%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX206+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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:04:33 PM UTC 2026
% Result : Theorem 0.15s 0.34s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 9 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 5 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_003,axiom,
! [Y] : x2(z,Y) = Y ).
fof(goal_005,conjecture,
? [X] : x2(X,X) = X ).
fof(subgoal_0,plain,
? [X] : x2(X,X) = X,
inference(strip,[],[goal_005]) ).
fof(negate_0_0,plain,
~ ? [X] : x2(X,X) = X,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : x2(X,X) != X,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] : x2(X,X) != X,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] : x2(z,Y) = Y,
inference(canonicalize,[],[axiom_003]) ).
fof(normalize_0_3,plain,
! [Y] : x2(z,Y) = Y,
inference(specialize,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
x2(X,X) != X,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
x2(z,z) != z,
inference(subst,[],[refute_0_0:[bind(X,$fot(z))]]) ).
cnf(refute_0_2,plain,
x2(z,Y) = Y,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
x2(z,z) = z,
inference(subst,[],[refute_0_2:[bind(Y,$fot(z))]]) ).
cnf(refute_0_4,plain,
( x2(z,z) != z
| z != z
| x2(z,z) = z ),
introduced(tautology,[equality,[$cnf( ~ $equal(x2(z,z),z) ),[0],$fot(z)]]) ).
cnf(refute_0_5,plain,
( z != z
| x2(z,z) = z ),
inference(resolve,[$cnf( $equal(x2(z,z),z) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
z != z,
inference(resolve,[$cnf( $equal(x2(z,z),z) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
z = z,
introduced(tautology,[refl,[$fot(z)]]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( $equal(z,z) )],[refute_0_7,refute_0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 11:32:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.34
% 0.15/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.34
%------------------------------------------------------------------------------