%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV020-2 : 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 : n017.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 07:34:21 AM UTC 2026
% Result : Unsatisfiable 39.20s 5.55s
% Output : CNFRefutation 39.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 64 ( 22 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_DOTempty_(t_206)),
file('theBenchmark.p',quest_4) ).
cnf(c_10,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(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_DOTwr_(t_206)),
file('theBenchmark.p',quest_2) ).
cnf(c_12,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('theBenchmark.p',quest_1) ).
cnf(c_13,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(clausify,[status(thm)],[quest_1]) ).
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_75,axiom,
! [VAR_0] : p_LES_EQU_(VAR_0,VAR_0),
file('theBenchmark.p',axiom_75) ).
cnf(c_88,plain,
p_LES_EQU_(A,A),
inference(clausify,[status(thm)],[axiom_75]) ).
fof(axiom_47,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)) = fwork_DOTfifo_DOTrtl_DOTint__level_(VAR_0) ),
file('theBenchmark.p',axiom_47) ).
cnf(c_122,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)) = fwork_DOTfifo_DOTrtl_DOTint__level_(A) ),
inference(clausify,[status(thm)],[axiom_47]) ).
cnf(c_123,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,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(A) ),
inference(paramod,[status(thm)],[c_80,c_122]) ).
fof(axiom_9,axiom,
! [VAR_0] :
( fwork_DOTfifo_DOTrtl_DOTint__level_(VAR_0) = n0
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(VAR_0)) ),
file('theBenchmark.p',axiom_9) ).
cnf(c_186,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) = n0
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_187,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_186]) ).
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_188,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != n0
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_189,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_188]) ).
cnf(c_12575,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,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ),
inference(resolve,[status(thm)],[c_123,c_13]) ).
cnf(c_12576,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,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ),
inference(resolve,[status(thm)],[c_12,c_12575]) ).
cnf(c_806,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ),
inference(resolve,[status(thm)],[c_11,c_12576]) ).
cnf(c_12577,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_),
inference(resolve,[status(thm)],[c_187,c_10]) ).
cnf(c_1055,plain,
f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(copy,[status(thm)],[c_12577]) ).
cnf(c_12578,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ),
inference(paramod,[status(thm)],[c_1055,c_806]) ).
cnf(c_1252,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(resolve,[status(thm)],[c_88,c_12578]) ).
cnf(c_12579,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(paramod,[status(thm)],[c_1055,c_189]) ).
cnf(c_1352,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != fwork_DOTfifo_DOTrtl_DOTint__level_(A)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(copy,[status(thm)],[c_12579]) ).
cnf(c_12580,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(copy,[status(thm)],[c_1352]) ).
cnf(c_12581,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
inference(resolve,[status(thm)],[c_1252,c_12580]) ).
cnf(c_12574,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_12581]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HWV020-2 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 15:57:02 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2705538 was started by sandbox2 on n017,
% 0.18/0.45 % Fri Sep 25 15:57:02 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 39.20/5.55
% 39.20/5.55 % given #500 (F,wt=22): 6617 -p__pred_(f__nand_(f__geq_(A,A),fwork_DOTfifo_DOTrtl_DOTrd_(t_206))). [resolve(331,a,634,a)].
% 39.20/5.55
% 39.20/5.55 % SZS status Unsatisfiable for theBenchmark
% 39.20/5.55
% 39.20/5.55 % Proof 1 at 4.46 (+ 0.54) seconds.
% 39.20/5.55 % Length of proof is 19.
% 39.20/5.55 % Level of proof is 5.
% 39.20/5.55 % Maximum clause weight is 36.000.
% 39.20/5.55 % Given clauses 636.
% 39.20/5.55
% 39.20/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------