%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT085+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.65s 0.90s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 23
% Syntax : Number of formulae : 148 ( 38 unt; 0 def)
% Number of atoms : 365 ( 94 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 370 ( 153 ~; 162 |; 42 &)
% ( 6 <=>; 7 =>; 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 : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 113 ( 1 sgn 73 !; 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(leq_less_trans,axiom,
! [X,Y,Z] :
( ( leq(X,Y)
& less(Y,Z) )
=> less(X,Z) ) ).
fof(less_leq_trans,axiom,
! [X,Y,Z] :
( ( less(X,Y)
& leq(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_v50_v100,axiom,
less(v50,v100) ).
fof(ord_v100_v200,axiom,
less(v100,v200) ).
fof(ord_v200_v400,axiom,
less(v200,v400) ).
fof(distinct,axiom,
( v0 != v50
& v0 != v100
& v0 != v200
& v0 != v400
& v50 != v100
& v50 != v200
& v50 != v400
& v100 != v200
& v100 != v400
& v200 != v400 ) ).
fof(odrl445,conjecture,
~ ? [X,Y,Z] :
( ( in_lopen(X,v0,v200)
| in_lopen(Y,v0,v100)
| in_lopen(Z,v0,v50) )
& leq(v400,X)
& leq(v200,Y)
& leq(v100,Z) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( ( in_lopen(X,v0,v200)
| in_lopen(Y,v0,v100)
| in_lopen(Z,v0,v50) )
& leq(v400,X)
& leq(v200,Y) )
=> ~ leq(v100,Z) ),
inference(strip,[],[odrl445]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( ( in_lopen(X,v0,v200)
| in_lopen(Y,v0,v100)
| in_lopen(Z,v0,v50) )
& leq(v400,X)
& leq(v200,Y) )
=> ~ leq(v100,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y,Z] :
( leq(v100,Z)
& leq(v200,Y)
& leq(v400,X)
& ( in_lopen(X,v0,v200)
| in_lopen(Y,v0,v100)
| in_lopen(Z,v0,v50) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( leq(v100,skolemFOFtoCNF_Z)
& leq(v200,skolemFOFtoCNF_Y)
& leq(v400,skolemFOFtoCNF_X_2)
& ( in_lopen(skolemFOFtoCNF_X_2,v0,v200)
| in_lopen(skolemFOFtoCNF_Y,v0,v100)
| in_lopen(skolemFOFtoCNF_Z,v0,v50) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
leq(v200,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
less(v100,v200),
inference(canonicalize,[],[ord_v100_v200]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ leq(Y,Z)
| ~ less(X,Y)
| less(X,Z) ),
inference(canonicalize,[],[less_leq_trans]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ leq(Y,Z)
| ~ less(X,Y)
| less(X,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
leq(v400,skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
less(v200,v400),
inference(canonicalize,[],[ord_v200_v400]) ).
fof(normalize_0_8,plain,
leq(v100,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[transitive]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(canonicalize,[],[in_lopen]) ).
fof(normalize_0_16,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
( in_lopen(skolemFOFtoCNF_X_2,v0,v200)
| in_lopen(skolemFOFtoCNF_Y,v0,v100)
| in_lopen(skolemFOFtoCNF_Z,v0,v50) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_20,plain,
less(v50,v100),
inference(canonicalize,[],[ord_v50_v100]) ).
fof(normalize_0_21,plain,
! [X,Y,Z] :
( ~ leq(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[leq_less_trans]) ).
fof(normalize_0_22,plain,
! [X,Y,Z] :
( ~ leq(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_24,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
( v0 != v100
& v0 != v200
& v0 != v400
& v0 != v50
& v100 != v200
& v100 != v400
& v200 != v400
& v50 != v100
& v50 != v200
& v50 != v400 ),
inference(canonicalize,[],[distinct]) ).
fof(normalize_0_30,plain,
v50 != v100,
inference(conjunct,[],[normalize_0_29]) ).
cnf(refute_0_0,plain,
leq(v200,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
less(v100,v200),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ leq(Y,Z)
| ~ less(X,Y)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ leq(v200,X_218)
| ~ less(v100,v200)
| less(v100,X_218) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(v100)),bind(Y,$fot(v200)),bind(Z,$fot(X_218))]]) ).
cnf(refute_0_4,plain,
( ~ leq(v200,X_218)
| less(v100,X_218) ),
inference(resolve,[$cnf( less(v100,v200) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ leq(v200,skolemFOFtoCNF_Y)
| less(v100,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_4:[bind(X_218,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_6,plain,
less(v100,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( leq(v200,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
leq(v400,skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
less(v200,v400),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( ~ leq(v400,X_218)
| ~ less(v200,v400)
| less(v200,X_218) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(v200)),bind(Y,$fot(v400)),bind(Z,$fot(X_218))]]) ).
cnf(refute_0_10,plain,
( ~ leq(v400,X_218)
| less(v200,X_218) ),
inference(resolve,[$cnf( less(v200,v400) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ leq(v400,skolemFOFtoCNF_X_2)
| less(v200,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_10:[bind(X_218,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_12,plain,
less(v200,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( leq(v400,skolemFOFtoCNF_X_2) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
leq(v100,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_14,plain,
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_15,plain,
( ~ leq(v100,skolemFOFtoCNF_Z)
| v100 = skolemFOFtoCNF_Z
| less(v100,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(v100)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_16,plain,
( v100 = skolemFOFtoCNF_Z
| less(v100,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( leq(v100,skolemFOFtoCNF_Z) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
( ~ less(X_129,v100)
| ~ less(v100,skolemFOFtoCNF_Z)
| less(X_129,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_129)),bind(Y,$fot(v100)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_19,plain,
( ~ less(X_129,v100)
| v100 = skolemFOFtoCNF_Z
| less(X_129,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( less(v100,skolemFOFtoCNF_Z) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ less(skolemFOFtoCNF_Z,v100)
| v100 = skolemFOFtoCNF_Z
| less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_19:[bind(X_129,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_21,plain,
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_22,plain,
( ~ in_lopen(skolemFOFtoCNF_X_2,v0,v200)
| leq(skolemFOFtoCNF_X_2,v200) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(v0)),bind(B,$fot(v200)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_23,plain,
( ~ in_lopen(skolemFOFtoCNF_Y,v0,v100)
| leq(skolemFOFtoCNF_Y,v100) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(v0)),bind(B,$fot(v100)),bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_24,plain,
( in_lopen(skolemFOFtoCNF_X_2,v0,v200)
| in_lopen(skolemFOFtoCNF_Y,v0,v100)
| in_lopen(skolemFOFtoCNF_Z,v0,v50) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_25,plain,
( ~ in_lopen(skolemFOFtoCNF_Z,v0,v50)
| leq(skolemFOFtoCNF_Z,v50) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(v0)),bind(B,$fot(v50)),bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_26,plain,
( in_lopen(skolemFOFtoCNF_X_2,v0,v200)
| in_lopen(skolemFOFtoCNF_Y,v0,v100)
| leq(skolemFOFtoCNF_Z,v50) ),
inference(resolve,[$cnf( in_lopen(skolemFOFtoCNF_Z,v0,v50) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( in_lopen(skolemFOFtoCNF_X_2,v0,v200)
| leq(skolemFOFtoCNF_Y,v100)
| leq(skolemFOFtoCNF_Z,v50) ),
inference(resolve,[$cnf( in_lopen(skolemFOFtoCNF_Y,v0,v100) )],[refute_0_26,refute_0_23]) ).
cnf(refute_0_28,plain,
( leq(skolemFOFtoCNF_X_2,v200)
| leq(skolemFOFtoCNF_Y,v100)
| leq(skolemFOFtoCNF_Z,v50) ),
inference(resolve,[$cnf( in_lopen(skolemFOFtoCNF_X_2,v0,v200) )],[refute_0_27,refute_0_22]) ).
cnf(refute_0_29,plain,
less(v50,v100),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_30,plain,
( ~ leq(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_31,plain,
( ~ leq(X_164,v50)
| ~ less(v50,v100)
| less(X_164,v100) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_164)),bind(Y,$fot(v50)),bind(Z,$fot(v100))]]) ).
cnf(refute_0_32,plain,
( ~ leq(X_164,v50)
| less(X_164,v100) ),
inference(resolve,[$cnf( less(v50,v100) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ leq(skolemFOFtoCNF_Z,v50)
| less(skolemFOFtoCNF_Z,v100) ),
inference(subst,[],[refute_0_32:[bind(X_164,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_34,plain,
( leq(skolemFOFtoCNF_X_2,v200)
| leq(skolemFOFtoCNF_Y,v100)
| less(skolemFOFtoCNF_Z,v100) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_Z,v50) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
( v100 = skolemFOFtoCNF_Z
| leq(skolemFOFtoCNF_X_2,v200)
| leq(skolemFOFtoCNF_Y,v100)
| less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_Z,v100) )],[refute_0_34,refute_0_20]) ).
cnf(refute_0_36,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_37,plain,
~ less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_36:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_38,plain,
( v100 = skolemFOFtoCNF_Z
| leq(skolemFOFtoCNF_X_2,v200)
| leq(skolemFOFtoCNF_Y,v100) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_40,plain,
( ~ leq(skolemFOFtoCNF_Y,v100)
| ~ leq(v100,skolemFOFtoCNF_Y)
| skolemFOFtoCNF_Y = v100 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(v100))]]) ).
cnf(refute_0_41,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_42,plain,
( ~ less(v100,skolemFOFtoCNF_Y)
| leq(v100,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(v100)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_43,plain,
leq(v100,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( less(v100,skolemFOFtoCNF_Y) )],[refute_0_6,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ leq(skolemFOFtoCNF_Y,v100)
| skolemFOFtoCNF_Y = v100 ),
inference(resolve,[$cnf( leq(v100,skolemFOFtoCNF_Y) )],[refute_0_43,refute_0_40]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_Y = v100
| v100 = skolemFOFtoCNF_Z
| leq(skolemFOFtoCNF_X_2,v200) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_Y,v100) )],[refute_0_38,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ leq(skolemFOFtoCNF_X_2,v200)
| ~ leq(v200,skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_X_2 = v200 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(v200))]]) ).
cnf(refute_0_47,plain,
( ~ less(v200,skolemFOFtoCNF_X_2)
| leq(v200,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(v200)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_48,plain,
leq(v200,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( less(v200,skolemFOFtoCNF_X_2) )],[refute_0_12,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ leq(skolemFOFtoCNF_X_2,v200)
| skolemFOFtoCNF_X_2 = v200 ),
inference(resolve,[$cnf( leq(v200,skolemFOFtoCNF_X_2) )],[refute_0_48,refute_0_46]) ).
cnf(refute_0_50,plain,
( skolemFOFtoCNF_X_2 = v200
| skolemFOFtoCNF_Y = v100
| v100 = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v200) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_52,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_53,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_X_2 != v200
| v200 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(skolemFOFtoCNF_X_2)),bind(Y0,$fot(v200))]]) ).
cnf(refute_0_55,plain,
( skolemFOFtoCNF_Y = v100
| v100 = skolemFOFtoCNF_Z
| v200 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,v200) )],[refute_0_50,refute_0_54]) ).
cnf(refute_0_56,plain,
( v200 != skolemFOFtoCNF_X_2
| ~ less(v200,skolemFOFtoCNF_X_2)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( less(v200,skolemFOFtoCNF_X_2) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_57,plain,
( ~ less(v200,skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_Y = v100
| v100 = skolemFOFtoCNF_Z
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(v200,skolemFOFtoCNF_X_2) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( skolemFOFtoCNF_Y = v100
| v100 = skolemFOFtoCNF_Z
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(v200,skolemFOFtoCNF_X_2) )],[refute_0_12,refute_0_57]) ).
cnf(refute_0_59,plain,
~ less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_36:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_Y = v100
| v100 = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( skolemFOFtoCNF_Y != v100
| v100 = skolemFOFtoCNF_Y ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(skolemFOFtoCNF_Y)),bind(Y0,$fot(v100))]]) ).
cnf(refute_0_62,plain,
( v100 = skolemFOFtoCNF_Y
| v100 = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,v100) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( v100 != skolemFOFtoCNF_Y
| ~ less(v100,skolemFOFtoCNF_Y)
| less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
introduced(tautology,[equality,[$cnf( less(v100,skolemFOFtoCNF_Y) ),[0],$fot(skolemFOFtoCNF_Y)]]) ).
cnf(refute_0_64,plain,
( ~ less(v100,skolemFOFtoCNF_Y)
| v100 = skolemFOFtoCNF_Z
| less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( $equal(v100,skolemFOFtoCNF_Y) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( v100 = skolemFOFtoCNF_Z
| less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( less(v100,skolemFOFtoCNF_Y) )],[refute_0_6,refute_0_64]) ).
cnf(refute_0_66,plain,
~ less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_36:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_67,plain,
v100 = skolemFOFtoCNF_Z,
inference(resolve,[$cnf( less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( v100 != skolemFOFtoCNF_Z
| ~ less(v100,skolemFOFtoCNF_Y)
| less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
introduced(tautology,[equality,[$cnf( less(v100,skolemFOFtoCNF_Y) ),[0],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_0_69,plain,
( ~ less(v100,skolemFOFtoCNF_Y)
| less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( $equal(v100,skolemFOFtoCNF_Z) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( less(v100,skolemFOFtoCNF_Y) )],[refute_0_6,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ leq(X,v200)
| ~ less(v200,skolemFOFtoCNF_X_2)
| less(X,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_30:[bind(Y,$fot(v200)),bind(Z,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_72,plain,
( ~ leq(X,v200)
| less(X,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(v200,skolemFOFtoCNF_X_2) )],[refute_0_12,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ leq(skolemFOFtoCNF_X_2,v200)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_72:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_74,plain,
( v100 != skolemFOFtoCNF_Z
| ~ leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| leq(skolemFOFtoCNF_Y,v100) ),
introduced(tautology,[equality,[$cnf( ~ leq(skolemFOFtoCNF_Y,v100) ),[1],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_0_75,plain,
( ~ leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| leq(skolemFOFtoCNF_Y,v100) ),
inference(resolve,[$cnf( $equal(v100,skolemFOFtoCNF_Z) )],[refute_0_67,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_Y = v100 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_Y,v100) )],[refute_0_75,refute_0_44]) ).
cnf(refute_0_77,plain,
( skolemFOFtoCNF_Y != v100
| v100 != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),[0],$fot(v100)]]) ).
cnf(refute_0_78,plain,
( skolemFOFtoCNF_Y != v100
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(v100,skolemFOFtoCNF_Z) )],[refute_0_67,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,v100) )],[refute_0_76,refute_0_78]) ).
cnf(refute_0_80,plain,
( v100 != skolemFOFtoCNF_Z
| ~ leq(skolemFOFtoCNF_Y,v100)
| leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_Y,v100) ),[1],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_0_81,plain,
( ~ leq(skolemFOFtoCNF_Y,v100)
| leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(v100,skolemFOFtoCNF_Z) )],[refute_0_67,refute_0_80]) ).
cnf(refute_0_82,plain,
( leq(skolemFOFtoCNF_X_2,v200)
| leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| leq(skolemFOFtoCNF_Z,v50) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_Y,v100) )],[refute_0_28,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ less(v50,v100)
| leq(v50,v100) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(v50)),bind(Y,$fot(v100))]]) ).
cnf(refute_0_84,plain,
leq(v50,v100),
inference(resolve,[$cnf( less(v50,v100) )],[refute_0_29,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ leq(v100,v50)
| ~ leq(v50,v100)
| v50 = v100 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(v50)),bind(Y,$fot(v100))]]) ).
cnf(refute_0_86,plain,
( ~ leq(v100,v50)
| v50 = v100 ),
inference(resolve,[$cnf( leq(v50,v100) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
v50 != v100,
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_88,plain,
~ leq(v100,v50),
inference(resolve,[$cnf( $equal(v50,v100) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( v100 != skolemFOFtoCNF_Z
| ~ leq(skolemFOFtoCNF_Z,v50)
| leq(v100,v50) ),
introduced(tautology,[equality,[$cnf( ~ leq(v100,v50) ),[0],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_0_90,plain,
( ~ leq(skolemFOFtoCNF_Z,v50)
| leq(v100,v50) ),
inference(resolve,[$cnf( $equal(v100,skolemFOFtoCNF_Z) )],[refute_0_67,refute_0_89]) ).
cnf(refute_0_91,plain,
~ leq(skolemFOFtoCNF_Z,v50),
inference(resolve,[$cnf( leq(v100,v50) )],[refute_0_90,refute_0_88]) ).
cnf(refute_0_92,plain,
( leq(skolemFOFtoCNF_X_2,v200)
| leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_Z,v50) )],[refute_0_82,refute_0_91]) ).
cnf(refute_0_93,plain,
( skolemFOFtoCNF_Y = skolemFOFtoCNF_Z
| leq(skolemFOFtoCNF_X_2,v200) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_92,refute_0_79]) ).
cnf(refute_0_94,plain,
( skolemFOFtoCNF_Y = skolemFOFtoCNF_Z
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v200) )],[refute_0_93,refute_0_73]) ).
cnf(refute_0_95,plain,
skolemFOFtoCNF_Y = skolemFOFtoCNF_Z,
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_94,refute_0_59]) ).
cnf(refute_0_96,plain,
( skolemFOFtoCNF_Y != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Z = skolemFOFtoCNF_Y ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(skolemFOFtoCNF_Y)),bind(Y0,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_97,plain,
skolemFOFtoCNF_Z = skolemFOFtoCNF_Y,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( skolemFOFtoCNF_Z != skolemFOFtoCNF_Y
| ~ less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
introduced(tautology,[equality,[$cnf( less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),[0],$fot(skolemFOFtoCNF_Y)]]) ).
cnf(refute_0_99,plain,
( ~ less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( less(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_70,refute_0_99]) ).
cnf(refute_0_101,plain,
$false,
inference(resolve,[$cnf( less(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_100,refute_0_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT085+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n028.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 7 14:21:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.65/0.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.65/0.90
% 0.65/0.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.65/0.92
%------------------------------------------------------------------------------