%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT086+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 1.25s 1.56s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 25 unt; 0 def)
% Number of atoms : 170 ( 9 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 188 ( 87 ~; 70 |; 23 &)
% ( 6 <=>; 2 =>; 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 86 ( 1 sgn 54 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X) ).
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( less(X,Y)
| X = Y ) ) ).
fof(less_implies_leq,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ) ).
fof(leq_less_trans,axiom,
! [X,Y,Z] :
( ( leq(X,Y)
& less(Y,Z) )
=> less(X,Z) ) ).
fof(in_lopen,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ) ).
fof(ord_v0_v200,axiom,
less(v0,v200) ).
fof(ord_v200_v400,axiom,
less(v200,v400) ).
fof(ord_v600_v800,axiom,
less(v600,v800) ).
fof(odrl462,conjecture,
? [X,Y] :
( leq(v800,X)
& in_lopen(Y,v0,v200)
& ( ( in_lopen(X,v0,v600)
& ~ in_lopen(Y,v0,v400) )
| ( ~ in_lopen(X,v0,v600)
& in_lopen(Y,v0,v400) ) ) ) ).
fof(subgoal_0,plain,
? [X,Y] :
( leq(v800,X)
& in_lopen(Y,v0,v200)
& ( ( in_lopen(X,v0,v600)
& ~ in_lopen(Y,v0,v400) )
| ( ~ in_lopen(X,v0,v600)
& in_lopen(Y,v0,v400) ) ) ),
inference(strip,[],[odrl462]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
( leq(v800,X)
& in_lopen(Y,v0,v200)
& ( ( in_lopen(X,v0,v600)
& ~ in_lopen(Y,v0,v400) )
| ( ~ in_lopen(X,v0,v600)
& in_lopen(Y,v0,v400) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
less(v600,v800),
inference(canonicalize,[],[ord_v600_v800]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ leq(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[leq_less_trans]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ leq(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(canonicalize,[],[in_lopen]) ).
fof(normalize_0_4,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( X != Y
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
less(v200,v400),
inference(canonicalize,[],[ord_v200_v400]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
less(v0,v200),
inference(canonicalize,[],[ord_v0_v200]) ).
fof(normalize_0_15,plain,
! [A,B,X] :
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ in_lopen(Y,v0,v200)
| ~ leq(v800,X)
| ( ( ~ in_lopen(X,v0,v600)
| in_lopen(Y,v0,v400) )
& ( ~ in_lopen(Y,v0,v400)
| in_lopen(X,v0,v600) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ in_lopen(Y,v0,v200)
| ~ leq(v800,X)
| ( ( ~ in_lopen(X,v0,v600)
| in_lopen(Y,v0,v400) )
& ( ~ in_lopen(Y,v0,v400)
| in_lopen(X,v0,v600) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v200)
| ~ leq(v800,X)
| in_lopen(Y,v0,v400) )
& ( ~ in_lopen(Y,v0,v200)
| ~ in_lopen(Y,v0,v400)
| ~ leq(v800,X)
| in_lopen(X,v0,v600) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ in_lopen(Y,v0,v200)
| ~ in_lopen(Y,v0,v400)
| ~ leq(v800,X)
| in_lopen(X,v0,v600) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_21,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
less(v600,v800),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ leq(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ leq(X_180,v600)
| ~ less(v600,v800)
| less(X_180,v800) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_180)),bind(Y,$fot(v600)),bind(Z,$fot(v800))]]) ).
cnf(refute_0_3,plain,
( ~ leq(X_180,v600)
| less(X_180,v800) ),
inference(resolve,[$cnf( less(v600,v800) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ leq(v800,v600)
| less(v800,v800) ),
inference(subst,[],[refute_0_3:[bind(X_180,$fot(v800))]]) ).
cnf(refute_0_5,plain,
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ in_lopen(v800,v0,v600)
| leq(v800,v600) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(v0)),bind(B,$fot(v600)),bind(X,$fot(v800))]]) ).
cnf(refute_0_7,plain,
( X != Y
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( Y != Y
| leq(Y,Y) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(Y))]]) ).
cnf(refute_0_9,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_10,plain,
leq(Y,Y),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
leq(v800,v800),
inference(subst,[],[refute_0_10:[bind(Y,$fot(v800))]]) ).
cnf(refute_0_12,plain,
less(v200,v400),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( ~ less(v200,v400)
| leq(v200,v400) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(v200)),bind(Y,$fot(v400))]]) ).
cnf(refute_0_15,plain,
leq(v200,v400),
inference(resolve,[$cnf( less(v200,v400) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
less(v0,v200),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_17,plain,
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
( ~ leq(v200,X_323)
| ~ less(v0,v200)
| in_lopen(v200,v0,X_323) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(v0)),bind(B,$fot(X_323)),bind(X,$fot(v200))]]) ).
cnf(refute_0_19,plain,
( ~ leq(v200,X_323)
| in_lopen(v200,v0,X_323) ),
inference(resolve,[$cnf( less(v0,v200) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ leq(v200,v400)
| in_lopen(v200,v0,v400) ),
inference(subst,[],[refute_0_19:[bind(X_323,$fot(v400))]]) ).
cnf(refute_0_21,plain,
in_lopen(v200,v0,v400),
inference(resolve,[$cnf( leq(v200,v400) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ in_lopen(Y,v0,v200)
| ~ in_lopen(Y,v0,v400)
| ~ leq(v800,X)
| in_lopen(X,v0,v600) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_23,plain,
( ~ in_lopen(v200,v0,v200)
| ~ in_lopen(v200,v0,v400)
| ~ leq(v800,X_1113)
| in_lopen(X_1113,v0,v600) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_1113)),bind(Y,$fot(v200))]]) ).
cnf(refute_0_24,plain,
( ~ in_lopen(v200,v0,v200)
| ~ leq(v800,X_1113)
| in_lopen(X_1113,v0,v600) ),
inference(resolve,[$cnf( in_lopen(v200,v0,v400) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
leq(v200,v200),
inference(subst,[],[refute_0_10:[bind(Y,$fot(v200))]]) ).
cnf(refute_0_26,plain,
( ~ leq(v200,v200)
| in_lopen(v200,v0,v200) ),
inference(subst,[],[refute_0_19:[bind(X_323,$fot(v200))]]) ).
cnf(refute_0_27,plain,
in_lopen(v200,v0,v200),
inference(resolve,[$cnf( leq(v200,v200) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ leq(v800,X_1113)
| in_lopen(X_1113,v0,v600) ),
inference(resolve,[$cnf( in_lopen(v200,v0,v200) )],[refute_0_27,refute_0_24]) ).
cnf(refute_0_29,plain,
( ~ leq(v800,v800)
| in_lopen(v800,v0,v600) ),
inference(subst,[],[refute_0_28:[bind(X_1113,$fot(v800))]]) ).
cnf(refute_0_30,plain,
in_lopen(v800,v0,v600),
inference(resolve,[$cnf( leq(v800,v800) )],[refute_0_11,refute_0_29]) ).
cnf(refute_0_31,plain,
leq(v800,v600),
inference(resolve,[$cnf( in_lopen(v800,v0,v600) )],[refute_0_30,refute_0_6]) ).
cnf(refute_0_32,plain,
less(v800,v800),
inference(resolve,[$cnf( leq(v800,v600) )],[refute_0_31,refute_0_4]) ).
cnf(refute_0_33,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_34,plain,
~ less(v800,v800),
inference(subst,[],[refute_0_33:[bind(X,$fot(v800))]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( less(v800,v800) )],[refute_0_32,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT086+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.12/0.36 % Computer : n015.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 7 14:23:00 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.25/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.25/1.56
% 1.25/1.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.25/1.56
%------------------------------------------------------------------------------