%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT081+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 : n026.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 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 62 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 17 ~; 13 |; 15 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 33 ( 1 sgn 12 !; 6 ?)
% 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(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',leq_def) ).
fof(leq_less_trans,axiom,
! [X,Y,Z] :
( ( less(Y,Z)
& leq(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',leq_less_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(odrl402,conjecture,
~ ? [X,Y] :
( leq(v200,Y)
& in_lopen(Y,v0,v600)
& leq(v800,X)
& in_lopen(X,v0,v400) ),
file('theBenchmark.p',odrl402) ).
fof(odrl402_neg,negated_conjecture,
~ ~ ? [X,Y] :
( leq(v200,Y)
& in_lopen(Y,v0,v600)
& leq(v800,X)
& in_lopen(X,v0,v400) ),
inference(assume_negation,[status(cth)],[odrl402]) ).
cnf(c_25,plain,
( leq(A,C)
| ~ in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
fof(nnf_23,plain,
? [X,Y] :
( leq(v200,Y)
& in_lopen(Y,v0,v600)
& leq(v800,X)
& in_lopen(X,v0,v400) ),
inference(fof_nnf,[status(thm)],[odrl402_neg]) ).
fof(sk_odrl402_neg,plain,
( leq(v200,sK1)
& in_lopen(sK1,v0,v600)
& leq(v800,sK0)
& in_lopen(sK0,v0,v400) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_23]) ).
cnf(c_27,negated_conjecture,
in_lopen(sK0,v0,v400),
inference(split_conjunct,[status(thm)],[sk_odrl402_neg]) ).
cnf(c_49,negated_conjecture,
leq(sK0,v400),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_51,negated_conjecture,
leq(v800,sK0),
inference(split_conjunct,[status(thm)],[sk_odrl402_neg]) ).
fof(ord_v400_v800,axiom,
less(v400,v800),
file('theBenchmark.p',ord_v400_v800) ).
cnf(c_63,plain,
less(v400,v800),
inference(clausify,[status(thm)],[ord_v400_v800]) ).
cnf(c_98,plain,
( less(A,C)
| ~ less(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_less_trans]) ).
cnf(c_102,plain,
( B = A
| less(A,B)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_def]) ).
cnf(c_104,plain,
( less(A,C)
| ~ less(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitive]) ).
cnf(c_105,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_315,negated_conjecture,
( v400 = sK0
| less(sK0,v400) ),
inference(resolve,[status(thm)],[c_102,c_49]) ).
cnf(c_179,negated_conjecture,
( sK0 = v400
| less(sK0,v400) ),
inference(copy,[status(thm)],[c_315]) ).
cnf(c_316,plain,
( less(A,v800)
| ~ less(A,v400) ),
inference(resolve,[status(thm)],[c_104,c_63]) ).
cnf(c_223,plain,
~ less(v800,v400),
inference(resolve,[status(thm)],[c_316,c_105]) ).
cnf(c_317,plain,
( less(A,v800)
| ~ leq(A,v400) ),
inference(resolve,[status(thm)],[c_98,c_63]) ).
cnf(c_235,plain,
~ leq(v800,v400),
inference(resolve,[status(thm)],[c_317,c_105]) ).
cnf(c_318,negated_conjecture,
( less(v800,A)
| ~ less(sK0,A) ),
inference(resolve,[status(thm)],[c_98,c_51]) ).
cnf(c_305,negated_conjecture,
~ less(sK0,v400),
inference(resolve,[status(thm)],[c_318,c_223]) ).
cnf(c_307,negated_conjecture,
sK0 = v400,
inference(resolve,[status(thm)],[c_305,c_179]) ).
cnf(c_319,plain,
leq(v800,v400),
inference(paramod,[status(thm)],[c_307,c_51]) ).
cnf(c_314,plain,
$false,
inference(resolve,[status(thm)],[c_235,c_319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT081+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 : n026.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 00:15:10 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 3802191 was started by sandbox on n026,
% 0.11/0.37 % Sat Sep 26 00:15:10 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).
% 0.11/0.41
% 0.11/0.41 % SZS status Theorem for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.41 % Length of proof is 21.
% 0.11/0.41 % Level of proof is 5.
% 0.11/0.41 % Maximum clause weight is 14.000.
% 0.11/0.41 % Given clauses 99.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------