%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT078+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 21 unt; 0 def)
% Number of atoms : 224 ( 81 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 265 ( 117 ~; 65 |; 72 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 81 ( 1 sgn 55 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X) ).
fof(transitive,axiom,
! [X,Y,Z] :
( ( less(X,Y)
& less(Y,Z) )
=> less(X,Z) ) ).
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(in_lopen,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ) ).
fof(ord_v600_v1200,axiom,
less(v600,v1200) ).
fof(distinct,axiom,
( v0 != v8
& v0 != v32
& v0 != v200
& v0 != v600
& v0 != v800
& v0 != v1200
& v8 != v32
& v8 != v200
& v8 != v600
& v8 != v800
& v8 != v1200
& v32 != v200
& v32 != v600
& v32 != v800
& v32 != v1200
& v200 != v600
& v200 != v800
& v200 != v1200
& v600 != v800
& v600 != v1200
& v800 != v1200 ) ).
fof(odrl341,conjecture,
~ ? [X,Y,Z] :
( in_lopen(X,v0,v600)
& leq(v1200,X)
& in_lopen(Y,v0,v800)
& leq(v200,Y)
& in_lopen(Z,v0,v32)
& leq(v8,Z) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( in_lopen(X,v0,v600)
& leq(v1200,X)
& in_lopen(Y,v0,v800)
& leq(v200,Y)
& in_lopen(Z,v0,v32) )
=> ~ leq(v8,Z) ),
inference(strip,[],[odrl341]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( in_lopen(X,v0,v600)
& leq(v1200,X)
& in_lopen(Y,v0,v800)
& leq(v200,Y)
& in_lopen(Z,v0,v32) )
=> ~ leq(v8,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
less(v600,v1200),
inference(canonicalize,[],[ord_v600_v1200]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( v0 != v1200
& v0 != v200
& v0 != v32
& v0 != v600
& v0 != v8
& v0 != v800
& v200 != v1200
& v200 != v600
& v200 != v800
& v32 != v1200
& v32 != v200
& v32 != v600
& v32 != v800
& v600 != v1200
& v600 != v800
& v8 != v1200
& v8 != v200
& v8 != v32
& v8 != v600
& v8 != v800
& v800 != v1200 ),
inference(canonicalize,[],[distinct]) ).
fof(normalize_0_6,plain,
v600 != v1200,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [X,Y,Z] :
( in_lopen(X,v0,v600)
& in_lopen(Y,v0,v800)
& in_lopen(Z,v0,v32)
& leq(v1200,X)
& leq(v200,Y)
& leq(v8,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
( in_lopen(skolemFOFtoCNF_X_2,v0,v600)
& in_lopen(skolemFOFtoCNF_Y,v0,v800)
& in_lopen(skolemFOFtoCNF_Z,v0,v32)
& leq(v1200,skolemFOFtoCNF_X_2)
& leq(v200,skolemFOFtoCNF_Y)
& leq(v8,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
leq(v1200,skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[transitive]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
in_lopen(skolemFOFtoCNF_X_2,v0,v600),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_17,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(canonicalize,[],[in_lopen]) ).
fof(normalize_0_18,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,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_18]) ).
fof(normalize_0_20,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_22,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_21]) ).
cnf(refute_0_0,plain,
less(v600,v1200),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ less(v600,v1200)
| leq(v600,v1200) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(v600)),bind(Y,$fot(v1200))]]) ).
cnf(refute_0_3,plain,
leq(v600,v1200),
inference(resolve,[$cnf( less(v600,v1200) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_5,plain,
( ~ leq(v1200,v600)
| ~ leq(v600,v1200)
| v600 = v1200 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v600)),bind(Y,$fot(v1200))]]) ).
cnf(refute_0_6,plain,
( ~ leq(v1200,v600)
| v600 = v1200 ),
inference(resolve,[$cnf( leq(v600,v1200) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
v600 != v1200,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
~ leq(v1200,v600),
inference(resolve,[$cnf( $equal(v600,v1200) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
leq(v1200,skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ leq(v1200,skolemFOFtoCNF_X_2)
| v1200 = skolemFOFtoCNF_X_2
| less(v1200,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(v1200)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_12,plain,
( v1200 = skolemFOFtoCNF_X_2
| less(v1200,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( leq(v1200,skolemFOFtoCNF_X_2) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( ~ less(v1200,X_97)
| ~ less(v600,v1200)
| less(v600,X_97) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(v600)),bind(Y,$fot(v1200)),bind(Z,$fot(X_97))]]) ).
cnf(refute_0_15,plain,
( ~ less(v1200,X_97)
| less(v600,X_97) ),
inference(resolve,[$cnf( less(v600,v1200) )],[refute_0_0,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ less(v1200,skolemFOFtoCNF_X_2)
| less(v600,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_15:[bind(X_97,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_17,plain,
( v1200 = skolemFOFtoCNF_X_2
| less(v600,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(v1200,skolemFOFtoCNF_X_2) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| ~ leq(v600,skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_X_2 = v600 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_19,plain,
( ~ less(v600,skolemFOFtoCNF_X_2)
| leq(v600,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(v600)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_20,plain,
( v1200 = skolemFOFtoCNF_X_2
| leq(v600,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(v600,skolemFOFtoCNF_X_2) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| skolemFOFtoCNF_X_2 = v600
| v1200 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(v600,skolemFOFtoCNF_X_2) )],[refute_0_20,refute_0_18]) ).
cnf(refute_0_22,plain,
in_lopen(skolemFOFtoCNF_X_2,v0,v600),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_23,plain,
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_24,plain,
( ~ in_lopen(skolemFOFtoCNF_X_2,v0,v600)
| leq(skolemFOFtoCNF_X_2,v600) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(v0)),bind(B,$fot(v600)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_25,plain,
leq(skolemFOFtoCNF_X_2,v600),
inference(resolve,[$cnf( in_lopen(skolemFOFtoCNF_X_2,v0,v600) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_X_2 = v600
| v1200 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v600) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_28,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_29,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_X_2 != v600
| v600 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(skolemFOFtoCNF_X_2)),bind(Y0,$fot(v600))]]) ).
cnf(refute_0_31,plain,
( v1200 = skolemFOFtoCNF_X_2
| v600 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,v600) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( v600 != skolemFOFtoCNF_X_2
| ~ less(v600,skolemFOFtoCNF_X_2)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( less(v600,skolemFOFtoCNF_X_2) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_33,plain,
( ~ less(v600,skolemFOFtoCNF_X_2)
| v1200 = skolemFOFtoCNF_X_2
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(v600,skolemFOFtoCNF_X_2) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( v1200 = skolemFOFtoCNF_X_2
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(v600,skolemFOFtoCNF_X_2) )],[refute_0_17,refute_0_33]) ).
cnf(refute_0_35,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_36,plain,
~ less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_37,plain,
v1200 = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( v1200 != skolemFOFtoCNF_X_2
| ~ leq(skolemFOFtoCNF_X_2,v600)
| leq(v1200,v600) ),
introduced(tautology,[equality,[$cnf( ~ leq(v1200,v600) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_39,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| leq(v1200,v600) ),
inference(resolve,[$cnf( $equal(v1200,skolemFOFtoCNF_X_2) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
~ leq(skolemFOFtoCNF_X_2,v600),
inference(resolve,[$cnf( leq(v1200,v600) )],[refute_0_39,refute_0_8]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v600) )],[refute_0_25,refute_0_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT078+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 : n005.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 14:13:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.10/0.45
%------------------------------------------------------------------------------