%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT077+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:03:04 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 18 unt; 0 def)
% Number of atoms : 76 ( 15 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 76 ( 35 ~; 22 |; 17 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(transitive,axiom,
! [X,Y,Z] :
( ( less(Y,Z)
& less(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',transitive) ).
fof(trichotomy,axiom,
! [X,Y] :
( less(Y,X)
| X = Y
| less(X,Y) ),
file('theBenchmark.p',trichotomy) ).
fof(in_open,axiom,
! [X,A,B] :
( in_open(X,A,B)
<=> ( less(X,B)
& less(A,X) ) ),
file('theBenchmark.p',in_open) ).
fof(distinct,axiom,
( v500 != v800
& v200 != v800
& v200 != v500
& v100 != v800
& v100 != v500
& v100 != v200
& v0 != v800
& v0 != v500
& v0 != v200
& v0 != v100 ),
file('theBenchmark.p',distinct) ).
fof(odrl327,conjecture,
? [X,Y] :
( in_open(Y,v0,v500)
& less(v100,Y)
& in_open(X,v0,v800)
& less(v200,X) ),
file('theBenchmark.p',odrl327) ).
fof(odrl327_neg,negated_conjecture,
~ ? [X,Y] :
( in_open(Y,v0,v500)
& less(v100,Y)
& in_open(X,v0,v800)
& less(v200,X) ),
inference(assume_negation,[status(cth)],[odrl327]) ).
cnf(c_42,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_43,plain,
( less(A,C)
| ~ less(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitive]) ).
cnf(c_44,plain,
( less(B,A)
| B = A
| less(A,B) ),
inference(clausify,[status(thm)],[trichotomy]) ).
cnf(c_59,plain,
( ~ less(A,C)
| ~ less(B,A)
| in_open(A,B,C) ),
inference(clausify,[status(thm)],[in_open]) ).
fof(ord_v0_v200,axiom,
less(v0,v200),
file('theBenchmark.p',ord_v0_v200) ).
cnf(c_82,plain,
less(v0,v200),
inference(clausify,[status(thm)],[ord_v0_v200]) ).
fof(ord_v0_v500,axiom,
less(v0,v500),
file('theBenchmark.p',ord_v0_v500) ).
cnf(c_83,plain,
less(v0,v500),
inference(clausify,[status(thm)],[ord_v0_v500]) ).
fof(ord_v100_v200,axiom,
less(v100,v200),
file('theBenchmark.p',ord_v100_v200) ).
cnf(c_85,plain,
less(v100,v200),
inference(clausify,[status(thm)],[ord_v100_v200]) ).
fof(ord_v200_v500,axiom,
less(v200,v500),
file('theBenchmark.p',ord_v200_v500) ).
cnf(c_88,plain,
less(v200,v500),
inference(clausify,[status(thm)],[ord_v200_v500]) ).
fof(ord_v500_v800,axiom,
less(v500,v800),
file('theBenchmark.p',ord_v500_v800) ).
cnf(c_90,plain,
less(v500,v800),
inference(clausify,[status(thm)],[ord_v500_v800]) ).
cnf(c_100,plain,
v800 != v500,
inference(clausify,[status(thm)],[distinct]) ).
cnf(c_101,negated_conjecture,
( ~ in_open(B,v0,v500)
| ~ less(v100,B)
| ~ in_open(A,v0,v800)
| ~ less(v200,A) ),
inference(clausify,[status(thm)],[odrl327_neg]) ).
cnf(c_131,plain,
( less(C,A)
| C = A
| ~ less(B,A)
| in_open(A,B,C) ),
inference(resolve,[status(thm)],[c_59,c_44]) ).
cnf(c_163,plain,
( ~ less(v200,A)
| in_open(v200,v0,A) ),
inference(resolve,[status(thm)],[c_82,c_59]) ).
cnf(c_811,plain,
( less(A,v800)
| ~ less(A,v500) ),
inference(resolve,[status(thm)],[c_43,c_90]) ).
cnf(c_242,plain,
~ less(v800,v500),
inference(resolve,[status(thm)],[c_811,c_42]) ).
cnf(c_773,plain,
in_open(v200,v0,v500),
inference(resolve,[status(thm)],[c_163,c_88]) ).
cnf(c_812,negated_conjecture,
( ~ in_open(A,v0,v500)
| ~ less(v100,A)
| ~ in_open(v500,v0,v800) ),
inference(resolve,[status(thm)],[c_101,c_88]) ).
cnf(c_813,negated_conjecture,
( ~ in_open(v200,v0,v500)
| ~ in_open(v500,v0,v800) ),
inference(resolve,[status(thm)],[c_812,c_85]) ).
cnf(c_809,negated_conjecture,
~ in_open(v500,v0,v800),
inference(resolve,[status(thm)],[c_813,c_773]) ).
cnf(c_814,plain,
( less(v800,v500)
| v800 = v500
| ~ less(v0,v500) ),
inference(resolve,[status(thm)],[c_131,c_809]) ).
cnf(c_815,plain,
( less(v800,v500)
| ~ less(v0,v500) ),
inference(resolve,[status(thm)],[c_814,c_100]) ).
cnf(c_816,plain,
~ less(v0,v500),
inference(resolve,[status(thm)],[c_815,c_242]) ).
cnf(c_810,plain,
$false,
inference(resolve,[status(thm)],[c_83,c_816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT077+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.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 00:12:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2244148 was started by sandbox on n008,
% 0.11/0.37 % Sat Sep 26 00:12:39 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.45
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45
% 0.11/0.45 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.11/0.45 % Length of proof is 23.
% 0.11/0.45 % Level of proof is 5.
% 0.11/0.45 % Maximum clause weight is 19.000.
% 0.11/0.45 % Given clauses 232.
% 0.11/0.45
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------