%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV022-1 : 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 : n004.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 5.39s 11.38s
% Output : CNFRefutation 5.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 95 ( 44 unt; 0 def)
% Number of atoms : 192 ( 78 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 47 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_6,axiom,
! [VAR_0,VAR_1] :
( ~ gt(VAR_1,VAR_0)
| ~ def_10(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_6) ).
cnf(c_1,plain,
( ~ gt(B,A)
| ~ def_10(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( def_10(VAR_1,VAR_0)
| plus(VAR_2,VAR_1) = VAR_0
| minus(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',axiom_4) ).
cnf(c_3,plain,
( def_10(B,A)
| plus(C,B) = A
| minus(A,B) != C ),
inference(clausify,[status(thm)],[axiom_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_23,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_3,axiom,
p_Wr(t_139),
file('theBenchmark.p',quest_3) ).
cnf(c_32,plain,
p_Wr(t_139),
inference(clausify,[status(thm)],[quest_3]) ).
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_56,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_65,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_83,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_65,c_32]) ).
cnf(c_170,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_56,c_23]) ).
cnf(c_2004,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_170]) ).
cnf(c_2005,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_2004]) ).
cnf(c_171,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_2005]) ).
fof(axiom_1,axiom,
! [VAR_0] : plus(VAR_0,n1) != n0,
file('theBenchmark.p',axiom_1) ).
cnf(c_465,plain,
plus(A,n1) != n0,
inference(clausify,[status(thm)],[axiom_1]) ).
fof(axiom_2,axiom,
! [VAR_0] : gt(plus(VAR_0,n1),n0),
file('theBenchmark.p',axiom_2) ).
cnf(c_466,plain,
gt(plus(A,n1),n0),
inference(clausify,[status(thm)],[axiom_2]) ).
fof(axiom_3,axiom,
! [VAR_0] :
( gt(VAR_0,minus(VAR_0,n1))
| ~ gt(VAR_0,n0) ),
file('theBenchmark.p',axiom_3) ).
cnf(c_467,plain,
( gt(A,minus(A,n1))
| ~ gt(A,n0) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_8,axiom,
! [VAR_0,VAR_1] :
( gt(plus(VAR_0,n1),plus(VAR_1,n1))
| ~ gt(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_468,plain,
( gt(plus(A,n1),plus(B,n1))
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
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_472,plain,
( gt(B,A)
| B = A
| gt(A,B) ),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(axiom_13,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ gt(VAR_1,VAR_2)
| gt(VAR_0,VAR_2)
| ~ gt(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_13) ).
cnf(c_473,plain,
( ~ gt(B,C)
| gt(A,C)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[axiom_13]) ).
fof(axiom_15,axiom,
! [VAR_0] :
( gt(VAR_0,n0)
| VAR_0 = n0 ),
file('theBenchmark.p',axiom_15) ).
cnf(c_475,plain,
( gt(A,n0)
| A = n0 ),
inference(clausify,[status(thm)],[axiom_15]) ).
cnf(c_476,plain,
( gt(A,n0)
| n0 = A ),
inference(copy,[status(thm)],[c_475]) ).
fof(axiom_16,axiom,
! [VAR_0] :
( VAR_0 = plus(y_27(VAR_0),n1)
| VAR_0 = n0 ),
file('theBenchmark.p',axiom_16) ).
cnf(c_477,plain,
( A = plus(y_27(A),n1)
| A = n0 ),
inference(clausify,[status(thm)],[axiom_16]) ).
cnf(c_2006,plain,
( A = plus(y_27(A),n1)
| n0 = A ),
inference(copy,[status(thm)],[c_477]) ).
cnf(c_478,plain,
( plus(y_27(A),n1) = A
| n0 = A ),
inference(copy,[status(thm)],[c_2006]) ).
fof(axiom_18,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| plus(VAR_0,n1) != plus(VAR_1,n1) ),
file('theBenchmark.p',axiom_18) ).
cnf(c_480,plain,
( A = B
| plus(A,n1) != plus(B,n1) ),
inference(clausify,[status(thm)],[axiom_18]) ).
fof(axiom_19,axiom,
! [VAR_0] : plus(n0,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_19) ).
cnf(c_481,plain,
plus(n0,A) = A,
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_21,axiom,
! [VAR_0] : level(VAR_0) = int_level(VAR_0),
file('theBenchmark.p',axiom_21) ).
cnf(c_483,plain,
level(A) = int_level(A),
inference(clausify,[status(thm)],[axiom_21]) ).
fof(quest_1,axiom,
plus(level(t_139),n1) = fifo_length,
file('theBenchmark.p',quest_1) ).
cnf(c_491,plain,
plus(level(t_139),n1) = fifo_length,
inference(clausify,[status(thm)],[quest_1]) ).
cnf(c_2007,plain,
plus(int_level(t_139),n1) = fifo_length,
inference(paramod,[status(thm)],[c_483,c_491]) ).
cnf(c_492,plain,
fifo_length = plus(int_level(t_139),n1),
inference(copy,[status(thm)],[c_2007]) ).
fof(quest_2,axiom,
~ p_Rd(t_139),
file('theBenchmark.p',quest_2) ).
cnf(c_493,plain,
~ p_Rd(t_139),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_4,axiom,
~ p_Reset(t_139),
file('theBenchmark.p',quest_4) ).
cnf(c_494,plain,
~ p_Reset(t_139),
inference(clausify,[status(thm)],[quest_4]) ).
fof(quest_5,axiom,
level(plus(t_139,n1)) != fifo_length,
file('theBenchmark.p',quest_5) ).
cnf(c_495,plain,
level(plus(t_139,n1)) != fifo_length,
inference(clausify,[status(thm)],[quest_5]) ).
cnf(c_2008,plain,
int_level(plus(t_139,n1)) != fifo_length,
inference(paramod,[status(thm)],[c_483,c_495]) ).
cnf(c_496,plain,
int_level(plus(t_139,n1)) != plus(int_level(t_139),n1),
inference(paramod,[status(thm)],[c_492,c_2008]) ).
cnf(c_498,plain,
( plus(C,B) = A
| minus(A,B) != C
| ~ gt(A,B) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_531,plain,
( int_level(plus(A,n1)) = int_level(A)
| gt(plus(int_level(t_139),n1),int_level(A))
| p_Rd(A)
| p_Reset(A) ),
inference(paramod,[status(thm)],[c_492,c_171]) ).
cnf(c_2009,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| ~ gt(plus(int_level(t_139),n1),int_level(t_139))
| p_Rd(t_139)
| p_Reset(t_139) ),
inference(paramod,[status(thm)],[c_492,c_83]) ).
cnf(c_2010,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| ~ gt(plus(int_level(t_139),n1),int_level(t_139))
| p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_494,c_2009]) ).
cnf(c_2011,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| ~ gt(plus(int_level(t_139),n1),int_level(t_139)) ),
inference(resolve,[status(thm)],[c_493,c_2010]) ).
cnf(c_564,plain,
~ gt(plus(int_level(t_139),n1),int_level(t_139)),
inference(resolve,[status(thm)],[c_496,c_2011]) ).
cnf(c_594,plain,
( gt(A,n0)
| ~ gt(A,plus(B,n1)) ),
inference(resolve,[status(thm)],[c_473,c_466]) ).
cnf(c_600,plain,
( gt(A,minus(A,n1))
| n0 = A ),
inference(resolve,[status(thm)],[c_476,c_467]) ).
cnf(c_2012,plain,
( n0 = plus(A,n1)
| y_27(plus(A,n1)) = A ),
inference(resolve,[status(thm)],[c_480,c_478]) ).
cnf(c_2013,plain,
( plus(A,n1) = n0
| y_27(plus(A,n1)) = A ),
inference(copy,[status(thm)],[c_2012]) ).
cnf(c_624,plain,
y_27(plus(A,n1)) = A,
inference(resolve,[status(thm)],[c_465,c_2013]) ).
cnf(c_2014,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolve,[status(thm)],[c_564,c_531]) ).
cnf(c_2015,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| p_Rd(t_139) ),
inference(resolve,[status(thm)],[c_494,c_2014]) ).
cnf(c_746,plain,
int_level(plus(t_139,n1)) = int_level(t_139),
inference(resolve,[status(thm)],[c_493,c_2015]) ).
cnf(c_747,plain,
( plus(int_level(t_139),n1) = int_level(t_139)
| gt(int_level(t_139),plus(int_level(t_139),n1)) ),
inference(resolve,[status(thm)],[c_564,c_472]) ).
cnf(c_2016,plain,
int_level(t_139) != plus(int_level(t_139),n1),
inference(paramod,[status(thm)],[c_746,c_496]) ).
cnf(c_748,plain,
plus(int_level(t_139),n1) != int_level(t_139),
inference(copy,[status(thm)],[c_2016]) ).
cnf(c_749,plain,
gt(int_level(t_139),plus(int_level(t_139),n1)),
inference(resolve,[status(thm)],[c_748,c_747]) ).
cnf(c_860,plain,
( ~ gt(plus(int_level(t_139),n1),A)
| gt(int_level(t_139),A) ),
inference(resolve,[status(thm)],[c_749,c_473]) ).
cnf(c_873,plain,
gt(int_level(t_139),n0),
inference(resolve,[status(thm)],[c_594,c_749]) ).
cnf(c_2017,plain,
gt(plus(int_level(t_139),n1),plus(n0,n1)),
inference(resolve,[status(thm)],[c_873,c_468]) ).
cnf(c_894,plain,
gt(plus(int_level(t_139),n1),n1),
inference(paramod,[status(thm)],[c_481,c_2017]) ).
cnf(c_895,plain,
gt(int_level(t_139),minus(int_level(t_139),n1)),
inference(resolve,[status(thm)],[c_873,c_467]) ).
cnf(c_899,plain,
( gt(A,n1)
| ~ gt(A,plus(int_level(t_139),n1)) ),
inference(resolve,[status(thm)],[c_894,c_473]) ).
cnf(c_954,plain,
gt(plus(int_level(t_139),n1),plus(minus(int_level(t_139),n1),n1)),
inference(resolve,[status(thm)],[c_895,c_468]) ).
cnf(c_995,plain,
( gt(B,minus(A,n1))
| ~ gt(B,A)
| n0 = A ),
inference(resolve,[status(thm)],[c_600,c_473]) ).
cnf(c_1174,plain,
gt(int_level(t_139),n1),
inference(resolve,[status(thm)],[c_899,c_749]) ).
cnf(c_2018,plain,
( plus(A,n1) = int_level(t_139)
| minus(int_level(t_139),n1) != A ),
inference(resolve,[status(thm)],[c_1174,c_498]) ).
cnf(c_1183,plain,
( int_level(t_139) = plus(A,n1)
| minus(int_level(t_139),n1) != A ),
inference(copy,[status(thm)],[c_2018]) ).
cnf(c_1474,plain,
gt(int_level(t_139),plus(minus(int_level(t_139),n1),n1)),
inference(resolve,[status(thm)],[c_954,c_860]) ).
cnf(c_2019,plain,
( gt(int_level(t_139),minus(plus(minus(int_level(t_139),n1),n1),n1))
| n0 = plus(minus(int_level(t_139),n1),n1) ),
inference(resolve,[status(thm)],[c_995,c_1474]) ).
cnf(c_2020,plain,
( gt(int_level(t_139),minus(plus(minus(int_level(t_139),n1),n1),n1))
| plus(minus(int_level(t_139),n1),n1) = n0 ),
inference(copy,[status(thm)],[c_2019]) ).
cnf(c_1504,plain,
gt(int_level(t_139),minus(plus(minus(int_level(t_139),n1),n1),n1)),
inference(resolve,[status(thm)],[c_465,c_2020]) ).
cnf(c_1720,plain,
gt(plus(int_level(t_139),n1),plus(minus(plus(minus(int_level(t_139),n1),n1),n1),n1)),
inference(resolve,[status(thm)],[c_1504,c_468]) ).
cnf(c_2021,plain,
A = y_27(plus(A,n1)),
inference(copy,[status(thm)],[c_624]) ).
cnf(c_2022,plain,
int_level(t_139) = plus(y_27(plus(minus(int_level(t_139),n1),n1)),n1),
inference(resolve,[status(thm)],[c_1183,c_2021]) ).
cnf(c_2023,plain,
int_level(t_139) = plus(minus(int_level(t_139),n1),n1),
inference(paramod,[status(thm)],[c_624,c_2022]) ).
cnf(c_2001,plain,
plus(minus(int_level(t_139),n1),n1) = int_level(t_139),
inference(copy,[status(thm)],[c_2023]) ).
cnf(c_2024,plain,
gt(plus(int_level(t_139),n1),plus(minus(int_level(t_139),n1),n1)),
inference(paramod,[status(thm)],[c_2001,c_1720]) ).
cnf(c_2025,plain,
gt(plus(int_level(t_139),n1),int_level(t_139)),
inference(paramod,[status(thm)],[c_2001,c_2024]) ).
cnf(c_2003,plain,
$false,
inference(resolve,[status(thm)],[c_564,c_2025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV022-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/10.61 % Computer : n004.cluster.edu
% 0.13/10.61 % Model : x86_64 x86_64
% 0.13/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.61 % Memory : 8046.5625MB
% 0.13/10.61 % OS : Linux 6.8.0-71-generic
% 0.13/10.61 % CPULimit : 300
% 0.13/10.61 % WCLimit : 300
% 0.13/10.61 % DateTime : Fri Sep 25 16:02:03 UTC 2026
% 0.13/10.61 % CPUTime :
% 0.13/10.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/10.62 % Process 3608912 was started by sandbox2 on n004,
% 0.13/10.62 % Fri Sep 25 16:02:03 2026
% 0.13/10.62 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/10.63
% 0.13/10.63 % From the command line: assign(max_seconds, 300).
% 5.39/11.38
% 5.39/11.38 % SZS status Unsatisfiable for theBenchmark
% 5.39/11.38
% 5.39/11.38 % Proof 1 at 0.60 (+ 0.13) seconds.
% 5.39/11.38 % Length of proof is 52.
% 5.39/11.38 % Level of proof is 13.
% 5.39/11.38 % Maximum clause weight is 18.000.
% 5.39/11.38 % Given clauses 321.
% 5.39/11.38
% 5.39/11.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------