%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV010-2 : 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 : n019.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 0.94s 1.06s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 15 unt; 0 def)
% Number of atoms : 21 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 3 |; 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 : 5 ( 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]) ).
fof(axiom_80,axiom,
f__length_(f__empty_) = n0,
file('theBenchmark.p',axiom_80) ).
cnf(c_73,plain,
f__length_(f__empty_) = n0,
inference(clausify,[status(thm)],[axiom_80]) ).
cnf(c_74,plain,
n0 = f__length_(f__empty_),
inference(copy,[status(thm)],[c_73]) ).
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_177,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) = n0
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_178,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) = f__length_(f__empty_)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(paramod,[status(thm)],[c_74,c_177]) ).
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_183,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(A) = fwork_DOTfifo_DOTrtl_DOTint__level_(A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_768,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != n0,
inference(paramod,[status(thm)],[c_183,c_10]) ).
cnf(c_769,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != f__length_(f__empty_),
inference(paramod,[status(thm)],[c_74,c_768]) ).
cnf(c_199,plain,
f__length_(f__empty_) != fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(copy,[status(thm)],[c_769]) ).
cnf(c_770,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_),
inference(resolve,[status(thm)],[c_178,c_9]) ).
cnf(c_771,plain,
f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(copy,[status(thm)],[c_770]) ).
cnf(c_767,plain,
$false,
inference(resolve,[status(thm)],[c_199,c_771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV010-2 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.93 % Computer : n019.cluster.edu
% 0.11/0.93 % Model : x86_64 x86_64
% 0.11/0.93 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.93 % Memory : 8046.5625MB
% 0.11/0.93 % OS : Linux 6.8.0-71-generic
% 0.11/0.93 % CPULimit : 300
% 0.11/0.93 % WCLimit : 300
% 0.11/0.93 % DateTime : Fri Sep 25 16:00:21 UTC 2026
% 0.11/0.93 % CPUTime :
% 0.11/0.94 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.94 % Process 3182504 was started by sandbox on n019,
% 0.11/0.94 % Fri Sep 25 16:00:21 2026
% 0.11/0.94 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.94
% 0.11/0.94 % From the command line: assign(max_seconds, 300).
% 0.94/1.06
% 0.94/1.06 % SZS status Unsatisfiable for theBenchmark
% 0.94/1.06
% 0.94/1.06 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.94/1.06 % Length of proof is 9.
% 0.94/1.06 % Level of proof is 3.
% 0.94/1.06 % Maximum clause weight is 8.000.
% 0.94/1.06 % Given clauses 124.
% 0.94/1.06
% 0.94/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------