%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT086+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:03:05 AM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 64 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 28 ~; 19 |; 10 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 2 sgn 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',leq_def) ).
fof(less_leq_trans,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& less(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',less_leq_trans) ).
fof(in_lopen,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( leq(X,B)
& less(A,X) ) ),
file('theBenchmark.p',in_lopen) ).
fof(odrl462,conjecture,
? [X,Y] :
( ( ( in_lopen(Y,v0,v400)
& ~ in_lopen(X,v0,v600) )
| ( ~ in_lopen(Y,v0,v400)
& in_lopen(X,v0,v600) ) )
& in_lopen(Y,v0,v200)
& leq(v800,X) ),
file('theBenchmark.p',odrl462) ).
fof(odrl462_neg,negated_conjecture,
~ ? [X,Y] :
( ( ( in_lopen(Y,v0,v400)
& ~ in_lopen(X,v0,v600) )
| ( ~ in_lopen(Y,v0,v400)
& in_lopen(X,v0,v600) ) )
& in_lopen(Y,v0,v200)
& leq(v800,X) ),
inference(assume_negation,[status(cth)],[odrl462]) ).
cnf(c_41,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_45,plain,
( ~ less(A,B)
| leq(A,B) ),
inference(clausify,[status(thm)],[leq_def]) ).
cnf(c_46,plain,
( B != A
| leq(A,B) ),
inference(clausify,[status(thm)],[leq_def]) ).
cnf(c_49,plain,
( less(A,C)
| ~ leq(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_leq_trans]) ).
cnf(c_55,plain,
( leq(A,C)
| ~ in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
cnf(c_56,plain,
( ~ leq(A,C)
| ~ less(B,A)
| in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
fof(ord_v0_v200,axiom,
less(v0,v200),
file('theBenchmark.p',ord_v0_v200) ).
cnf(c_78,plain,
less(v0,v200),
inference(clausify,[status(thm)],[ord_v0_v200]) ).
fof(ord_v200_v400,axiom,
less(v200,v400),
file('theBenchmark.p',ord_v200_v400) ).
cnf(c_82,plain,
less(v200,v400),
inference(clausify,[status(thm)],[ord_v200_v400]) ).
fof(ord_v600_v800,axiom,
less(v600,v800),
file('theBenchmark.p',ord_v600_v800) ).
cnf(c_87,plain,
less(v600,v800),
inference(clausify,[status(thm)],[ord_v600_v800]) ).
cnf(c_99,negated_conjecture,
( ~ in_lopen(B,v0,v400)
| in_lopen(A,v0,v600)
| ~ in_lopen(B,v0,v200)
| ~ leq(v800,A) ),
inference(clausify,[status(thm)],[odrl462_neg]) ).
cnf(c_117,plain,
leq(A,A),
inference(xxres,[status(thm)],[c_46]) ).
cnf(c_158,plain,
leq(v200,v400),
inference(resolve,[status(thm)],[c_82,c_45]) ).
cnf(c_404,plain,
( less(v600,A)
| ~ leq(v800,A) ),
inference(resolve,[status(thm)],[c_49,c_87]) ).
cnf(c_186,plain,
~ leq(v800,v600),
inference(resolve,[status(thm)],[c_404,c_41]) ).
cnf(c_211,plain,
( ~ less(B,A)
| in_lopen(A,B,A) ),
inference(resolve,[status(thm)],[c_117,c_56]) ).
cnf(c_321,plain,
~ in_lopen(v800,A,v600),
inference(resolve,[status(thm)],[c_55,c_186]) ).
cnf(c_388,plain,
in_lopen(v200,v0,v200),
inference(resolve,[status(thm)],[c_211,c_78]) ).
cnf(c_405,negated_conjecture,
( ~ in_lopen(A,v0,v400)
| in_lopen(v800,v0,v600)
| ~ in_lopen(A,v0,v200) ),
inference(resolve,[status(thm)],[c_99,c_117]) ).
cnf(c_406,negated_conjecture,
( ~ in_lopen(v200,v0,v400)
| in_lopen(v800,v0,v600) ),
inference(resolve,[status(thm)],[c_405,c_388]) ).
cnf(c_401,negated_conjecture,
~ in_lopen(v200,v0,v400),
inference(resolve,[status(thm)],[c_406,c_321]) ).
cnf(c_407,plain,
( ~ leq(v200,v400)
| ~ less(v0,v200) ),
inference(resolve,[status(thm)],[c_56,c_401]) ).
cnf(c_408,plain,
~ less(v0,v200),
inference(resolve,[status(thm)],[c_407,c_158]) ).
cnf(c_403,plain,
$false,
inference(resolve,[status(thm)],[c_78,c_408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT086+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 00:14:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1487549 was started by sandbox2 on n003,
% 0.11/0.38 % Sat Sep 26 00:14:23 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.46
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46
% 0.11/0.46 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.11/0.46 % Length of proof is 23.
% 0.11/0.46 % Level of proof is 6.
% 0.11/0.46 % Maximum clause weight is 15.000.
% 0.11/0.46 % Given clauses 227.
% 0.11/0.46
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------