%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT089+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 06:16:17 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 49 ( 9 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 48 ( 24 ~; 13 |; 5 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_def,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( less(X,Y)
| X = Y ) ) ).
fof(prec_oo,axiom,
! [U,L] :
( prec(U,L,o,o)
<=> leq(U,L) ) ).
fof(odrl604,conjecture,
prec(v5,v5,o,o) ).
fof(subgoal_0,plain,
prec(v5,v5,o,o),
inference(strip,[],[odrl604]) ).
fof(negate_0_0,plain,
~ prec(v5,v5,o,o),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ prec(v5,v5,o,o),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(canonicalize,[],[leq_def]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ( X != Y
& ~ less(X,Y) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,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_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( X != Y
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [L,U] :
( ~ leq(U,L)
<=> ~ prec(U,L,o,o) ),
inference(canonicalize,[],[prec_oo]) ).
fof(normalize_0_6,plain,
! [L,U] :
( ~ leq(U,L)
<=> ~ prec(U,L,o,o) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [L,U] :
( ( ~ leq(U,L)
| prec(U,L,o,o) )
& ( ~ prec(U,L,o,o)
| leq(U,L) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [L,U] :
( ~ leq(U,L)
| prec(U,L,o,o) ),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
~ prec(v5,v5,o,o),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( X != Y
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( Y != Y
| leq(Y,Y) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_3,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_4,plain,
leq(Y,Y),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
leq(X_13,X_13),
inference(subst,[],[refute_0_4:[bind(Y,$fot(X_13))]]) ).
cnf(refute_0_6,plain,
( ~ leq(U,L)
| prec(U,L,o,o) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ leq(X_13,X_13)
| prec(X_13,X_13,o,o) ),
inference(subst,[],[refute_0_6:[bind(L,$fot(X_13)),bind(U,$fot(X_13))]]) ).
cnf(refute_0_8,plain,
prec(X_13,X_13,o,o),
inference(resolve,[$cnf( leq(X_13,X_13) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
prec(v5,v5,o,o),
inference(subst,[],[refute_0_8:[bind(X_13,$fot(v5))]]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( prec(v5,v5,o,o) )],[refute_0_9,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT089+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.34 % Computer : n004.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 7 14:00:00 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------