c_11]) ).
cnf(c_1342,plain,
( p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n1),fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)))
| f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ),
inference(paramod,[status(thm)],[c_1040,c_650]) ).
cnf(c_1343,plain,
( p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n1),f__length_(f__empty_))
| f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ),
inference(paramod,[status(thm)],[c_1040,c_1342]) ).
cnf(c_1042,plain,
f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTfifo__length_,
inference(resolve,[status(thm)],[c_101,c_1343]) ).
cnf(c_1344,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_),
inference(paramod,[status(thm)],[c_1042,c_209]) ).
cnf(c_1340,plain,
$false,
inference(resolve,[status(thm)],[c_86,c_1344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV030-2 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/20.84 % CPULimit : 300
% 0.09/20.84 % WCLimit : 300
% 0.09/20.84 % DateTime : Fri Sep 25 16:05:57 UTC 2026
% 0.09/20.84 % CPUTime :
% 0.09/20.84 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/20.84 % Process 3718504 was started by sandbox2 on n002,
% 0.09/20.84 % Fri Sep 25 16:05:57 2026
% 0.09/20.84 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/20.85
% 0.09/20.85 % From the command line: assign(max_seconds, 300).
% 1.52/21.09
% 1.52/21.09 % SZS status Unsatisfiable for theBenchmark
% 1.52/21.09
% 1.52/21.09 % Proof 1 at 0.16 (+ 0.04) seconds.
% 1.52/21.09 % Length of proof is 16.
% 1.52/21.09 % Level of proof is 5.
% 1.52/21.09 % Maximum clause weight is 29.000.
% 1.52/21.09 % Given clauses 123.
% 1.52/21.09
% 1.52/21.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------