%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT071+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n001.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 0.15s 0.53s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 22 unt; 0 def)
% Number of atoms : 183 ( 47 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 80 ~; 74 |; 13 &)
% ( 7 <=>; 5 =>; 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 82 ( 2 sgn 57 !; 2 ?)
% 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_closed,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(A,X)
& leq(X,B) ) ) ).
fof(shape_closed,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(A,X)
& leq(X,B) ) ) ).
fof(order_5_10,hypothesis,
less(n5,n10) ).
fof(no_false_conflict,conjecture,
~ ? [X] :
( in_closed(X,n0,n5)
& in_closed(X,n10,n15) ) ).
fof(subgoal_0,plain,
! [X] :
( in_closed(X,n0,n5)
=> ~ in_closed(X,n10,n15) ),
inference(strip,[],[no_false_conflict]) ).
fof(negate_0_0,plain,
~ ! [X] :
( in_closed(X,n0,n5)
=> ~ in_closed(X,n10,n15) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
less(n5,n10),
inference(canonicalize,[],[order_5_10]) ).
fof(normalize_0_1,plain,
? [X] :
( in_closed(X,n0,n5)
& in_closed(X,n10,n15) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_2,plain,
( in_closed(skolemFOFtoCNF_X_2,n0,n5)
& in_closed(skolemFOFtoCNF_X_2,n10,n15) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
in_closed(skolemFOFtoCNF_X_2,n10,n15),
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,[],[shape_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)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(conjunct,[],[normalize_0_10]) ).
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,
in_closed(skolemFOFtoCNF_X_2,n0,n5),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_15,plain,
! [A,B,X] :
( ~ in_closed(X,A,B)
| leq(X,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_21,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
less(n5,n10),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
in_closed(skolemFOFtoCNF_X_2,n10,n15),
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,n10,n15)
| leq(n10,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(n10)),bind(B,$fot(n15)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_4,plain,
leq(n10,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X_2,n10,n15) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ leq(X,Y)
| X = Y
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ leq(n10,skolemFOFtoCNF_X_2)
| n10 = skolemFOFtoCNF_X_2
| less(n10,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(n10)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_7,plain,
( n10 = skolemFOFtoCNF_X_2
| less(n10,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( leq(n10,skolemFOFtoCNF_X_2) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ less(n10,X_100)
| ~ less(n5,n10)
| less(n5,X_100) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(n5)),bind(Y,$fot(n10)),bind(Z,$fot(X_100))]]) ).
cnf(refute_0_10,plain,
( ~ less(n10,X_100)
| less(n5,X_100) ),
inference(resolve,[$cnf( less(n5,n10) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ less(n10,skolemFOFtoCNF_X_2)
| less(n5,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_10:[bind(X_100,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_12,plain,
( n10 = skolemFOFtoCNF_X_2
| less(n5,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(n10,skolemFOFtoCNF_X_2) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
in_closed(skolemFOFtoCNF_X_2,n0,n5),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_14,plain,
( ~ in_closed(X,A,B)
| leq(X,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_15,plain,
( ~ in_closed(skolemFOFtoCNF_X_2,n0,n5)
| leq(skolemFOFtoCNF_X_2,n5) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(n0)),bind(B,$fot(n5)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_16,plain,
leq(skolemFOFtoCNF_X_2,n5),
inference(resolve,[$cnf( in_closed(skolemFOFtoCNF_X_2,n0,n5) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_18,plain,
( ~ leq(n5,skolemFOFtoCNF_X_2)
| ~ leq(skolemFOFtoCNF_X_2,n5)
| skolemFOFtoCNF_X_2 = n5 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(n5))]]) ).
cnf(refute_0_19,plain,
( ~ leq(n5,skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_X_2 = n5 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,n5) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_21,plain,
( ~ less(n5,skolemFOFtoCNF_X_2)
| leq(n5,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(n5)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_22,plain,
( n10 = skolemFOFtoCNF_X_2
| leq(n5,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( less(n5,skolemFOFtoCNF_X_2) )],[refute_0_12,refute_0_21]) ).
cnf(refute_0_23,plain,
( n10 = skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = n5 ),
inference(resolve,[$cnf( leq(n5,skolemFOFtoCNF_X_2) )],[refute_0_22,refute_0_19]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_X_2 != n5
| ~ less(n5,skolemFOFtoCNF_X_2)
| less(n5,n5) ),
introduced(tautology,[equality,[$cnf( less(n5,skolemFOFtoCNF_X_2) ),[1],$fot(n5)]]) ).
cnf(refute_0_25,plain,
( ~ less(n5,skolemFOFtoCNF_X_2)
| n10 = skolemFOFtoCNF_X_2
| less(n5,n5) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,n5) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( n10 = skolemFOFtoCNF_X_2
| less(n5,n5) ),
inference(resolve,[$cnf( less(n5,skolemFOFtoCNF_X_2) )],[refute_0_12,refute_0_25]) ).
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( $equal(X0,X0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( n10 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = n10 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(n10)),bind(Y0,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_X_2 = n10
| skolemFOFtoCNF_X_2 = n5 ),
inference(resolve,[$cnf( $equal(n10,skolemFOFtoCNF_X_2) )],[refute_0_23,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_X_2 != n10
| ~ leq(n5,n10)
| leq(n5,skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( ~ leq(n5,skolemFOFtoCNF_X_2) ),[1],$fot(n10)]]) ).
cnf(refute_0_33,plain,
( ~ leq(n5,n10)
| skolemFOFtoCNF_X_2 = n5
| leq(n5,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,n10) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ leq(n5,n10)
| skolemFOFtoCNF_X_2 = n5 ),
inference(resolve,[$cnf( leq(n5,skolemFOFtoCNF_X_2) )],[refute_0_33,refute_0_19]) ).
cnf(refute_0_35,plain,
( ~ less(n5,n10)
| leq(n5,n10) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(n5)),bind(Y,$fot(n10))]]) ).
cnf(refute_0_36,plain,
leq(n5,n10),
inference(resolve,[$cnf( less(n5,n10) )],[refute_0_0,refute_0_35]) ).
cnf(refute_0_37,plain,
skolemFOFtoCNF_X_2 = n5,
inference(resolve,[$cnf( leq(n5,n10) )],[refute_0_36,refute_0_34]) ).
cnf(refute_0_38,plain,
( n10 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 != n5
| n10 = n5 ),
introduced(tautology,[equality,[$cnf( ~ $equal(n10,n5) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_39,plain,
( n10 != skolemFOFtoCNF_X_2
| n10 = n5 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,n5) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( n10 = n5
| less(n5,n5) ),
inference(resolve,[$cnf( $equal(n10,skolemFOFtoCNF_X_2) )],[refute_0_26,refute_0_39]) ).
cnf(refute_0_41,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_42,plain,
~ less(n5,n5),
inference(subst,[],[refute_0_41:[bind(X,$fot(n5))]]) ).
cnf(refute_0_43,plain,
n10 = n5,
inference(resolve,[$cnf( less(n5,n5) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
( n10 != n5
| n5 = n10 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(n10)),bind(Y0,$fot(n5))]]) ).
cnf(refute_0_45,plain,
n5 = n10,
inference(resolve,[$cnf( $equal(n10,n5) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( n5 != n10
| ~ less(n5,n10)
| less(n10,n10) ),
introduced(tautology,[equality,[$cnf( less(n5,n10) ),[0],$fot(n10)]]) ).
cnf(refute_0_47,plain,
( ~ less(n5,n10)
| less(n10,n10) ),
inference(resolve,[$cnf( $equal(n5,n10) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
less(n10,n10),
inference(resolve,[$cnf( less(n5,n10) )],[refute_0_0,refute_0_47]) ).
cnf(refute_0_49,plain,
~ less(n10,n10),
inference(subst,[],[refute_0_41:[bind(X,$fot(n10))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( less(n10,n10) )],[refute_0_48,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT071+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.44 % Computer : n001.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8046.5625MB
% 0.11/0.44 % OS : Linux 6.8.0-71-generic
% 0.11/0.44 % CPULimit : 300
% 0.11/0.44 % WCLimit : 300
% 0.11/0.44 % DateTime : Mon Sep 7 13:59:37 UTC 2026
% 0.11/0.44 % CPUTime :
% 0.11/0.45 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.53
% 0.15/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.54
%------------------------------------------------------------------------------