%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT079+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 15.95s 16.23s
% Output : CNFRefutation 15.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 81 ( 32 unt; 0 def)
% Number of atoms : 193 ( 9 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 204 ( 92 ~; 75 |; 29 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 99 ( 5 sgn 58 !; 9 ?)
% 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_v16,axiom,
less(v0,v16) ).
fof(ord_v0_v32,axiom,
less(v0,v32) ).
fof(ord_v16_v32,axiom,
less(v16,v32) ).
fof(ord_v16_v400,axiom,
less(v16,v400) ).
fof(ord_v16_v600,axiom,
less(v16,v600) ).
fof(odrl350,conjecture,
? [X,Y,Z] :
( in_lopen(X,v0,v600)
& in_lopen(Y,v0,v400)
& in_lopen(Z,v0,v32)
& ~ ( in_lopen(X,v0,v1200)
& in_lopen(Y,v0,v800)
& in_lopen(Z,v0,v16) ) ) ).
fof(subgoal_0,plain,
? [X,Y,Z] :
( in_lopen(X,v0,v600)
& in_lopen(Y,v0,v400)
& in_lopen(Z,v0,v32)
& ~ ( in_lopen(X,v0,v1200)
& in_lopen(Y,v0,v800)
& in_lopen(Z,v0,v16) ) ),
inference(strip,[],[odrl350]) ).
fof(negate_0_0,plain,
~ ? [X,Y,Z] :
( in_lopen(X,v0,v600)
& in_lopen(Y,v0,v400)
& in_lopen(Z,v0,v32)
& ~ ( in_lopen(X,v0,v1200)
& in_lopen(Y,v0,v800)
& in_lopen(Z,v0,v16) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
less(v16,v32),
inference(canonicalize,[],[ord_v16_v32]) ).
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(v0,v32),
inference(canonicalize,[],[ord_v0_v32]) ).
fof(normalize_0_12,plain,
! [A,B,X] :
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_13,plain,
less(v16,v400),
inference(canonicalize,[],[ord_v16_v400]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
less(v0,v16),
inference(canonicalize,[],[ord_v0_v16]) ).
fof(normalize_0_17,plain,
less(v16,v600),
inference(canonicalize,[],[ord_v16_v600]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| ( in_lopen(X,v0,v1200)
& in_lopen(Y,v0,v800)
& in_lopen(Z,v0,v16) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_19,plain,
! [X,Y,Z] :
( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| ( in_lopen(X,v0,v1200)
& in_lopen(Y,v0,v800)
& in_lopen(Z,v0,v16) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y,Z] :
( ( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| in_lopen(X,v0,v1200) )
& ( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| in_lopen(Y,v0,v800) )
& ( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| in_lopen(Z,v0,v16) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X,Y,Z] :
( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| in_lopen(Z,v0,v16) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_23,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
less(v16,v32),
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_189,v16)
| ~ less(v16,v32)
| less(X_189,v32) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_189)),bind(Y,$fot(v16)),bind(Z,$fot(v32))]]) ).
cnf(refute_0_3,plain,
( ~ leq(X_189,v16)
| less(X_189,v32) ),
inference(resolve,[$cnf( less(v16,v32) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ leq(v32,v16)
| less(v32,v32) ),
inference(subst,[],[refute_0_3:[bind(X_189,$fot(v32))]]) ).
cnf(refute_0_5,plain,
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ in_lopen(v32,v0,v16)
| leq(v32,v16) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(v0)),bind(B,$fot(v16)),bind(X,$fot(v32))]]) ).
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( $equal(Y,Y) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
leq(v32,v32),
inference(subst,[],[refute_0_10:[bind(Y,$fot(v32))]]) ).
cnf(refute_0_12,plain,
less(v0,v32),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
( ~ leq(v32,X_428)
| ~ less(v0,v32)
| in_lopen(v32,v0,X_428) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(v0)),bind(B,$fot(X_428)),bind(X,$fot(v32))]]) ).
cnf(refute_0_15,plain,
( ~ leq(v32,X_428)
| in_lopen(v32,v0,X_428) ),
inference(resolve,[$cnf( less(v0,v32) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ leq(v32,v32)
| in_lopen(v32,v0,v32) ),
inference(subst,[],[refute_0_15:[bind(X_428,$fot(v32))]]) ).
cnf(refute_0_17,plain,
in_lopen(v32,v0,v32),
inference(resolve,[$cnf( leq(v32,v32) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
less(v16,v400),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_19,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_20,plain,
( ~ less(v16,v400)
| leq(v16,v400) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(v16)),bind(Y,$fot(v400))]]) ).
cnf(refute_0_21,plain,
leq(v16,v400),
inference(resolve,[$cnf( less(v16,v400) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
less(v0,v16),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_23,plain,
( ~ leq(v16,X_428)
| ~ less(v0,v16)
| in_lopen(v16,v0,X_428) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(v0)),bind(B,$fot(X_428)),bind(X,$fot(v16))]]) ).
cnf(refute_0_24,plain,
( ~ leq(v16,X_428)
| in_lopen(v16,v0,X_428) ),
inference(resolve,[$cnf( less(v0,v16) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ leq(v16,v400)
| in_lopen(v16,v0,v400) ),
inference(subst,[],[refute_0_24:[bind(X_428,$fot(v400))]]) ).
cnf(refute_0_26,plain,
in_lopen(v16,v0,v400),
inference(resolve,[$cnf( leq(v16,v400) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
less(v16,v600),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_28,plain,
( ~ less(v16,v600)
| leq(v16,v600) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(v16)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_29,plain,
leq(v16,v600),
inference(resolve,[$cnf( less(v16,v600) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ leq(v16,v600)
| in_lopen(v16,v0,v600) ),
inference(subst,[],[refute_0_24:[bind(X_428,$fot(v600))]]) ).
cnf(refute_0_31,plain,
in_lopen(v16,v0,v600),
inference(resolve,[$cnf( leq(v16,v600) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ in_lopen(X,v0,v600)
| ~ in_lopen(Y,v0,v400)
| ~ in_lopen(Z,v0,v32)
| in_lopen(Z,v0,v16) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_33,plain,
( ~ in_lopen(X_5799,v0,v400)
| ~ in_lopen(X_5800,v0,v32)
| ~ in_lopen(v16,v0,v600)
| in_lopen(X_5800,v0,v16) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(v16)),bind(Y,$fot(X_5799)),bind(Z,$fot(X_5800))]]) ).
cnf(refute_0_34,plain,
( ~ in_lopen(X_5799,v0,v400)
| ~ in_lopen(X_5800,v0,v32)
| in_lopen(X_5800,v0,v16) ),
inference(resolve,[$cnf( in_lopen(v16,v0,v600) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ in_lopen(X_5802,v0,v32)
| ~ in_lopen(v16,v0,v400)
| in_lopen(X_5802,v0,v16) ),
inference(subst,[],[refute_0_34:[bind(X_5799,$fot(v16)),bind(X_5800,$fot(X_5802))]]) ).
cnf(refute_0_36,plain,
( ~ in_lopen(X_5802,v0,v32)
| in_lopen(X_5802,v0,v16) ),
inference(resolve,[$cnf( in_lopen(v16,v0,v400) )],[refute_0_26,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ in_lopen(v32,v0,v32)
| in_lopen(v32,v0,v16) ),
inference(subst,[],[refute_0_36:[bind(X_5802,$fot(v32))]]) ).
cnf(refute_0_38,plain,
in_lopen(v32,v0,v16),
inference(resolve,[$cnf( in_lopen(v32,v0,v32) )],[refute_0_17,refute_0_37]) ).
cnf(refute_0_39,plain,
leq(v32,v16),
inference(resolve,[$cnf( in_lopen(v32,v0,v16) )],[refute_0_38,refute_0_6]) ).
cnf(refute_0_40,plain,
less(v32,v32),
inference(resolve,[$cnf( leq(v32,v16) )],[refute_0_39,refute_0_4]) ).
cnf(refute_0_41,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_42,plain,
~ less(v32,v32),
inference(subst,[],[refute_0_41:[bind(X,$fot(v32))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( less(v32,v32) )],[refute_0_40,refute_0_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT079+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.09/0.35 % Computer : n020.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 14:15:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 15.95/16.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.95/16.23
% 15.95/16.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.95/16.24
%------------------------------------------------------------------------------