%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT080+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 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 126 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 46 ~; 33 |; 37 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 52 ( 2 sgn 35 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X) ).
fof(leq_antisym,axiom,
! [X,Y] :
( ( leq(X,Y)
& leq(Y,X) )
=> X = Y ) ).
fof(in_closed,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(A,X)
& leq(X,B) ) ) ).
fof(ord_v600_v800,axiom,
less(v600,v800) ).
fof(odrl365,conjecture,
~ ? [X,Y,Z,W] :
( in_closed(X,v600,v600)
& in_closed(X,v800,v800)
& less(v100,Y)
& in_open(Y,v0,v500)
& leq(v8,Z)
& in_lopen(Z,v0,v32)
& in_lopen(W,v0,v300)
& leq(v150,W) ) ).
fof(subgoal_0,plain,
! [X,Y,Z,W] :
( ( in_closed(X,v600,v600)
& in_closed(X,v800,v800)
& less(v100,Y)
& in_open(Y,v0,v500)
& leq(v8,Z)
& in_lopen(Z,v0,v32)
& in_lopen(W,v0,v300) )
=> ~ leq(v150,W) ),
inference(strip,[],[odrl365]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z,W] :
( ( in_closed(X,v600,v600)
& in_closed(X,v800,v800)
& less(v100,Y)
& in_open(Y,v0,v500)
& leq(v8,Z)
& in_lopen(Z,v0,v32)
& in_lopen(W,v0,v300) )
=> ~ leq(v150,W) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
less(v600,v800),
inference(canonicalize,[],[ord_v600_v800]) ).
fof(normalize_0_1,plain,
? [W,X,Y,Z] :
( in_closed(X,v600,v600)
& in_closed(X,v800,v800)
& in_lopen(W,v0,v300)
& in_lopen(Z,v0,v32)
& in_open(Y,v0,v500)
& leq(v150,W)
& leq(v8,Z)
& less(v100,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_2,plain,
( in_closed(skolemFOFtoCNF_X_2,v600,v600)
& in_closed(skolemFOFtoCNF_X_2,v800,v800)
& in_lopen(skolemFOFtoCNF_W,v0,v300)
& in_lopen(skolemFOFtoCNF_Z,v0,v32)
& in_open(skolemFOFtoCNF_Y,v0,v500)
& leq(v150,skolemFOFtoCNF_W)
& leq(v8,skolemFOFtoCNF_Z)
& less(v100,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
in_closed(skolemFOFtoCNF_X_2,v600,v600),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,X] :
( ~ in_closed(X,A,B)
<=> ( ~ leq(A,X)
| ~ leq(X,B) ) ),
inference(canonicalize,[],[in_closed]) ).
fof(normalize_0_5,plain,
! [A,B,X] :
( ~ in_closed(X,A,B)
<=> ( ~ leq(A,X)
| ~ leq(X,B) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,X] :
( ( ~ in_closed(X,A,B)
| leq(A,X) )
& ( ~ in_closed(X,A,B)
| leq(X,B) )
& ( ~ leq(A,X)
| ~ leq(X,B)
| in_closed(X,A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,X] :
( ~ in_closed(X,A,B)
| leq(A,X) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,X] :
( ~ in_closed(X,A,B)
| leq(X,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_11,plain,
in_closed(skolemFOFtoCNF_X_2,v800,v800),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_13,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
less(v600,v800),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
in_closed(skolemFOFtoCNF_X_2,v600,v600),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ in_closed(X,A,B)
| leq(A,X) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ in_closed(skolemFOFtoCNF_X_2,v600,v600)
| leq(v600,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(v600)),bind(B,$fot(v600)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_4,plain,
leq(v600,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X_2,v600,v600) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| ~ leq(v600,skolemFOFtoCNF_X_2)
| v600 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(v600)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_7,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| v600 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(v600,skolemFOFtoCNF_X_2) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ in_closed(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ in_closed(skolemFOFtoCNF_X_2,v600,v600)
| leq(skolemFOFtoCNF_X_2,v600) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(v600)),bind(B,$fot(v600)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_10,plain,
leq(skolemFOFtoCNF_X_2,v600),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X_2,v600,v600) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
v600 = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v600) )],[refute_0_10,refute_0_7]) ).
cnf(refute_0_12,plain,
( v600 != skolemFOFtoCNF_X_2
| ~ less(v600,v800)
| less(skolemFOFtoCNF_X_2,v800) ),
introduced(tautology,[equality,[$cnf( less(v600,v800) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_13,plain,
( ~ less(v600,v800)
| less(skolemFOFtoCNF_X_2,v800) ),
inference(resolve,[$cnf( $equal(v600,skolemFOFtoCNF_X_2) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
in_closed(skolemFOFtoCNF_X_2,v800,v800),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
( ~ in_closed(skolemFOFtoCNF_X_2,v800,v800)
| leq(v800,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(v800)),bind(B,$fot(v800)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_16,plain,
leq(v800,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X_2,v800,v800) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ leq(skolemFOFtoCNF_X_2,v800)
| ~ leq(v800,skolemFOFtoCNF_X_2)
| v800 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(v800)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_18,plain,
( ~ leq(skolemFOFtoCNF_X_2,v800)
| v800 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(v800,skolemFOFtoCNF_X_2) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ in_closed(skolemFOFtoCNF_X_2,v800,v800)
| leq(skolemFOFtoCNF_X_2,v800) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(v800)),bind(B,$fot(v800)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_20,plain,
leq(skolemFOFtoCNF_X_2,v800),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X_2,v800,v800) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
v800 = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v800) )],[refute_0_20,refute_0_18]) ).
cnf(refute_0_22,plain,
( v800 != skolemFOFtoCNF_X_2
| ~ less(skolemFOFtoCNF_X_2,v800)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( less(skolemFOFtoCNF_X_2,v800) ),[1],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_23,plain,
( ~ less(skolemFOFtoCNF_X_2,v800)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(v800,skolemFOFtoCNF_X_2) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ less(v600,v800)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,v800) )],[refute_0_13,refute_0_23]) ).
cnf(refute_0_25,plain,
less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( less(v600,v800) )],[refute_0_0,refute_0_24]) ).
cnf(refute_0_26,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_27,plain,
~ less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_26:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_25,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT080+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 14:18:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.10/0.45
%------------------------------------------------------------------------------