%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV028-1 : 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 : n013.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 07:34:23 AM UTC 2026
% Result : Unsatisfiable 10.97s 2.84s
% Output : CNFRefutation 10.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 23 unt; 0 def)
% Number of atoms : 39 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quest_1,axiom,
p_Reset(t_139),
file('theBenchmark.p',quest_1) ).
cnf(c_68,plain,
p_Reset(t_139),
inference(clausify,[status(thm)],[quest_1]) ).
fof(axiom_26,axiom,
! [VAR_0] :
( int_level(plus(VAR_0,n1)) = n0
| ~ p_Reset(VAR_0) ),
file('theBenchmark.p',axiom_26) ).
cnf(c_74,plain,
( int_level(plus(A,n1)) = n0
| ~ p_Reset(A) ),
inference(clausify,[status(thm)],[axiom_26]) ).
cnf(c_501,plain,
int_level(plus(t_139,n1)) = n0,
inference(resolve,[status(thm)],[c_74,c_68]) ).
cnf(c_502,plain,
n0 = int_level(plus(t_139,n1)),
inference(copy,[status(thm)],[c_501]) ).
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_517,plain,
( gt(plus(A,n1),plus(B,n1))
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
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_522,plain,
( ~ gt(B,C)
| gt(A,C)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[axiom_13]) ).
fof(axiom_17,axiom,
! [VAR_0] : ~ gt(VAR_0,VAR_0),
file('theBenchmark.p',axiom_17) ).
cnf(c_528,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[axiom_17]) ).
fof(axiom_19,axiom,
! [VAR_0] : plus(n0,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_19) ).
cnf(c_530,plain,
plus(n0,A) = A,
inference(clausify,[status(thm)],[axiom_19]) ).
cnf(c_531,plain,
plus(int_level(plus(t_139,n1)),A) = A,
inference(paramod,[status(thm)],[c_502,c_530]) ).
fof(axiom_21,axiom,
! [VAR_0] : level(VAR_0) = int_level(VAR_0),
file('theBenchmark.p',axiom_21) ).
cnf(c_533,plain,
level(A) = int_level(A),
inference(clausify,[status(thm)],[axiom_21]) ).
fof(quest_2,axiom,
gt(level(plus(t_139,n1)),fifo_length),
file('theBenchmark.p',quest_2) ).
cnf(c_534,plain,
gt(level(plus(t_139,n1)),fifo_length),
inference(clausify,[status(thm)],[quest_2]) ).
cnf(c_535,plain,
gt(int_level(plus(t_139,n1)),fifo_length),
inference(paramod,[status(thm)],[c_533,c_534]) ).
fof(quest_3,axiom,
gt(fifo_length,n0),
file('theBenchmark.p',quest_3) ).
cnf(c_536,plain,
gt(fifo_length,n0),
inference(clausify,[status(thm)],[quest_3]) ).
cnf(c_537,plain,
gt(fifo_length,int_level(plus(t_139,n1))),
inference(paramod,[status(thm)],[c_502,c_536]) ).
cnf(c_3024,plain,
gt(plus(int_level(plus(t_139,n1)),n1),plus(fifo_length,n1)),
inference(resolve,[status(thm)],[c_535,c_517]) ).
cnf(c_2303,plain,
gt(n1,plus(fifo_length,n1)),
inference(paramod,[status(thm)],[c_531,c_3024]) ).
cnf(c_3025,plain,
gt(plus(fifo_length,n1),plus(int_level(plus(t_139,n1)),n1)),
inference(resolve,[status(thm)],[c_537,c_517]) ).
cnf(c_2307,plain,
gt(plus(fifo_length,n1),n1),
inference(paramod,[status(thm)],[c_531,c_3025]) ).
cnf(c_2658,plain,
( gt(A,plus(fifo_length,n1))
| ~ gt(A,n1) ),
inference(resolve,[status(thm)],[c_2303,c_522]) ).
cnf(c_3026,plain,
gt(plus(fifo_length,n1),plus(fifo_length,n1)),
inference(resolve,[status(thm)],[c_2658,c_2307]) ).
cnf(c_3023,plain,
$false,
inference(resolve,[status(thm)],[c_528,c_3026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV028-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/1.41 % Computer : n013.cluster.edu
% 0.11/1.41 % Model : x86_64 x86_64
% 0.11/1.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.41 % Memory : 8046.5625MB
% 0.11/1.41 % OS : Linux 6.8.0-71-generic
% 0.11/1.41 % CPULimit : 300
% 0.11/1.41 % WCLimit : 300
% 0.11/1.41 % DateTime : Fri Sep 25 16:02:32 UTC 2026
% 0.11/1.41 % CPUTime :
% 0.11/1.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/1.42 % Process 792251 was started by sandbox2 on n013,
% 0.11/1.42 % Fri Sep 25 16:02:32 2026
% 0.11/1.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/1.42
% 0.11/1.42 % From the command line: assign(max_seconds, 300).
% 10.97/2.84
% 10.97/2.84 % SZS status Unsatisfiable for theBenchmark
% 10.97/2.84
% 10.97/2.84 % Proof 1 at 1.37 (+ 0.03) seconds.
% 10.97/2.84 % Length of proof is 18.
% 10.97/2.84 % Level of proof is 6.
% 10.97/2.84 % Maximum clause weight is 10.000.
% 10.97/2.84 % Given clauses 308.
% 10.97/2.84
% 10.97/2.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------