%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV028-2 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 07:34:23 AM UTC 2026
% Result : Unsatisfiable 1.91s 0.78s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 20 unt; 0 def)
% Number of atoms : 34 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 6 !; 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_DOTlevel_(f_ADD_(t_206,n1)),fwork_DOTfifo_DOTrtl_DOTfifo__length_),
file('theBenchmark.p',quest_2) ).
cnf(c_10,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)),fwork_DOTfifo_DOTrtl_DOTfifo__length_),
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_74,plain,
f__length_(f__empty_) = n0,
inference(clausify,[status(thm)],[axiom_80]) ).
cnf(c_75,plain,
n0 = f__length_(f__empty_),
inference(copy,[status(thm)],[c_74]) ).
fof(axiom_75,axiom,
! [VAR_0] : p_LES_EQU_(VAR_0,VAR_0),
file('theBenchmark.p',axiom_75) ).
cnf(c_82,plain,
p_LES_EQU_(A,A),
inference(clausify,[status(thm)],[axiom_75]) ).
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_88,plain,
( p_LES_EQU_(A,C)
| p_LES_EQU_(C,B)
| ~ p_LES_EQU_(A,B) ),
inference(clausify,[status(thm)],[axiom_71]) ).
fof(axiom_12,axiom,
! [VAR_0] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(VAR_0))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(VAR_0,n1)) = n0 ),
file('theBenchmark.p',axiom_12) ).
cnf(c_172,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,n1)) = n0 ),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_173,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(A))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(A,n1)) = f__length_(f__empty_) ),
inference(paramod,[status(thm)],[c_75,c_172]) ).
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_184,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(A) = fwork_DOTfifo_DOTrtl_DOTint__level_(A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_200,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_)),
inference(paramod,[status(thm)],[c_75,c_9]) ).
cnf(c_216,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)),fwork_DOTfifo_DOTrtl_DOTfifo__length_),
inference(paramod,[status(thm)],[c_184,c_10]) ).
cnf(c_450,plain,
( p_LES_EQU_(B,A)
| p_LES_EQU_(A,B) ),
inference(resolve,[status(thm)],[c_88,c_82]) ).
cnf(c_1698,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_),
inference(resolve,[status(thm)],[c_173,c_11]) ).
cnf(c_769,plain,
f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)),
inference(copy,[status(thm)],[c_1698]) ).
cnf(c_1057,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1))),
inference(paramod,[status(thm)],[c_769,c_200]) ).
cnf(c_1699,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)),fwork_DOTfifo_DOTrtl_DOTfifo__length_),
inference(resolve,[status(thm)],[c_450,c_1057]) ).
cnf(c_1697,plain,
$false,
inference(resolve,[status(thm)],[c_216,c_1699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HWV028-2 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n020.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 16:03:34 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3318207 was started by sandbox on n020,
% 0.16/0.44 % Fri Sep 25 16:03:34 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 1.91/0.78
% 1.91/0.78 % SZS status Unsatisfiable for theBenchmark
% 1.91/0.78
% 1.91/0.78 % Proof 1 at 0.25 (+ 0.03) seconds.
% 1.91/0.78 % Length of proof is 16.
% 1.91/0.78 % Level of proof is 5.
% 1.91/0.78 % Maximum clause weight is 10.000.
% 1.91/0.78 % Given clauses 199.
% 1.91/0.78
% 1.91/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------