%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV069+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 09:06:45 AM UTC 2026
% Result : Theorem 5.87s 1.26s
% Output : CNFRefutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 45 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 20 ~; 13 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_leq,axiom,
! [X] : leq(X,X),
file('theBenchmark.p',reflexivity_leq) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('theBenchmark.p',leq_gt_pred) ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X),
file('theBenchmark.p',pred_minus_1) ).
fof(cl5_nebula_array_0010,conjecture,
( ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) )
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,n0) ) ),
file('theBenchmark.p',cl5_nebula_array_0010) ).
fof(cl5_nebula_array_0010_neg,negated_conjecture,
~ ( ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) )
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,minus(n5,n1))
& leq(n0,pv10)
& leq(n0,n0) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0010]) ).
cnf(c_64,plain,
leq(A,A),
inference(clausify,[status(thm)],[reflexivity_leq]) ).
cnf(c_69,plain,
( ~ gt(B,A)
| leq(A,pred(B)) ),
inference(clausify,[status(thm)],[leq_gt_pred]) ).
cnf(c_300,plain,
minus(A,n1) = pred(A),
inference(clausify,[status(thm)],[pred_minus_1]) ).
fof(gt_5_0,axiom,
gt(n5,n0),
file('theBenchmark.p',gt_5_0) ).
cnf(c_333,plain,
gt(n5,n0),
inference(clausify,[status(thm)],[gt_5_0]) ).
cnf(c_365,negated_conjecture,
leq(n0,pv10),
inference(clausify,[status(thm)],[cl5_nebula_array_0010_neg]) ).
cnf(c_366,negated_conjecture,
leq(pv10,minus(n135300,n1)),
inference(clausify,[status(thm)],[cl5_nebula_array_0010_neg]) ).
cnf(c_367,negated_conjecture,
leq(pv10,pred(n135300)),
inference(paramod,[status(thm)],[c_300,c_366]) ).
cnf(c_368,negated_conjecture,
( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,minus(n5,n1))
| ~ leq(n0,pv10)
| ~ leq(n0,n0) ),
inference(clausify,[status(thm)],[cl5_nebula_array_0010_neg]) ).
cnf(c_1287,negated_conjecture,
( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pred(n5))
| ~ leq(n0,pv10)
| ~ leq(n0,n0) ),
inference(paramod,[status(thm)],[c_300,c_368]) ).
cnf(c_1288,negated_conjecture,
( ~ leq(pv10,pred(n135300))
| ~ leq(n0,pred(n5))
| ~ leq(n0,pv10)
| ~ leq(n0,n0) ),
inference(paramod,[status(thm)],[c_300,c_1287]) ).
cnf(c_1289,negated_conjecture,
( ~ leq(pv10,pred(n135300))
| ~ leq(n0,pred(n5))
| ~ leq(n0,pv10) ),
inference(resolve,[status(thm)],[c_64,c_1288]) ).
cnf(c_1290,negated_conjecture,
( ~ leq(pv10,pred(n135300))
| ~ leq(n0,pred(n5)) ),
inference(resolve,[status(thm)],[c_365,c_1289]) ).
cnf(c_369,negated_conjecture,
~ leq(n0,pred(n5)),
inference(resolve,[status(thm)],[c_367,c_1290]) ).
cnf(c_1291,plain,
leq(n0,pred(n5)),
inference(resolve,[status(thm)],[c_333,c_69]) ).
cnf(c_1286,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_369,c_1291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV069+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 13:10:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3236856 was started by sandbox2 on n014,
% 0.09/0.36 % Sat Sep 26 13:10:32 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.48
% 0.13/0.48 % From the command line: assign(max_seconds, 300).
% 5.87/1.26
% 5.87/1.26 % SZS status Theorem for theBenchmark
% 5.87/1.26
% 5.87/1.26 % Proof 1 at 0.66 (+ 0.09) seconds.
% 5.87/1.26 % Length of proof is 14.
% 5.87/1.26 % Level of proof is 4.
% 5.87/1.26 % Maximum clause weight is 17.000.
% 5.87/1.26 % Given clauses 263.
% 5.87/1.26
% 5.87/1.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------