%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV010-1 : 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 : n001.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 07:34:18 AM UTC 2026
% Result : Unsatisfiable 15.97s 2.70s
% Output : CNFRefutation 15.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 29 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quest_2,axiom,
( level(t_139) = n0
| p_Empty(t_139) ),
file('theBenchmark.p',quest_2) ).
cnf(c_550,plain,
( level(t_139) = n0
| p_Empty(t_139) ),
inference(clausify,[status(thm)],[quest_2]) ).
fof(quest_1,axiom,
( level(t_139) != n0
| ~ p_Empty(t_139) ),
file('theBenchmark.p',quest_1) ).
cnf(c_551,plain,
( level(t_139) != n0
| ~ p_Empty(t_139) ),
inference(clausify,[status(thm)],[quest_1]) ).
fof(axiom_25,axiom,
! [VAR_0] :
( ~ p_Empty(VAR_0)
| int_level(VAR_0) = n0 ),
file('theBenchmark.p',axiom_25) ).
cnf(c_552,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_553,plain,
( p_Empty(A)
| int_level(A) != n0 ),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_21,axiom,
! [VAR_0] : level(VAR_0) = int_level(VAR_0),
file('theBenchmark.p',axiom_21) ).
cnf(c_554,plain,
level(A) = int_level(A),
inference(clausify,[status(thm)],[axiom_21]) ).
cnf(c_4046,plain,
( level(t_139) = n0
| int_level(t_139) = n0 ),
inference(resolve,[status(thm)],[c_552,c_550]) ).
cnf(c_4829,plain,
( n0 = int_level(t_139)
| int_level(t_139) = n0 ),
inference(paramod,[status(thm)],[c_4046,c_554]) ).
cnf(c_4830,plain,
( int_level(t_139) = n0
| int_level(t_139) = n0 ),
inference(copy,[status(thm)],[c_4829]) ).
cnf(c_4813,plain,
int_level(t_139) = n0,
inference(copy,[status(thm)],[c_4830]) ).
cnf(c_4814,plain,
p_Empty(t_139),
inference(resolve,[status(thm)],[c_4813,c_553]) ).
cnf(c_4821,plain,
level(t_139) = n0,
inference(paramod,[status(thm)],[c_4813,c_554]) ).
cnf(c_4831,plain,
level(t_139) != n0,
inference(resolve,[status(thm)],[c_4814,c_551]) ).
cnf(c_4828,plain,
$false,
inference(resolve,[status(thm)],[c_4821,c_4831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV010-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 16:05:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3771900 was started by sandbox on n001,
% 0.10/0.38 % Fri Sep 25 16:05:55 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 15.97/2.70
% 15.97/2.70 % SZS status Unsatisfiable for theBenchmark
% 15.97/2.70
% 15.97/2.70 % Proof 1 at 2.22 (+ 0.05) seconds.
% 15.97/2.70 % Length of proof is 10.
% 15.97/2.70 % Level of proof is 4.
% 15.97/2.70 % Maximum clause weight is 18.000.
% 15.97/2.70 % Given clauses 407.
% 15.97/2.70
% 15.97/2.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------