%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 06:16:18 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 23 unt; 0 def)
% Number of atoms : 171 ( 55 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 171 ( 78 ~; 71 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 69 ( 1 sgn 49 !; 0 ?)
% 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_v800,axiom,
less(v600,v800) ).
fof(distinct,axiom,
( v0 != v600
& v0 != v800
& v600 != v800 ) ).
fof(wit_in_lopen,axiom,
in_lopen(w,v0,v600) ).
fof(wit_leq,axiom,
leq(v800,w) ).
fof(normalize_0_0,plain,
less(v600,v800),
inference(canonicalize,[],[ord_v600_v800]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[transitive]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
leq(v800,w),
inference(canonicalize,[],[wit_leq]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
in_lopen(w,v0,v600),
inference(canonicalize,[],[wit_in_lopen]) ).
fof(normalize_0_9,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(canonicalize,[],[in_lopen]) ).
fof(normalize_0_10,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
<=> ( ~ leq(X,B)
| ~ less(A,X) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,plain,
! [A,B,X] :
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(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,
( v0 != v600
& v0 != v800
& v600 != v800 ),
inference(canonicalize,[],[distinct]) ).
fof(normalize_0_20,plain,
v600 != v800,
inference(conjunct,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
less(v600,v800),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ less(X_87,v600)
| ~ less(v600,v800)
| less(X_87,v800) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_87)),bind(Y,$fot(v600)),bind(Z,$fot(v800))]]) ).
cnf(refute_0_3,plain,
( ~ less(X_87,v600)
| less(X_87,v800) ),
inference(resolve,[$cnf( less(v600,v800) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ less(v800,v600)
| less(v800,v800) ),
inference(subst,[],[refute_0_3:[bind(X_87,$fot(v800))]]) ).
cnf(refute_0_5,plain,
leq(v800,w),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_6,plain,
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( ~ leq(v800,w)
| v800 = w
| less(v800,w) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(v800)),bind(Y,$fot(w))]]) ).
cnf(refute_0_8,plain,
( v800 = w
| less(v800,w) ),
inference(resolve,[$cnf( leq(v800,w) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
in_lopen(w,v0,v600),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( ~ in_lopen(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( ~ in_lopen(w,v0,v600)
| leq(w,v600) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(v0)),bind(B,$fot(v600)),bind(X,$fot(w))]]) ).
cnf(refute_0_12,plain,
leq(w,v600),
inference(resolve,[$cnf( in_lopen(w,v0,v600) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ leq(w,v600)
| w = v600
| less(w,v600) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(w)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_14,plain,
( w = v600
| less(w,v600) ),
inference(resolve,[$cnf( leq(w,v600) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ less(w,v600)
| less(w,v800) ),
inference(subst,[],[refute_0_3:[bind(X_87,$fot(w))]]) ).
cnf(refute_0_16,plain,
( w = v600
| less(w,v800) ),
inference(resolve,[$cnf( less(w,v600) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
( ~ leq(v800,w)
| ~ leq(w,v800)
| v800 = w ),
inference(subst,[],[refute_0_17:[bind(X,$fot(v800)),bind(Y,$fot(w))]]) ).
cnf(refute_0_19,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_20,plain,
( ~ less(w,v800)
| leq(w,v800) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(w)),bind(Y,$fot(v800))]]) ).
cnf(refute_0_21,plain,
( w = v600
| leq(w,v800) ),
inference(resolve,[$cnf( less(w,v800) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ leq(v800,w)
| v800 = w
| w = v600 ),
inference(resolve,[$cnf( leq(w,v800) )],[refute_0_21,refute_0_18]) ).
cnf(refute_0_23,plain,
( v800 = w
| w = v600 ),
inference(resolve,[$cnf( leq(v800,w) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_25,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_26,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( v800 != w
| w = v800 ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(v800)),bind(Y0,$fot(w))]]) ).
cnf(refute_0_28,plain,
( w = v600
| w = v800 ),
inference(resolve,[$cnf( $equal(v800,w) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( w != v800
| ~ less(w,v800)
| less(v800,v800) ),
introduced(tautology,[equality,[$cnf( less(w,v800) ),[0],$fot(v800)]]) ).
cnf(refute_0_30,plain,
( ~ less(w,v800)
| w = v600
| less(v800,v800) ),
inference(resolve,[$cnf( $equal(w,v800) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( w = v600
| less(v800,v800) ),
inference(resolve,[$cnf( less(w,v800) )],[refute_0_16,refute_0_30]) ).
cnf(refute_0_32,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_33,plain,
~ less(v800,v800),
inference(subst,[],[refute_0_32:[bind(X,$fot(v800))]]) ).
cnf(refute_0_34,plain,
w = v600,
inference(resolve,[$cnf( less(v800,v800) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
( v800 != w
| w != v600
| v800 = v600 ),
introduced(tautology,[equality,[$cnf( ~ $equal(v800,v600) ),[0],$fot(w)]]) ).
cnf(refute_0_36,plain,
( v800 != w
| v800 = v600 ),
inference(resolve,[$cnf( $equal(w,v600) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( v800 = v600
| less(v800,w) ),
inference(resolve,[$cnf( $equal(v800,w) )],[refute_0_8,refute_0_36]) ).
cnf(refute_0_38,plain,
( w != v600
| ~ less(v800,w)
| less(v800,v600) ),
introduced(tautology,[equality,[$cnf( less(v800,w) ),[1],$fot(v600)]]) ).
cnf(refute_0_39,plain,
( ~ less(v800,w)
| less(v800,v600) ),
inference(resolve,[$cnf( $equal(w,v600) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
( v800 = v600
| less(v800,v600) ),
inference(resolve,[$cnf( less(v800,w) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
v600 != v800,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_42,plain,
( v800 != v600
| v600 = v800 ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(v800)),bind(Y0,$fot(v600))]]) ).
cnf(refute_0_43,plain,
v800 != v600,
inference(resolve,[$cnf( $equal(v600,v800) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
less(v800,v600),
inference(resolve,[$cnf( $equal(v800,v600) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
less(v800,v800),
inference(resolve,[$cnf( less(v800,v600) )],[refute_0_44,refute_0_4]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( less(v800,v800) )],[refute_0_45,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT106+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 : n014.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 14:41:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.42
%------------------------------------------------------------------------------