%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT076+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 06:16:15 AM UTC 2026
% Result : Theorem 0.02s 0.32s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 20 unt; 0 def)
% Number of atoms : 173 ( 51 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 156 ( 62 ~; 77 |; 8 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 82 ( 0 sgn 45 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X) ).
fof(transitive,axiom,
! [X,Y,Z] :
( ( less(X,Y)
& less(Y,Z) )
=> less(X,Z) ) ).
fof(trichotomy,axiom,
! [X,Y] :
( less(X,Y)
| X = Y
| less(Y,X) ) ).
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( less(X,Y)
| X = Y ) ) ).
fof(leq_antisym,axiom,
! [X,Y] :
( ( leq(X,Y)
& leq(Y,X) )
=> X = Y ) ).
fof(less_implies_leq,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ) ).
fof(ord_v400_v800,axiom,
less(v400,v800) ).
fof(odrl311,conjecture,
! [X] :
( leq(v800,X)
=> leq(v400,X) ) ).
fof(subgoal_0,plain,
! [X] :
( leq(v800,X)
=> leq(v400,X) ),
inference(strip,[],[odrl311]) ).
fof(negate_0_0,plain,
~ ! [X] :
( leq(v800,X)
=> leq(v400,X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ leq(v400,X)
& leq(v800,X) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(v400,skolemFOFtoCNF_X_2)
& leq(v800,skolemFOFtoCNF_X_2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(v400,skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( X = Y
| less(X,Y)
| less(Y,X) ),
inference(canonicalize,[],[trichotomy]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( X = Y
| less(X,Y)
| less(Y,X) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
less(v400,v800),
inference(canonicalize,[],[ord_v400_v800]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[transitive]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
leq(v800,skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_18,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( X != Y
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
~ leq(v400,skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ leq(skolemFOFtoCNF_X_2,v400)
| skolemFOFtoCNF_X_2 = v400
| less(skolemFOFtoCNF_X_2,v400) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(v400))]]) ).
cnf(refute_0_3,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ less(X_43,X_42)
| leq(X_43,X_42) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_43)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_5,plain,
( ~ less(X_36,X_37)
| leq(X_36,X_37) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_6,plain,
( X = Y
| less(X,Y)
| less(Y,X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( X_36 = X_37
| less(X_36,X_37)
| less(X_37,X_36) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_8,plain,
( X_36 = X_37
| leq(X_36,X_37)
| less(X_37,X_36) ),
inference(resolve,[$cnf( less(X_36,X_37) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
( X_42 = X_43
| leq(X_42,X_43)
| less(X_43,X_42) ),
inference(subst,[],[refute_0_8:[bind(X_36,$fot(X_42)),bind(X_37,$fot(X_43))]]) ).
cnf(refute_0_10,plain,
( X_42 = X_43
| leq(X_42,X_43)
| leq(X_43,X_42) ),
inference(resolve,[$cnf( less(X_43,X_42) )],[refute_0_9,refute_0_4]) ).
cnf(refute_0_11,plain,
( v400 = skolemFOFtoCNF_X_2
| leq(skolemFOFtoCNF_X_2,v400)
| leq(v400,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_10:[bind(X_42,$fot(v400)),bind(X_43,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_12,plain,
( v400 = skolemFOFtoCNF_X_2
| leq(skolemFOFtoCNF_X_2,v400) ),
inference(resolve,[$cnf( leq(v400,skolemFOFtoCNF_X_2) )],[refute_0_11,refute_0_0]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_X_2 = v400
| v400 = skolemFOFtoCNF_X_2
| less(skolemFOFtoCNF_X_2,v400) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v400) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( v400 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = v400 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(v400)),bind(Y0,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_X_2 = v400
| less(skolemFOFtoCNF_X_2,v400) ),
inference(resolve,[$cnf( $equal(v400,skolemFOFtoCNF_X_2) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
less(v400,v800),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_20,plain,
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( ~ less(X_83,v400)
| ~ less(v400,v800)
| less(X_83,v800) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_83)),bind(Y,$fot(v400)),bind(Z,$fot(v800))]]) ).
cnf(refute_0_22,plain,
( ~ less(X_83,v400)
| less(X_83,v800) ),
inference(resolve,[$cnf( less(v400,v800) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ less(skolemFOFtoCNF_X_2,v400)
| less(skolemFOFtoCNF_X_2,v800) ),
inference(subst,[],[refute_0_22:[bind(X_83,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_X_2 = v400
| less(skolemFOFtoCNF_X_2,v800) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,v400) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
leq(v800,skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_26,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_27,plain,
( ~ leq(skolemFOFtoCNF_X_2,v800)
| ~ leq(v800,skolemFOFtoCNF_X_2)
| v800 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_26:[bind(X,$fot(v800)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_28,plain,
( ~ leq(skolemFOFtoCNF_X_2,v800)
| v800 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(v800,skolemFOFtoCNF_X_2) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ less(skolemFOFtoCNF_X_2,v800)
| leq(skolemFOFtoCNF_X_2,v800) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(v800))]]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_X_2 = v400
| leq(skolemFOFtoCNF_X_2,v800) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,v800) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_X_2 = v400
| v800 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v800) )],[refute_0_30,refute_0_28]) ).
cnf(refute_0_32,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_33,plain,
( ~ less(skolemFOFtoCNF_X_2,v800)
| skolemFOFtoCNF_X_2 = v400
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(v800,skolemFOFtoCNF_X_2) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_X_2 = v400
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,v800) )],[refute_0_24,refute_0_33]) ).
cnf(refute_0_35,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_36,plain,
~ less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_37,plain,
skolemFOFtoCNF_X_2 = v400,
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_X_2 != v400
| v400 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(skolemFOFtoCNF_X_2)),bind(Y0,$fot(v400))]]) ).
cnf(refute_0_39,plain,
v400 = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,v400) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( v400 != skolemFOFtoCNF_X_2
| ~ leq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)
| leq(v400,skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( ~ leq(v400,skolemFOFtoCNF_X_2) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_41,plain,
( ~ leq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)
| leq(v400,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(v400,skolemFOFtoCNF_X_2) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
~ leq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( leq(v400,skolemFOFtoCNF_X_2) )],[refute_0_41,refute_0_0]) ).
cnf(refute_0_43,plain,
( X != Y
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_44,plain,
( Y != Y
| leq(Y,Y) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(Y))]]) ).
cnf(refute_0_45,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_46,plain,
leq(Y,Y),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
leq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_46:[bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_47,refute_0_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT076+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : metis --show proof --show saturation %s
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 7 14:11:56 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.02/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.32
% 0.02/0.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.02/0.32
%------------------------------------------------------------------------------