%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT102+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 59 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 27 ~; 18 |; 7 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(ord_v600_v700,axiom,
less(v600,v700) ).
fof(distinct,axiom,
( v0 != v600
& v0 != v700
& v600 != v700 ) ).
fof(contradiction,axiom,
( less(v700,v600)
& less(v600,v700) ) ).
fof(normalize_0_0,plain,
( less(v600,v700)
& less(v700,v600) ),
inference(canonicalize,[],[contradiction]) ).
fof(normalize_0_1,plain,
less(v600,v700),
inference(canonicalize,[],[ord_v600_v700]) ).
fof(normalize_0_2,plain,
less(v700,v600),
inference(simplify,[],[normalize_0_0,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,
( v0 != v600
& v0 != v700
& v600 != v700 ),
inference(canonicalize,[],[distinct]) ).
fof(normalize_0_8,plain,
v600 != v700,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
less(v700,v600),
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(v700,v600)
| leq(v700,v600) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(v700)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_3,plain,
leq(v700,v600),
inference(resolve,[$cnf( less(v700,v600) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ leq(X,Y)
| ~ leq(Y,X)
| X = Y ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ leq(v600,v700)
| ~ leq(v700,v600)
| v700 = v600 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v700)),bind(Y,$fot(v600))]]) ).
cnf(refute_0_6,plain,
( ~ leq(v600,v700)
| v700 = v600 ),
inference(resolve,[$cnf( leq(v700,v600) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
less(v600,v700),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_8,plain,
( ~ less(v600,v700)
| leq(v600,v700) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(v600)),bind(Y,$fot(v700))]]) ).
cnf(refute_0_9,plain,
leq(v600,v700),
inference(resolve,[$cnf( less(v600,v700) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
v700 = v600,
inference(resolve,[$cnf( leq(v600,v700) )],[refute_0_9,refute_0_6]) ).
cnf(refute_0_11,plain,
v600 != v700,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( v700 != v600
| v600 = v700 ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(v700)),bind(Y0,$fot(v600))]]) ).
cnf(refute_0_16,plain,
v700 != v600,
inference(resolve,[$cnf( $equal(v600,v700) )],[refute_0_15,refute_0_11]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(v700,v600) )],[refute_0_10,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT102+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 : n010.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 14:38:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.10/0.40
%------------------------------------------------------------------------------