%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV010-3 : 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 : 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 07:34:18 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 27 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quest_2,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
file('theBenchmark.p',quest_2) ).
cnf(c_9,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n0,
file('theBenchmark.p',quest_1) ).
cnf(c_10,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n0,
inference(clausify,[status(thm)],[quest_1]) ).
cnf(c_11,plain,
n0 = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(copy,[status(thm)],[c_10]) ).
fof(axiom_80,axiom,
f__length_(f__empty_) = n0,
file('theBenchmark.p',axiom_80) ).
cnf(c_75,plain,
f__length_(f__empty_) = n0,
inference(clausify,[status(thm)],[axiom_80]) ).
cnf(c_660,plain,
f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(paramod,[status(thm)],[c_11,c_75]) ).
cnf(c_76,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = f__length_(f__empty_),
inference(copy,[status(thm)],[c_660]) ).
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_181,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != n0
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_661,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(paramod,[status(thm)],[c_11,c_181]) ).
cnf(c_182,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != f__length_(f__empty_)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(paramod,[status(thm)],[c_76,c_661]) ).
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_185,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(A) = fwork_DOTfifo_DOTrtl_DOTint__level_(A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_662,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_),
inference(paramod,[status(thm)],[c_185,c_76]) ).
cnf(c_217,plain,
f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(copy,[status(thm)],[c_662]) ).
cnf(c_663,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_217,c_182]) ).
cnf(c_233,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_663]) ).
cnf(c_664,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
inference(xxres,[status(thm)],[c_233]) ).
cnf(c_659,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV010-3 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Fri Sep 25 15:56:02 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 2703268 was started by sandbox on n017,
% 0.07/0.36 % Fri Sep 25 15:56:02 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.47
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.47
% 0.13/0.47 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.13/0.47 % Length of proof is 11.
% 0.13/0.47 % Level of proof is 5.
% 0.13/0.47 % Maximum clause weight is 8.000.
% 0.13/0.47 % Given clauses 123.
% 0.13/0.47
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------