%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : Tue Sep 8 06:16:16 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 66 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 35 ~; 22 |; 7 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 41 ( 1 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( less(X,Y)
| X = Y ) ) ).
fof(in_lopen,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ) ).
fof(ord_v0_v600,axiom,
less(v0,v600) ).
fof(odrl500,conjecture,
? [X] : in_lopen(X,v0,v600) ).
fof(subgoal_0,plain,
? [X] : in_lopen(X,v0,v600),
inference(strip,[],[odrl500]) ).
fof(negate_0_0,plain,
~ ? [X] : in_lopen(X,v0,v600),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( X != Y
| leq(X,Y) )
& ( ~ less(X,Y)
| leq(X,Y) )
& ( ~ leq(X,Y)
| X = Y
| less(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( X != Y
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
less(v0,v600),
inference(canonicalize,[],[ord_v0_v600]) ).
fof(normalize_0_5,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(canonicalize,[],[in_lopen]) ).
fof(normalize_0_6,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,X] :
( ( ~ in_lopen(X,A,B)
| leq(X,B) )
& ( ~ in_lopen(X,A,B)
| less(A,X) )
& ( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,X] :
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] : ~ in_lopen(X,v0,v600),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
! [X] : ~ in_lopen(X,v0,v600),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( X != Y
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( Y != Y
| leq(Y,Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(Y))]]) ).
cnf(refute_0_2,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_3,plain,
leq(Y,Y),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
leq(v600,v600),
inference(subst,[],[refute_0_3:[bind(Y,$fot(v600))]]) ).
cnf(refute_0_5,plain,
less(v0,v600),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_6,plain,
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ leq(v600,X_119)
| ~ less(v0,v600)
| in_lopen(v600,v0,X_119) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(v0)),bind(B,$fot(X_119)),bind(X,$fot(v600))]]) ).
cnf(refute_0_8,plain,
( ~ leq(v600,X_119)
| in_lopen(v600,v0,X_119) ),
inference(resolve,[$cnf( less(v0,v600) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ leq(v600,v600)
| in_lopen(v600,v0,v600) ),
inference(subst,[],[refute_0_8:[bind(X_119,$fot(v600))]]) ).
cnf(refute_0_10,plain,
in_lopen(v600,v0,v600),
inference(resolve,[$cnf( leq(v600,v600) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
~ in_lopen(X,v0,v600),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_12,plain,
~ in_lopen(v600,v0,v600),
inference(subst,[],[refute_0_11:[bind(X,$fot(v600))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( in_lopen(v600,v0,v600) )],[refute_0_10,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.35 % Computer : n003.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 : Mon Sep 7 14:22:24 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.41
%------------------------------------------------------------------------------