%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV016-1 : 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 : n009.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 07:34:19 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.83s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 28 unt; 0 def)
% Number of atoms : 205 ( 68 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 187 ( 53 ~; 134 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 3 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_25,axiom,
! [VAR_0] :
( ~ p_Empty(VAR_0)
| int_level(VAR_0) = n0 ),
file('theBenchmark.p',axiom_25) ).
cnf(c_7,plain,
( ~ p_Empty(A)
| int_level(A) = n0 ),
inference(clausify,[status(thm)],[axiom_25]) ).
fof(quest_4,axiom,
p_Empty(plus(t_139,n1)),
file('theBenchmark.p',quest_4) ).
cnf(c_9,plain,
p_Empty(plus(t_139,n1)),
inference(clausify,[status(thm)],[quest_4]) ).
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_24,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_2,axiom,
p_Wr(t_139),
file('theBenchmark.p',quest_2) ).
cnf(c_33,plain,
p_Wr(t_139),
inference(clausify,[status(thm)],[quest_2]) ).
fof(axiom_59,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = plus(int_level(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_59) ).
cnf(c_42,plain,
( int_level(plus(A,n1)) = plus(int_level(A),n1)
| gt(int_level(A),n0)
| ~ p_Rd(A)
| ~ p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_59]) ).
fof(axiom_53,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_53) ).
cnf(c_48,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_53]) ).
fof(axiom_44,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = int_level(VAR_0)
| gt(fifo_length,int_level(VAR_0))
| p_Rd(VAR_0)
| ~ p_Wr(VAR_0)
| p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_44) ).
cnf(c_57,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(fifo_length,int_level(A))
| p_Rd(A)
| ~ p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_44]) ).
fof(axiom_35,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = plus(int_level(VAR_0),n1)
| ~ gt(fifo_length,int_level(VAR_0))
| p_Rd(VAR_0)
| ~ p_Wr(VAR_0)
| p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_35) ).
cnf(c_66,plain,
( int_level(plus(A,n1)) = plus(int_level(A),n1)
| ~ gt(fifo_length,int_level(A))
| p_Rd(A)
| ~ p_Wr(A)
| p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_35]) ).
cnf(c_84,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| ~ gt(fifo_length,int_level(t_139))
| p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolve,[status(thm)],[c_66,c_33]) ).
cnf(c_92,plain,
( int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Reset(A)
| int_level(plus(A,n1)) = plus(int_level(A),n1)
| ~ gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(resolve,[status(thm)],[c_66,c_24]) ).
cnf(c_1202,plain,
( int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| int_level(plus(A,n1)) = plus(int_level(A),n1)
| ~ gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_93,plain,
( int_level(plus(A,n1)) = int_level(A)
| int_level(plus(A,n1)) = plus(int_level(A),n1)
| ~ gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_1202]) ).
cnf(c_171,plain,
( int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Reset(A)
| int_level(plus(A,n1)) = int_level(A)
| gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(resolve,[status(thm)],[c_57,c_24]) ).
cnf(c_1203,plain,
( int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| int_level(plus(A,n1)) = int_level(A)
| gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_171]) ).
cnf(c_1204,plain,
( int_level(plus(A,n1)) = int_level(A)
| int_level(plus(A,n1)) = int_level(A)
| gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_1203]) ).
cnf(c_172,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(fifo_length,int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_1204]) ).
cnf(c_233,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| ~ gt(int_level(t_139),n0)
| ~ p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolve,[status(thm)],[c_48,c_33]) ).
cnf(c_279,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| gt(int_level(t_139),n0)
| ~ p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolve,[status(thm)],[c_42,c_33]) ).
fof(axiom_1,axiom,
! [VAR_0] : plus(VAR_0,n1) != n0,
file('theBenchmark.p',axiom_1) ).
cnf(c_466,plain,
plus(A,n1) != n0,
inference(clausify,[status(thm)],[axiom_1]) ).
fof(axiom_12,axiom,
! [VAR_0,VAR_1] :
( gt(VAR_1,VAR_0)
| VAR_1 = VAR_0
| gt(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_12) ).
cnf(c_473,plain,
( gt(B,A)
| B = A
| gt(A,B) ),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(axiom_17,axiom,
! [VAR_0] : ~ gt(VAR_0,VAR_0),
file('theBenchmark.p',axiom_17) ).
cnf(c_480,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[axiom_17]) ).
fof(axiom_21,axiom,
! [VAR_0] : level(VAR_0) = int_level(VAR_0),
file('theBenchmark.p',axiom_21) ).
cnf(c_484,plain,
level(A) = int_level(A),
inference(clausify,[status(thm)],[axiom_21]) ).
fof(quest_1,axiom,
~ gt(n0,level(t_139)),
file('theBenchmark.p',quest_1) ).
cnf(c_492,plain,
~ gt(n0,level(t_139)),
inference(clausify,[status(thm)],[quest_1]) ).
cnf(c_493,plain,
~ gt(n0,int_level(t_139)),
inference(paramod,[status(thm)],[c_484,c_492]) ).
fof(quest_3,axiom,
~ p_Reset(t_139),
file('theBenchmark.p',quest_3) ).
cnf(c_494,plain,
~ p_Reset(t_139),
inference(clausify,[status(thm)],[quest_3]) ).
fof(quest_5,axiom,
gt(fifo_length,n0),
file('theBenchmark.p',quest_5) ).
cnf(c_495,plain,
gt(fifo_length,n0),
inference(clausify,[status(thm)],[quest_5]) ).
cnf(c_500,plain,
int_level(plus(t_139,n1)) = n0,
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_501,plain,
n0 = int_level(plus(t_139,n1)),
inference(copy,[status(thm)],[c_500]) ).
cnf(c_1205,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| gt(int_level(t_139),int_level(plus(t_139,n1)))
| ~ p_Rd(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_501,c_279]) ).
cnf(c_522,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| gt(int_level(t_139),int_level(plus(t_139,n1)))
| ~ p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_494,c_1205]) ).
cnf(c_1206,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| ~ gt(int_level(t_139),int_level(plus(t_139,n1)))
| ~ p_Rd(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_501,c_233]) ).
cnf(c_523,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| ~ gt(int_level(t_139),int_level(plus(t_139,n1)))
| ~ p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_494,c_1206]) ).
cnf(c_530,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| ~ gt(fifo_length,int_level(t_139))
| p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_494,c_84]) ).
cnf(c_532,plain,
gt(fifo_length,int_level(plus(t_139,n1))),
inference(paramod,[status(thm)],[c_501,c_495]) ).
cnf(c_533,plain,
~ gt(int_level(plus(t_139,n1)),int_level(t_139)),
inference(paramod,[status(thm)],[c_501,c_493]) ).
cnf(c_1207,plain,
plus(A,n1) != int_level(plus(t_139,n1)),
inference(paramod,[status(thm)],[c_501,c_466]) ).
cnf(c_542,plain,
int_level(plus(t_139,n1)) != plus(A,n1),
inference(copy,[status(thm)],[c_1207]) ).
cnf(c_577,plain,
( ~ gt(fifo_length,int_level(t_139))
| p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_542,c_530]) ).
cnf(c_578,plain,
( gt(int_level(t_139),int_level(plus(t_139,n1)))
| ~ p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_542,c_522]) ).
cnf(c_1208,plain,
( int_level(plus(A,n1)) = int_level(A)
| int_level(plus(A,n1)) = plus(int_level(A),n1)
| p_Rd(A)
| p_Reset(A)
| int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Reset(A) ),
inference(resolve,[status(thm)],[c_172,c_93]) ).
cnf(c_1209,plain,
( int_level(plus(A,n1)) = int_level(A)
| int_level(plus(A,n1)) = plus(int_level(A),n1)
| p_Rd(A)
| int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_1208]) ).
cnf(c_1210,plain,
( int_level(plus(A,n1)) = int_level(A)
| int_level(plus(A,n1)) = plus(int_level(A),n1)
| int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_1209]) ).
cnf(c_581,plain,
( int_level(plus(A,n1)) = plus(int_level(A),n1)
| int_level(plus(A,n1)) = int_level(A)
| p_Rd(A)
| p_Reset(A) ),
inference(copy,[status(thm)],[c_1210]) ).
cnf(c_1211,plain,
( int_level(t_139) = int_level(plus(t_139,n1))
| gt(int_level(plus(t_139,n1)),int_level(t_139))
| int_level(plus(t_139,n1)) = int_level(t_139)
| ~ p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_523,c_473]) ).
cnf(c_1212,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| gt(int_level(plus(t_139,n1)),int_level(t_139))
| int_level(plus(t_139,n1)) = int_level(t_139)
| ~ p_Rd(t_139) ),
inference(copy,[status(thm)],[c_1211]) ).
cnf(c_1213,plain,
( gt(int_level(plus(t_139,n1)),int_level(t_139))
| int_level(plus(t_139,n1)) = int_level(t_139)
| ~ p_Rd(t_139) ),
inference(copy,[status(thm)],[c_1212]) ).
cnf(c_620,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| ~ p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_533,c_1213]) ).
cnf(c_1214,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| int_level(plus(t_139,n1)) = int_level(t_139)
| p_Reset(t_139)
| int_level(plus(t_139,n1)) = int_level(t_139) ),
inference(resolve,[status(thm)],[c_620,c_581]) ).
cnf(c_1215,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| p_Reset(t_139)
| int_level(plus(t_139,n1)) = int_level(t_139) ),
inference(copy,[status(thm)],[c_1214]) ).
cnf(c_1216,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| int_level(plus(t_139,n1)) = int_level(t_139) ),
inference(resolve,[status(thm)],[c_494,c_1215]) ).
cnf(c_991,plain,
int_level(plus(t_139,n1)) = int_level(t_139),
inference(resolve,[status(thm)],[c_542,c_1216]) ).
cnf(c_1217,plain,
( gt(int_level(t_139),int_level(t_139))
| ~ p_Rd(t_139) ),
inference(paramod,[status(thm)],[c_991,c_578]) ).
cnf(c_1151,plain,
~ p_Rd(t_139),
inference(resolve,[status(thm)],[c_480,c_1217]) ).
cnf(c_1190,plain,
gt(fifo_length,int_level(t_139)),
inference(paramod,[status(thm)],[c_991,c_532]) ).
cnf(c_1218,plain,
~ gt(fifo_length,int_level(t_139)),
inference(resolve,[status(thm)],[c_1151,c_577]) ).
cnf(c_1201,plain,
$false,
inference(resolve,[status(thm)],[c_1190,c_1218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV016-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.58 % Computer : n009.cluster.edu
% 0.13/0.58 % Model : x86_64 x86_64
% 0.13/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.58 % Memory : 8046.5625MB
% 0.13/0.58 % OS : Linux 6.8.0-71-generic
% 0.13/0.58 % CPULimit : 300
% 0.13/0.58 % WCLimit : 300
% 0.13/0.58 % DateTime : Fri Sep 25 16:00:59 UTC 2026
% 0.13/0.59 % CPUTime :
% 0.13/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.59 % Process 1993031 was started by sandbox2 on n009,
% 0.13/0.59 % Fri Sep 25 16:00:59 2026
% 0.13/0.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.60
% 0.13/0.60 % From the command line: assign(max_seconds, 300).
% 0.16/0.83
% 0.16/0.83 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.83
% 0.16/0.83 % Proof 1 at 0.21 (+ 0.02) seconds.
% 0.16/0.83 % Length of proof is 39.
% 0.16/0.83 % Level of proof is 7.
% 0.16/0.83 % Maximum clause weight is 24.000.
% 0.16/0.83 % Given clauses 183.
% 0.16/0.83
% 0.16/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------