%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT085+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 : n005.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 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 24 ~; 24 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 37 ( 3 sgn 10 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X),
file('theBenchmark.p',irreflexive) ).
fof(less_leq_trans,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& less(X,Y) )
=> less(X,Z) ),
file('theBenchmark.p',less_leq_trans) ).
fof(leq_trans,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('theBenchmark.p',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(odrl445,conjecture,
~ ? [X,Y,Z] :
( leq(v100,Z)
& leq(v200,Y)
& leq(v400,X)
& ( in_lopen(Z,v0,v50)
| in_lopen(Y,v0,v100)
| in_lopen(X,v0,v200) ) ),
file('theBenchmark.p',odrl445) ).
fof(odrl445_neg,negated_conjecture,
~ ~ ? [X,Y,Z] :
( leq(v100,Z)
& leq(v200,Y)
& leq(v400,X)
& ( in_lopen(Z,v0,v50)
| in_lopen(Y,v0,v100)
| in_lopen(X,v0,v200) ) ),
inference(assume_negation,[status(cth)],[odrl445]) ).
cnf(c_41,plain,
~ less(A,A),
inference(clausify,[status(thm)],[irreflexive]) ).
cnf(c_49,plain,
( less(A,C)
| ~ leq(B,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_leq_trans]) ).
cnf(c_50,plain,
( leq(A,C)
| ~ leq(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_trans]) ).
cnf(c_55,plain,
( leq(A,C)
| ~ in_lopen(A,B,C) ),
inference(clausify,[status(thm)],[in_lopen]) ).
fof(ord_v50_v100,axiom,
less(v50,v100),
file('theBenchmark.p',ord_v50_v100) ).
cnf(c_82,plain,
less(v50,v100),
inference(clausify,[status(thm)],[ord_v50_v100]) ).
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_v400,axiom,
less(v200,v400),
file('theBenchmark.p',ord_v200_v400) ).
cnf(c_87,plain,
less(v200,v400),
inference(clausify,[status(thm)],[ord_v200_v400]) ).
fof(nnf_23,plain,
? [X,Y,Z] :
( leq(v100,Z)
& leq(v200,Y)
& leq(v400,X)
& ( in_lopen(Z,v0,v50)
| in_lopen(Y,v0,v100)
| in_lopen(X,v0,v200) ) ),
inference(fof_nnf,[status(thm)],[odrl445_neg]) ).
fof(sk_odrl445_neg,plain,
( leq(v100,sK2)
& leq(v200,sK1)
& leq(v400,sK0)
& ( in_lopen(sK2,v0,v50)
| in_lopen(sK1,v0,v100)
| in_lopen(sK0,v0,v200) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_23]) ).
cnf(c_101,negated_conjecture,
( in_lopen(sK2,v0,v50)
| in_lopen(sK1,v0,v100)
| in_lopen(sK0,v0,v200) ),
inference(split_conjunct,[status(thm)],[sk_odrl445_neg]) ).
cnf(c_102,negated_conjecture,
leq(v400,sK0),
inference(split_conjunct,[status(thm)],[sk_odrl445_neg]) ).
cnf(c_103,negated_conjecture,
leq(v200,sK1),
inference(split_conjunct,[status(thm)],[sk_odrl445_neg]) ).
cnf(c_104,negated_conjecture,
leq(v100,sK2),
inference(split_conjunct,[status(thm)],[sk_odrl445_neg]) ).
cnf(c_518,plain,
( less(v50,A)
| ~ leq(v100,A) ),
inference(resolve,[status(thm)],[c_49,c_82]) ).
cnf(c_170,plain,
~ leq(v100,v50),
inference(resolve,[status(thm)],[c_518,c_41]) ).
cnf(c_519,plain,
( less(v100,A)
| ~ leq(v200,A) ),
inference(resolve,[status(thm)],[c_49,c_85]) ).
cnf(c_185,plain,
~ leq(v200,v100),
inference(resolve,[status(thm)],[c_519,c_41]) ).
cnf(c_520,plain,
( less(v200,A)
| ~ leq(v400,A) ),
inference(resolve,[status(thm)],[c_49,c_87]) ).
cnf(c_195,plain,
~ leq(v400,v200),
inference(resolve,[status(thm)],[c_520,c_41]) ).
cnf(c_197,plain,
( leq(sK0,v200)
| in_lopen(sK2,v0,v50)
| in_lopen(sK1,v0,v100) ),
inference(resolve,[status(thm)],[c_101,c_55]) ).
cnf(c_521,negated_conjecture,
( leq(v100,A)
| ~ leq(sK2,A) ),
inference(resolve,[status(thm)],[c_50,c_104]) ).
cnf(c_335,negated_conjecture,
~ leq(sK2,v50),
inference(resolve,[status(thm)],[c_521,c_170]) ).
cnf(c_522,negated_conjecture,
( leq(v200,A)
| ~ leq(sK1,A) ),
inference(resolve,[status(thm)],[c_50,c_103]) ).
cnf(c_390,negated_conjecture,
~ leq(sK1,v100),
inference(resolve,[status(thm)],[c_522,c_185]) ).
cnf(c_523,negated_conjecture,
( leq(v400,A)
| ~ leq(sK0,A) ),
inference(resolve,[status(thm)],[c_50,c_102]) ).
cnf(c_428,negated_conjecture,
~ leq(sK0,v200),
inference(resolve,[status(thm)],[c_523,c_195]) ).
cnf(c_429,plain,
( in_lopen(sK2,v0,v50)
| in_lopen(sK1,v0,v100) ),
inference(resolve,[status(thm)],[c_428,c_197]) ).
cnf(c_475,plain,
~ in_lopen(sK2,A,v50),
inference(resolve,[status(thm)],[c_55,c_335]) ).
cnf(c_479,plain,
in_lopen(sK1,v0,v100),
inference(resolve,[status(thm)],[c_475,c_429]) ).
cnf(c_516,plain,
~ in_lopen(sK1,A,v100),
inference(resolve,[status(thm)],[c_55,c_390]) ).
cnf(c_517,plain,
$false,
inference(resolve,[status(thm)],[c_516,c_479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT085+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 00:12:46 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 618425 was started by sandbox on n005,
% 0.09/0.36 % Sat Sep 26 00:12:46 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.44 % Length of proof is 28.
% 0.09/0.44 % Level of proof is 6.
% 0.09/0.44 % Maximum clause weight is 17.000.
% 0.09/0.44 % Given clauses 143.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------