%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT083+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 81 ( 8 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 79 ( 39 ~; 26 |; 7 &)
% ( 3 <=>; 4 =>; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 42 ( 1 sgn 32 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexive,axiom,
! [X] : ~ less(X,X) ).
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_open,axiom,
! [X,A,B] :
( in_open(X,A,B)
<=> ( less(A,X)
& less(X,B) ) ) ).
fof(odrl423,conjecture,
~ ? [X] :
( in_open(X,v0,v600)
& less(v600,X) ) ).
fof(subgoal_0,plain,
! [X] :
( in_open(X,v0,v600)
=> ~ less(v600,X) ),
inference(strip,[],[odrl423]) ).
fof(negate_0_0,plain,
~ ! [X] :
( in_open(X,v0,v600)
=> ~ less(v600,X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( in_open(X,v0,v600)
& less(v600,X) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( in_open(skolemFOFtoCNF_X_2,v0,v600)
& less(v600,skolemFOFtoCNF_X_2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
less(v600,skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[less_implies_leq]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[leq_antisym]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
in_open(skolemFOFtoCNF_X_2,v0,v600),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [A,B,X] :
( ~ in_open(X,A,B)
<=> ( ~ less(A,X)
| ~ less(X,B) ) ),
inference(canonicalize,[],[in_open]) ).
fof(normalize_0_9,plain,
! [A,B,X] :
( ~ in_open(X,A,B)
<=> ( ~ less(A,X)
| ~ less(X,B) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,X] :
( ( ~ in_open(X,A,B)
| less(A,X) )
& ( ~ in_open(X,A,B)
| less(X,B) )
& ( ~ less(A,X)
| ~ less(X,B)
| in_open(X,A,B) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,X] :
( ~ in_open(X,A,B)
| less(X,B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : ~ less(X,X),
inference(canonicalize,[],[irreflexive]) ).
fof(normalize_0_13,plain,
! [X] : ~ less(X,X),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
less(v600,skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ less(X,Y)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,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_3,plain,
leq(v600,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( less(v600,skolemFOFtoCNF_X_2) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| ~ leq(v600,skolemFOFtoCNF_X_2)
| v600 = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v600)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_6,plain,
( ~ leq(skolemFOFtoCNF_X_2,v600)
| v600 = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( leq(v600,skolemFOFtoCNF_X_2) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ less(skolemFOFtoCNF_X_2,v600)
| leq(skolemFOFtoCNF_X_2,v600) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_8,plain,
in_open(skolemFOFtoCNF_X_2,v0,v600),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( ~ in_open(X,A,B)
| less(X,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
( ~ in_open(skolemFOFtoCNF_X_2,v0,v600)
| less(skolemFOFtoCNF_X_2,v600) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(v0)),bind(B,$fot(v600)),bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_11,plain,
less(skolemFOFtoCNF_X_2,v600),
inference(resolve,[$cnf( in_open(skolemFOFtoCNF_X_2,v0,v600) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
leq(skolemFOFtoCNF_X_2,v600),
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,v600) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
v600 = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X_2,v600) )],[refute_0_12,refute_0_6]) ).
cnf(refute_0_14,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_15,plain,
( ~ less(v600,skolemFOFtoCNF_X_2)
| less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(v600,skolemFOFtoCNF_X_2) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( less(v600,skolemFOFtoCNF_X_2) )],[refute_0_0,refute_0_15]) ).
cnf(refute_0_17,plain,
~ less(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
~ less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( less(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_16,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT083+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 7 14:22:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.11/0.39
%------------------------------------------------------------------------------