%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV020-1 : 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 : n015.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 2.02s 0.73s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 102 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 81 ( 19 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_76,axiom,
! [VAR_0] :
( p_Rd_error(plus(VAR_0,n1))
| gt(int_level(VAR_0),n0)
| ~ p_Rd(VAR_0)
| p_Wr(VAR_0)
| p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_76) ).
cnf(c_49,plain,
( p_Rd_error(plus(A,n1))
| gt(int_level(A),n0)
| ~ p_Rd(A)
| p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_76]) ).
fof(axiom_78,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = int_level(VAR_0)
| gt(int_level(VAR_0),n0)
| ~ p_Rd(VAR_0)
| p_Wr(VAR_0)
| p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_78) ).
cnf(c_51,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(int_level(A),n0)
| ~ p_Rd(A)
| p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_78]) ).
fof(axiom_82,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = int_level(VAR_0)
| p_Rd(VAR_0)
| p_Wr(VAR_0)
| p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_82) ).
cnf(c_55,plain,
( int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_82]) ).
fof(quest_1,axiom,
p_Rd(t_139),
file('theBenchmark.p',quest_1) ).
cnf(c_60,plain,
p_Rd(t_139),
inference(clausify,[status(thm)],[quest_1]) ).
cnf(c_67,plain,
( p_Rd_error(plus(t_139,n1))
| gt(int_level(t_139),n0)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(resolve,[status(thm)],[c_60,c_49]) ).
cnf(c_129,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(int_level(A),n0)
| p_Wr(A)
| p_Reset(A)
| int_level(plus(A,n1)) = int_level(A)
| p_Wr(A)
| p_Reset(A) ),
inference(resolve,[status(thm)],[c_55,c_51]) ).
cnf(c_926,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(int_level(A),n0)
| p_Wr(A)
| int_level(plus(A,n1)) = int_level(A)
| p_Wr(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_927,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(int_level(A),n0)
| int_level(plus(A,n1)) = int_level(A)
| p_Wr(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_926]) ).
cnf(c_130,plain,
( gt(int_level(A),n0)
| int_level(plus(A,n1)) = int_level(A)
| p_Wr(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_927]) ).
fof(quest_5,axiom,
( ~ p_Rd_error(plus(t_139,n1))
| ~ p_Empty(plus(t_139,n1)) ),
file('theBenchmark.p',quest_5) ).
cnf(c_563,plain,
( ~ p_Rd_error(plus(t_139,n1))
| ~ p_Empty(plus(t_139,n1)) ),
inference(clausify,[status(thm)],[quest_5]) ).
fof(quest_4,axiom,
~ p_Reset(t_139),
file('theBenchmark.p',quest_4) ).
cnf(c_564,plain,
~ p_Reset(t_139),
inference(clausify,[status(thm)],[quest_4]) ).
fof(quest_3,axiom,
~ p_Wr(t_139),
file('theBenchmark.p',quest_3) ).
cnf(c_565,plain,
~ p_Wr(t_139),
inference(clausify,[status(thm)],[quest_3]) ).
fof(quest_2,axiom,
p_Empty(t_139),
file('theBenchmark.p',quest_2) ).
cnf(c_566,plain,
p_Empty(t_139),
inference(clausify,[status(thm)],[quest_2]) ).
fof(axiom_25,axiom,
! [VAR_0] :
( ~ p_Empty(VAR_0)
| int_level(VAR_0) = n0 ),
file('theBenchmark.p',axiom_25) ).
cnf(c_579,plain,
( ~ p_Empty(A)
| int_level(A) = n0 ),
inference(clausify,[status(thm)],[axiom_25]) ).
fof(axiom_24,axiom,
! [VAR_0] :
( p_Empty(VAR_0)
| int_level(VAR_0) != n0 ),
file('theBenchmark.p',axiom_24) ).
cnf(c_580,plain,
( p_Empty(A)
| int_level(A) != n0 ),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_17,axiom,
! [VAR_0] : ~ gt(VAR_0,VAR_0),
file('theBenchmark.p',axiom_17) ).
cnf(c_586,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[axiom_17]) ).
cnf(c_928,plain,
( p_Rd_error(plus(t_139,n1))
| gt(int_level(t_139),n0)
| p_Wr(t_139) ),
inference(resolve,[status(thm)],[c_564,c_67]) ).
cnf(c_623,plain,
( p_Rd_error(plus(t_139,n1))
| gt(int_level(t_139),n0) ),
inference(resolve,[status(thm)],[c_565,c_928]) ).
cnf(c_653,plain,
int_level(t_139) = n0,
inference(resolve,[status(thm)],[c_579,c_566]) ).
cnf(c_929,plain,
( p_Rd_error(plus(t_139,n1))
| gt(n0,n0) ),
inference(paramod,[status(thm)],[c_653,c_623]) ).
cnf(c_654,plain,
p_Rd_error(plus(t_139,n1)),
inference(resolve,[status(thm)],[c_586,c_929]) ).
cnf(c_655,plain,
~ p_Empty(plus(t_139,n1)),
inference(resolve,[status(thm)],[c_654,c_563]) ).
cnf(c_930,plain,
( gt(n0,n0)
| int_level(plus(t_139,n1)) = int_level(t_139)
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_653,c_130]) ).
cnf(c_931,plain,
( gt(n0,n0)
| int_level(plus(t_139,n1)) = n0
| p_Wr(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_653,c_930]) ).
cnf(c_932,plain,
( gt(n0,n0)
| int_level(plus(t_139,n1)) = n0
| p_Wr(t_139) ),
inference(resolve,[status(thm)],[c_564,c_931]) ).
cnf(c_933,plain,
( gt(n0,n0)
| int_level(plus(t_139,n1)) = n0 ),
inference(resolve,[status(thm)],[c_565,c_932]) ).
cnf(c_905,plain,
int_level(plus(t_139,n1)) = n0,
inference(resolve,[status(thm)],[c_586,c_933]) ).
cnf(c_934,plain,
p_Empty(plus(t_139,n1)),
inference(resolve,[status(thm)],[c_905,c_580]) ).
cnf(c_925,plain,
$false,
inference(resolve,[status(thm)],[c_655,c_934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV020-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 16:04:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1783953 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 16:04:57 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 2.02/0.73
% 2.02/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.02/0.73
% 2.02/0.73 % Proof 1 at 0.23 (+ 0.02) seconds.
% 2.02/0.73 % Length of proof is 20.
% 2.02/0.73 % Level of proof is 5.
% 2.02/0.73 % Maximum clause weight is 15.000.
% 2.02/0.73 % Given clauses 237.
% 2.02/0.73
% 2.02/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------