%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV023-2 : 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 : n015.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 07:34:22 AM UTC 2026
% Result : Unsatisfiable 173.15s 23.45s
% Output : CNFRefutation 173.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 35 unt; 0 def)
% Number of atoms : 144 ( 53 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 46 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 4 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_64,axiom,
! [VAR_0,VAR_1] :
( ~ def_89(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',axiom_64) ).
cnf(c_1,plain,
( ~ def_89(B,A)
| A != B ),
inference(clausify,[status(thm)],[axiom_64]) ).
fof(axiom_63,axiom,
! [VAR_0,VAR_1,VAR_2] :
( f_SUB_(VAR_1,VAR_0) = VAR_2
| f_ADD_(VAR_2,VAR_0) != VAR_1
| def_89(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_63) ).
cnf(c_2,plain,
( f_SUB_(B,A) = C
| f_ADD_(C,A) != B
| def_89(A,B) ),
inference(clausify,[status(thm)],[axiom_63]) ).
cnf(c_8,plain,
( f_SUB_(A,B) = C
| f_ADD_(C,B) != A
| A != B ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(quest_5,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
file('theBenchmark.p',quest_5) ).
cnf(c_9,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
inference(clausify,[status(thm)],[quest_5]) ).
fof(quest_4,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
file('theBenchmark.p',quest_4) ).
cnf(c_10,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(clausify,[status(thm)],[quest_4]) ).
fof(quest_3,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('theBenchmark.p',quest_3) ).
cnf(c_11,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(clausify,[status(thm)],[quest_3]) ).
fof(quest_2,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('theBenchmark.p',quest_2) ).
cnf(c_12,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n1,
file('theBenchmark.p',quest_1) ).
cnf(c_13,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n1,
inference(clausify,[status(thm)],[quest_1]) ).
cnf(c_14,plain,
n1 = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(copy,[status(thm)],[c_13]) ).
fof(axiom_80,axiom,
f__length_(f__empty_) = n0,
file('theBenchmark.p',axiom_80) ).
cnf(c_79,plain,
f__length_(f__empty_) = n0,
inference(clausify,[status(thm)],[axiom_80]) ).
cnf(c_80,plain,
n0 = f__length_(f__empty_),
inference(copy,[status(thm)],[c_79]) ).
fof(axiom_77,axiom,
! [VAR_0] : f_ADD_(n0,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_77) ).
cnf(c_85,plain,
f_ADD_(n0,A) = A,
inference(clausify,[status(thm)],[axiom_77]) ).
cnf(c_86,plain,
f_ADD_(f__length_(f__empty_),A) = A,
inference(paramod,[status(thm)],[c_80,c_85]) ).
fof(axiom_75,axiom,
! [VAR_0] : p_LES_EQU_(VAR_0,VAR_0),
file('theBenchmark.p',axiom_75) ).
cnf(c_89,plain,
p_LES_EQU_(A,A),
inference(clausify,[status(thm)],[axiom_75]) ).
fof(axiom_73,axiom,
! [VAR_0] :
( VAR_0 = n0
| ~ p_LES_EQU_(VAR_0,n0) ),
file('theBenchmark.p',axiom_73) ).
cnf(c_92,plain,
( A = n0
| ~ p_LES_EQU_(A,n0) ),
inference(clausify,[status(thm)],[axiom_73]) ).
cnf(c_12087,plain,
( A = n0
| ~ p_LES_EQU_(A,f__length_(f__empty_)) ),
inference(paramod,[status(thm)],[c_80,c_92]) ).
cnf(c_12088,plain,
( A = f__length_(f__empty_)
| ~ p_LES_EQU_(A,f__length_(f__empty_)) ),
inference(paramod,[status(thm)],[c_80,c_12087]) ).
cnf(c_93,plain,
( f__length_(f__empty_) = A
| ~ p_LES_EQU_(A,f__length_(f__empty_)) ),
inference(copy,[status(thm)],[c_12088]) ).
fof(axiom_71,axiom,
! [VAR_0,VAR_1,VAR_2] :
( p_LES_EQU_(VAR_0,VAR_2)
| p_LES_EQU_(VAR_2,VAR_1)
| ~ p_LES_EQU_(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_71) ).
cnf(c_96,plain,
( p_LES_EQU_(A,C)
| p_LES_EQU_(C,B)
| ~ p_LES_EQU_(A,B) ),
inference(clausify,[status(thm)],[axiom_71]) ).
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_98,plain,
( p_LES_EQU_(f_ADD_(A,n1),B)
| A = B
| ~ p_LES_EQU_(A,B) ),
inference(clausify,[status(thm)],[axiom_69]) ).
cnf(c_99,plain,
( p_LES_EQU_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),B)
| A = B
| ~ p_LES_EQU_(A,B) ),
inference(paramod,[status(thm)],[c_14,c_98]) ).
fof(axiom_60,axiom,
! [VAR_0] : ~ p_LES_EQU_(f_ADD_(VAR_0,n1),n0),
file('theBenchmark.p',axiom_60) ).
cnf(c_108,plain,
~ p_LES_EQU_(f_ADD_(A,n1),n0),
inference(clausify,[status(thm)],[axiom_60]) ).
cnf(c_12089,plain,
~ p_LES_EQU_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),n0),
inference(paramod,[status(thm)],[c_14,c_108]) ).
cnf(c_109,plain,
~ p_LES_EQU_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)),
inference(paramod,[status(thm)],[c_80,c_12089]) ).
fof(axiom_43,axiom,
! [VAR_0] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(VAR_0))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(VAR_0))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(VAR_0))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(VAR_0),n0)
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(VAR_0,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(VAR_0),n1) ),
file('theBenchmark.p',axiom_43) ).
cnf(c_142,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(A))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),n0)
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),n1) ),
inference(clausify,[status(thm)],[axiom_43]) ).
cnf(c_12090,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(A))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),n0)
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),n1) ),
inference(paramod,[status(thm)],[c_14,c_142]) ).
cnf(c_12091,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(A))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),n0)
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ),
inference(paramod,[status(thm)],[c_14,c_12090]) ).
cnf(c_143,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(A))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ),
inference(paramod,[status(thm)],[c_80,c_12091]) ).
fof(axiom_8,axiom,
! [VAR_0] :
( fwork_DOTfifo_DOTrtl_DOTint__level_(VAR_0) != n0
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(VAR_0)) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_212,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != n0
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_213,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != f__length_(f__empty_)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(paramod,[status(thm)],[c_80,c_212]) ).
fof(axiom_5,axiom,
! [VAR_0] : fwork_DOTfifo_DOTrtl_DOTlevel_(VAR_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(VAR_0),
file('theBenchmark.p',axiom_5) ).
cnf(c_216,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(A) = fwork_DOTfifo_DOTrtl_DOTint__level_(A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_12092,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))),
inference(paramod,[status(thm)],[c_14,c_9]) ).
cnf(c_223,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
inference(paramod,[status(thm)],[c_216,c_12092]) ).
cnf(c_12093,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(A))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ),
inference(paramod,[status(thm)],[c_216,c_143]) ).
cnf(c_284,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(A))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(A),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) ),
inference(paramod,[status(thm)],[c_216,c_12093]) ).
cnf(c_301,plain,
~ p_LES_EQU_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),f__length_(f__empty_)),
inference(paramod,[status(thm)],[c_216,c_109]) ).
cnf(c_306,plain,
( p_LES_EQU_(f_ADD_(A,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),B)
| A = B
| ~ p_LES_EQU_(A,B) ),
inference(paramod,[status(thm)],[c_216,c_99]) ).
cnf(c_12094,plain,
( f_SUB_(A,A) = f__length_(f__empty_)
| A != A ),
inference(resolve,[status(thm)],[c_86,c_8]) ).
cnf(c_1036,plain,
f_SUB_(A,A) = f__length_(f__empty_),
inference(copy,[status(thm)],[c_12094]) ).
cnf(c_1048,plain,
( p_LES_EQU_(B,A)
| p_LES_EQU_(A,B) ),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_12095,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) ),
inference(resolve,[status(thm)],[c_284,c_12]) ).
cnf(c_12096,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) ),
inference(resolve,[status(thm)],[c_10,c_12095]) ).
cnf(c_1711,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) ),
inference(resolve,[status(thm)],[c_11,c_12096]) ).
cnf(c_2044,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_)),
inference(paramod,[status(thm)],[c_86,c_301]) ).
cnf(c_2046,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
inference(resolve,[status(thm)],[c_2044,c_1711]) ).
cnf(c_2563,plain,
( f__length_(f__empty_) = A
| p_LES_EQU_(f__length_(f__empty_),A) ),
inference(resolve,[status(thm)],[c_1048,c_93]) ).
cnf(c_4750,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f_SUB_(A,A)),
inference(paramod,[status(thm)],[c_1036,c_2044]) ).
cnf(c_12097,plain,
( p_LES_EQU_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),A)
| f__length_(f__empty_) = A
| f__length_(f__empty_) = A ),
inference(resolve,[status(thm)],[c_2563,c_306]) ).
cnf(c_12098,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),A)
| f__length_(f__empty_) = A
| f__length_(f__empty_) = A ),
inference(paramod,[status(thm)],[c_86,c_12097]) ).
cnf(c_6749,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),A)
| f__length_(f__empty_) = A ),
inference(copy,[status(thm)],[c_12098]) ).
cnf(c_12099,plain,
( f__length_(f__empty_) != fwork_DOTfifo_DOTrtl_DOTint__level_(A)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(copy,[status(thm)],[c_213]) ).
cnf(c_11943,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(A)) ),
inference(resolve,[status(thm)],[c_6749,c_12099]) ).
cnf(c_12100,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
inference(resolve,[status(thm)],[c_11943,c_223]) ).
cnf(c_12101,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
inference(paramod,[status(thm)],[c_2046,c_12100]) ).
cnf(c_12086,plain,
$false,
inference(resolve,[status(thm)],[c_4750,c_12101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HWV023-2 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.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 : Fri Sep 25 16:05:28 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 1785788 was started by sandbox2 on n015,
% 0.17/0.43 % Fri Sep 25 16:05:28 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).
% 173.15/23.45
% 173.15/23.45 % SZS status Unsatisfiable for theBenchmark
% 173.15/23.45
% 173.15/23.45 % Proof 1 at 6.24 (+ 0.62) seconds.
% 173.15/23.45 % Length of proof is 40.
% 173.15/23.45 % Level of proof is 6.
% 173.15/23.45 % Maximum clause weight is 45.000.
% 173.15/23.45 % Given clauses 465.
% 173.15/23.45
% 173.15/23.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------