%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV064+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:06:44 AM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 74 ( 29 ~; 21 |; 22 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_leq,axiom,
! [X] : leq(X,X),
file('theBenchmark.p',reflexivity_leq) ).
fof(cl5_nebula_array_0005,conjecture,
( ( leq(pv54,minus(n5,n1))
& leq(pv53,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv54)
& leq(n0,pv53)
& leq(n0,pv10) )
=> ( leq(pv54,minus(n5,n1))
& leq(pv53,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv54)
& leq(n0,pv53)
& leq(n0,pv10)
& leq(n0,n0) ) ),
file('theBenchmark.p',cl5_nebula_array_0005) ).
fof(cl5_nebula_array_0005_neg,negated_conjecture,
~ ( ( leq(pv54,minus(n5,n1))
& leq(pv53,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv54)
& leq(n0,pv53)
& leq(n0,pv10) )
=> ( leq(pv54,minus(n5,n1))
& leq(pv53,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv54)
& leq(n0,pv53)
& leq(n0,pv10)
& leq(n0,n0) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0005]) ).
cnf(c_64,plain,
leq(A,A),
inference(clausify,[status(thm)],[reflexivity_leq]) ).
cnf(c_374,negated_conjecture,
leq(n0,pv10),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_375,negated_conjecture,
leq(n0,pv53),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_376,negated_conjecture,
leq(n0,pv54),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_377,negated_conjecture,
leq(pv10,minus(n135300,n1)),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_378,negated_conjecture,
leq(pv53,minus(n5,n1)),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_379,negated_conjecture,
leq(pv54,minus(n5,n1)),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_380,negated_conjecture,
( ~ leq(pv54,minus(n5,n1))
| ~ leq(pv53,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv54)
| ~ leq(n0,pv53)
| ~ leq(n0,pv10)
| ~ leq(n0,n0) ),
inference(clausify,[status(thm)],[cl5_nebula_array_0005_neg]) ).
cnf(c_382,negated_conjecture,
( ~ leq(pv54,minus(n5,n1))
| ~ leq(pv53,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv54)
| ~ leq(n0,pv53)
| ~ leq(n0,pv10) ),
inference(resolve,[status(thm)],[c_64,c_380]) ).
cnf(c_383,negated_conjecture,
( ~ leq(pv54,minus(n5,n1))
| ~ leq(pv53,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv54)
| ~ leq(n0,pv53) ),
inference(resolve,[status(thm)],[c_374,c_382]) ).
cnf(c_384,negated_conjecture,
( ~ leq(pv54,minus(n5,n1))
| ~ leq(pv53,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv54) ),
inference(resolve,[status(thm)],[c_375,c_383]) ).
cnf(c_385,negated_conjecture,
( ~ leq(pv54,minus(n5,n1))
| ~ leq(pv53,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) ),
inference(resolve,[status(thm)],[c_376,c_384]) ).
cnf(c_386,negated_conjecture,
( ~ leq(pv54,minus(n5,n1))
| ~ leq(pv53,minus(n5,n1)) ),
inference(resolve,[status(thm)],[c_377,c_385]) ).
cnf(c_387,negated_conjecture,
~ leq(pv54,minus(n5,n1)),
inference(resolve,[status(thm)],[c_378,c_386]) ).
cnf(c_381,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_379,c_387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV064+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.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 : Sat Sep 26 13:09:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2816885 was started by sandbox on n013,
% 0.10/0.37 % Sat Sep 26 13:09:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.40
% 0.15/0.40 % From the command line: assign(max_seconds, 300).
% 0.15/0.47
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47
% 0.15/0.47 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.15/0.47 % Length of proof is 11.
% 0.15/0.47 % Level of proof is 2.
% 0.15/0.47 % Maximum clause weight is 5.000.
% 0.15/0.47 % Given clauses 0.
% 0.15/0.47
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------