%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV021-2 : 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 : 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 07:34:21 AM UTC 2026
% Result : Unsatisfiable 8.91s 6.54s
% Output : CNFRefutation 8.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 68 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quest_4,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
file('theBenchmark.p',quest_4) ).
cnf(c_9,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
inference(clausify,[status(thm)],[quest_4]) ).
fof(quest_3,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('theBenchmark.p',quest_3) ).
cnf(c_10,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(clausify,[status(thm)],[quest_3]) ).
fof(quest_2,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('theBenchmark.p',quest_2) ).
cnf(c_11,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1))),
file('theBenchmark.p',quest_1) ).
cnf(c_12,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1))),
inference(clausify,[status(thm)],[quest_1]) ).
fof(axiom_68,axiom,
! [VAR_0,VAR_1] :
( p_LES_EQU_(f_ADD_(VAR_1,n1),VAR_0)
| ~ p_LES_EQU_(VAR_1,VAR_0)
| VAR_0 = VAR_1 ),
file('theBenchmark.p',axiom_68) ).
cnf(c_91,plain,
( p_LES_EQU_(f_ADD_(B,n1),A)
| ~ p_LES_EQU_(B,A)
| A = B ),
inference(clausify,[status(thm)],[axiom_68]) ).
fof(axiom_60,axiom,
! [VAR_0] : ~ p_LES_EQU_(f_ADD_(VAR_0,n1),n0),
file('theBenchmark.p',axiom_60) ).
cnf(c_95,plain,
~ p_LES_EQU_(f_ADD_(A,n1),n0),
inference(clausify,[status(thm)],[axiom_60]) ).
fof(axiom_46,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)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(VAR_0,n1))) ),
file('theBenchmark.p',axiom_46) ).
cnf(c_109,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)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(A,n1))) ),
inference(clausify,[status(thm)],[axiom_46]) ).
fof(axiom_34,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)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(VAR_0,n1))) ),
file('theBenchmark.p',axiom_34) ).
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),n0)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(A,n1))) ),
inference(clausify,[status(thm)],[axiom_34]) ).
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_151,plain,
( fwork_DOTfifo_DOTrtl_DOTint__level_(A) != n0
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(A)) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_7428,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(resolve,[status(thm)],[c_109,c_12]) ).
cnf(c_7429,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),n0) ),
inference(resolve,[status(thm)],[c_10,c_7428]) ).
cnf(c_1257,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(resolve,[status(thm)],[c_11,c_7429]) ).
cnf(c_7430,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(resolve,[status(thm)],[c_123,c_12]) ).
cnf(c_7431,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),n0) ),
inference(resolve,[status(thm)],[c_10,c_7430]) ).
cnf(c_1426,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(resolve,[status(thm)],[c_11,c_7431]) ).
cnf(c_7432,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0)
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(resolve,[status(thm)],[c_1426,c_1257]) ).
cnf(c_7414,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0),
inference(copy,[status(thm)],[c_7432]) ).
cnf(c_7433,plain,
( p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1),n0)
| n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ),
inference(resolve,[status(thm)],[c_7414,c_91]) ).
cnf(c_7434,plain,
( p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1),n0)
| fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 ),
inference(copy,[status(thm)],[c_7433]) ).
cnf(c_7418,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0,
inference(resolve,[status(thm)],[c_95,c_7434]) ).
cnf(c_7435,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
inference(resolve,[status(thm)],[c_7418,c_151]) ).
cnf(c_7427,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_7435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV021-2 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n019.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 16:02:09 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3188144 was started by sandbox2 on n019,
% 0.10/5.38 % Fri Sep 25 16:02:09 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 8.91/6.54
% 8.91/6.54 % SZS status Unsatisfiable for theBenchmark
% 8.91/6.54
% 8.91/6.54 % Proof 1 at 1.05 (+ 0.09) seconds.
% 8.91/6.54 % Length of proof is 14.
% 8.91/6.54 % Level of proof is 4.
% 8.91/6.54 % Maximum clause weight is 33.000.
% 8.91/6.54 % Given clauses 275.
% 8.91/6.54
% 8.91/6.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------