%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:04:32 PM UTC 2026
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 65 ( 6 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 20 |; 3 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 9 sgn 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_007,axiom,
! [Z] : ~ leqNat(s(Z),z) ).
fof(axiom_009,axiom,
! [Y] : merge(nil,Y) = Y ).
fof(axiom_013,axiom,
ord(nil) ).
fof(axiom_015,axiom,
! [Y,Y2,Xs] :
( ord(cons(Y,cons(Y2,Xs)))
<=> ( leqNat(Y,Y2)
& ord(cons(Y2,Xs)) ) ) ).
fof(goal_016,conjecture,
? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ) ).
fof(subgoal_0,plain,
? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
inference(strip,[],[goal_016]) ).
fof(negate_0_0,plain,
~ ? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Z] : ~ leqNat(s(Z),z),
inference(canonicalize,[],[axiom_007]) ).
fof(normalize_0_1,plain,
! [Z] : ~ leqNat(s(Z),z),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Xs,Y,Y2] :
( ~ ord(cons(Y,cons(Y2,Xs)))
<=> ( ~ leqNat(Y,Y2)
| ~ ord(cons(Y2,Xs)) ) ),
inference(canonicalize,[],[axiom_015]) ).
fof(normalize_0_3,plain,
! [Xs,Y,Y2] :
( ~ ord(cons(Y,cons(Y2,Xs)))
<=> ( ~ leqNat(Y,Y2)
| ~ ord(cons(Y2,Xs)) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Xs,Y,Y2] :
( ( ~ ord(cons(Y,cons(Y2,Xs)))
| leqNat(Y,Y2) )
& ( ~ ord(cons(Y,cons(Y2,Xs)))
| ord(cons(Y2,Xs)) )
& ( ~ leqNat(Y,Y2)
| ~ ord(cons(Y2,Xs))
| ord(cons(Y,cons(Y2,Xs))) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Xs,Y,Y2] :
( ~ ord(cons(Y,cons(Y2,Xs)))
| leqNat(Y,Y2) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
ord(nil),
inference(canonicalize,[],[axiom_013]) ).
fof(normalize_0_7,plain,
! [Xs,Ys] :
( ~ ord(Xs)
| ord(Ys)
| ord(merge(Xs,Ys)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
! [Xs,Ys] :
( ~ ord(Xs)
| ord(Ys)
| ord(merge(Xs,Ys)) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] : merge(nil,Y) = Y,
inference(canonicalize,[],[axiom_009]) ).
fof(normalize_0_10,plain,
! [Y] : merge(nil,Y) = Y,
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
~ leqNat(s(Z),z),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ ord(cons(Y,cons(Y2,Xs)))
| leqNat(Y,Y2) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
ord(nil),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ ord(Xs)
| ord(Ys)
| ord(merge(Xs,Ys)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ ord(nil)
| ord(X_42)
| ord(merge(nil,X_42)) ),
inference(subst,[],[refute_0_3:[bind(Xs,$fot(nil)),bind(Ys,$fot(X_42))]]) ).
cnf(refute_0_5,plain,
( ord(X_42)
| ord(merge(nil,X_42)) ),
inference(resolve,[$cnf( ord(nil) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
merge(nil,Y) = Y,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
merge(nil,X_42) = X_42,
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_8,plain,
( merge(nil,X_42) != X_42
| ~ ord(merge(nil,X_42))
| ord(X_42) ),
introduced(tautology,[equality,[$cnf( ord(merge(nil,X_42)) ),[0],$fot(X_42)]]) ).
cnf(refute_0_9,plain,
( ~ ord(merge(nil,X_42))
| ord(X_42) ),
inference(resolve,[$cnf( $equal(merge(nil,X_42),X_42) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
ord(X_42),
inference(resolve,[$cnf( ord(merge(nil,X_42)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
ord(cons(Y,cons(Y2,Xs))),
inference(subst,[],[refute_0_10:[bind(X_42,$fot(cons(Y,cons(Y2,Xs))))]]) ).
cnf(refute_0_12,plain,
leqNat(Y,Y2),
inference(resolve,[$cnf( ord(cons(Y,cons(Y2,Xs))) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
leqNat(s(Z),z),
inference(subst,[],[refute_0_12:[bind(Y,$fot(s(Z))),bind(Y2,$fot(z))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( leqNat(s(Z),z) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 11:16:53 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------