%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 07:04:30 PM UTC 2026
% Result : Theorem 0.18s 0.44s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 26
% Syntax : Number of formulae : 103 ( 64 unt; 0 def)
% Number of atoms : 159 ( 158 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 121 ( 65 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 6 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_008,axiom,
! [X,X2,X3] : n(X) != x(X2,X3) ).
fof(axiom_039,axiom,
! [Y] : d(n(Y)) = n(z) ).
fof(axiom_040,axiom,
! [F,G] : d(x(F,G)) = x(d(F),d(G)) ).
fof(axiom_042,axiom,
d(x2) = n(s(z)) ).
fof(axiom_050,axiom,
! [E] : opt(x(n(z),E)) = E ).
fof(goal_054,conjecture,
? [E] : opt(d(E)) != opt(d(opt(E))) ).
fof(subgoal_0,plain,
? [E] : opt(d(E)) != opt(d(opt(E))),
inference(strip,[],[goal_054]) ).
fof(negate_0_0,plain,
~ ? [E] : opt(d(E)) != opt(d(opt(E))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [F,G] : d(x(F,G)) = x(d(F),d(G)),
inference(canonicalize,[],[axiom_040]) ).
fof(normalize_0_1,plain,
! [F,G] : d(x(F,G)) = x(d(F),d(G)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] : d(n(Y)) = n(z),
inference(canonicalize,[],[axiom_039]) ).
fof(normalize_0_3,plain,
! [Y] : d(n(Y)) = n(z),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
d(x2) = n(s(z)),
inference(canonicalize,[],[axiom_042]) ).
fof(normalize_0_5,plain,
! [E] : opt(x(n(z),E)) = E,
inference(canonicalize,[],[axiom_050]) ).
fof(normalize_0_6,plain,
! [E] : opt(x(n(z),E)) = E,
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [E] : opt(d(E)) = opt(d(opt(E))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
! [E] : opt(d(E)) = opt(d(opt(E))),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,X2,X3] : n(X) != x(X2,X3),
inference(canonicalize,[],[axiom_008]) ).
fof(normalize_0_10,plain,
! [X,X2,X3] : n(X) != x(X2,X3),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
d(x(F,G)) = x(d(F),d(G)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
d(x(X_37,d(x2))) = x(d(X_37),d(d(x2))),
inference(subst,[],[refute_0_0:[bind(F,$fot(X_37)),bind(G,$fot(d(x2)))]]) ).
cnf(refute_0_2,plain,
d(n(Y)) = n(z),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
d(n(s(z))) = n(z),
inference(subst,[],[refute_0_2:[bind(Y,$fot(s(z)))]]) ).
cnf(refute_0_4,plain,
d(x2) = n(s(z)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( d(x2) != n(s(z))
| n(s(z)) = d(x2) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(d(x2))),bind(Y0,$fot(n(s(z))))]]) ).
cnf(refute_0_9,plain,
n(s(z)) = d(x2),
inference(resolve,[$cnf( $equal(d(x2),n(s(z))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( d(n(s(z))) != n(z)
| n(s(z)) != d(x2)
| d(d(x2)) = n(z) ),
introduced(tautology,[equality,[$cnf( $equal(d(n(s(z))),n(z)) ),[0,0],$fot(d(x2))]]) ).
cnf(refute_0_11,plain,
( d(n(s(z))) != n(z)
| d(d(x2)) = n(z) ),
inference(resolve,[$cnf( $equal(n(s(z)),d(x2)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
d(d(x2)) = n(z),
inference(resolve,[$cnf( $equal(d(n(s(z))),n(z)) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( d(d(x2)) != n(z)
| d(x(X_37,d(x2))) != x(d(X_37),d(d(x2)))
| d(x(X_37,d(x2))) = x(d(X_37),n(z)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(X_37,d(x2))),x(d(X_37),d(d(x2)))) ),[1,1],$fot(n(z))]]) ).
cnf(refute_0_14,plain,
( d(x(X_37,d(x2))) != x(d(X_37),d(d(x2)))
| d(x(X_37,d(x2))) = x(d(X_37),n(z)) ),
inference(resolve,[$cnf( $equal(d(d(x2)),n(z)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
d(x(X_37,d(x2))) = x(d(X_37),n(z)),
inference(resolve,[$cnf( $equal(d(x(X_37,d(x2))),x(d(X_37),d(d(x2)))) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
d(x(d(x2),d(x2))) = x(d(d(x2)),n(z)),
inference(subst,[],[refute_0_15:[bind(X_37,$fot(d(x2)))]]) ).
cnf(refute_0_17,plain,
( d(d(x2)) != n(z)
| d(x(d(x2),d(x2))) != x(d(d(x2)),n(z))
| d(x(d(x2),d(x2))) = x(n(z),n(z)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(d(x2),d(x2))),x(d(d(x2)),n(z))) ),[1,0],$fot(n(z))]]) ).
cnf(refute_0_18,plain,
( d(x(d(x2),d(x2))) != x(d(d(x2)),n(z))
| d(x(d(x2),d(x2))) = x(n(z),n(z)) ),
inference(resolve,[$cnf( $equal(d(d(x2)),n(z)) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
d(x(d(x2),d(x2))) = x(n(z),n(z)),
inference(resolve,[$cnf( $equal(d(x(d(x2),d(x2))),x(d(d(x2)),n(z))) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( d(x(F,G)) != x(d(F),d(G))
| x(d(F),d(G)) = d(x(F,G)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(d(x(F,G)))),bind(Y0,$fot(x(d(F),d(G))))]]) ).
cnf(refute_0_21,plain,
x(d(F),d(G)) = d(x(F,G)),
inference(resolve,[$cnf( $equal(d(x(F,G)),x(d(F),d(G))) )],[refute_0_0,refute_0_20]) ).
cnf(refute_0_22,plain,
x(d(x2),d(x2)) = d(x(x2,x2)),
inference(subst,[],[refute_0_21:[bind(F,$fot(x2)),bind(G,$fot(x2))]]) ).
cnf(refute_0_23,plain,
d(x(d(x2),d(x2))) = d(x(d(x2),d(x2))),
introduced(tautology,[refl,[$fot(d(x(d(x2),d(x2))))]]) ).
cnf(refute_0_24,plain,
( d(x(d(x2),d(x2))) != d(x(d(x2),d(x2)))
| x(d(x2),d(x2)) != d(x(x2,x2))
| d(x(d(x2),d(x2))) = d(d(x(x2,x2))) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(d(x2),d(x2))),d(x(d(x2),d(x2)))) ),[1,0],$fot(d(x(x2,x2)))]]) ).
cnf(refute_0_25,plain,
( x(d(x2),d(x2)) != d(x(x2,x2))
| d(x(d(x2),d(x2))) = d(d(x(x2,x2))) ),
inference(resolve,[$cnf( $equal(d(x(d(x2),d(x2))),d(x(d(x2),d(x2)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
d(x(d(x2),d(x2))) = d(d(x(x2,x2))),
inference(resolve,[$cnf( $equal(x(d(x2),d(x2)),d(x(x2,x2))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( d(x(d(x2),d(x2))) != d(d(x(x2,x2)))
| d(x(d(x2),d(x2))) != x(n(z),n(z))
| d(d(x(x2,x2))) = x(n(z),n(z)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(d(x2),d(x2))),x(n(z),n(z))) ),[0],$fot(d(d(x(x2,x2))))]]) ).
cnf(refute_0_28,plain,
( d(x(d(x2),d(x2))) != x(n(z),n(z))
| d(d(x(x2,x2))) = x(n(z),n(z)) ),
inference(resolve,[$cnf( $equal(d(x(d(x2),d(x2))),d(d(x(x2,x2)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
d(d(x(x2,x2))) = x(n(z),n(z)),
inference(resolve,[$cnf( $equal(d(x(d(x2),d(x2))),x(n(z),n(z))) )],[refute_0_19,refute_0_28]) ).
cnf(refute_0_30,plain,
opt(x(n(z),E)) = E,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_31,plain,
opt(x(n(z),n(z))) = n(z),
inference(subst,[],[refute_0_30:[bind(E,$fot(n(z)))]]) ).
cnf(refute_0_32,plain,
( d(d(x(x2,x2))) != x(n(z),n(z))
| x(n(z),n(z)) = d(d(x(x2,x2))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(d(d(x(x2,x2))))),bind(Y0,$fot(x(n(z),n(z))))]]) ).
cnf(refute_0_33,plain,
x(n(z),n(z)) = d(d(x(x2,x2))),
inference(resolve,[$cnf( $equal(d(d(x(x2,x2))),x(n(z),n(z))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( opt(x(n(z),n(z))) != n(z)
| x(n(z),n(z)) != d(d(x(x2,x2)))
| opt(d(d(x(x2,x2)))) = n(z) ),
introduced(tautology,[equality,[$cnf( $equal(opt(x(n(z),n(z))),n(z)) ),[0,0],$fot(d(d(x(x2,x2))))]]) ).
cnf(refute_0_35,plain,
( opt(x(n(z),n(z))) != n(z)
| opt(d(d(x(x2,x2)))) = n(z) ),
inference(resolve,[$cnf( $equal(x(n(z),n(z)),d(d(x(x2,x2)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
opt(d(d(x(x2,x2)))) = n(z),
inference(resolve,[$cnf( $equal(opt(x(n(z),n(z))),n(z)) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
opt(x(n(z),d(X_45))) = d(X_45),
inference(subst,[],[refute_0_30:[bind(E,$fot(d(X_45)))]]) ).
cnf(refute_0_38,plain,
d(x(d(x2),X_38)) = x(d(d(x2)),d(X_38)),
inference(subst,[],[refute_0_0:[bind(F,$fot(d(x2))),bind(G,$fot(X_38))]]) ).
cnf(refute_0_39,plain,
( d(d(x2)) != n(z)
| d(x(d(x2),X_38)) != x(d(d(x2)),d(X_38))
| d(x(d(x2),X_38)) = x(n(z),d(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(d(x2),X_38)),x(d(d(x2)),d(X_38))) ),[1,0],$fot(n(z))]]) ).
cnf(refute_0_40,plain,
( d(x(d(x2),X_38)) != x(d(d(x2)),d(X_38))
| d(x(d(x2),X_38)) = x(n(z),d(X_38)) ),
inference(resolve,[$cnf( $equal(d(d(x2)),n(z)) )],[refute_0_12,refute_0_39]) ).
cnf(refute_0_41,plain,
d(x(d(x2),X_38)) = x(n(z),d(X_38)),
inference(resolve,[$cnf( $equal(d(x(d(x2),X_38)),x(d(d(x2)),d(X_38))) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
d(x(d(x2),X_45)) = x(n(z),d(X_45)),
inference(subst,[],[refute_0_41:[bind(X_38,$fot(X_45))]]) ).
cnf(refute_0_43,plain,
( d(x(d(x2),X_45)) != x(n(z),d(X_45))
| x(n(z),d(X_45)) = d(x(d(x2),X_45)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(d(x(d(x2),X_45)))),bind(Y0,$fot(x(n(z),d(X_45))))]]) ).
cnf(refute_0_44,plain,
x(n(z),d(X_45)) = d(x(d(x2),X_45)),
inference(resolve,[$cnf( $equal(d(x(d(x2),X_45)),x(n(z),d(X_45))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( opt(x(n(z),d(X_45))) != d(X_45)
| x(n(z),d(X_45)) != d(x(d(x2),X_45))
| opt(d(x(d(x2),X_45))) = d(X_45) ),
introduced(tautology,[equality,[$cnf( $equal(opt(x(n(z),d(X_45))),d(X_45)) ),[0,0],$fot(d(x(d(x2),X_45)))]]) ).
cnf(refute_0_46,plain,
( opt(x(n(z),d(X_45))) != d(X_45)
| opt(d(x(d(x2),X_45))) = d(X_45) ),
inference(resolve,[$cnf( $equal(x(n(z),d(X_45)),d(x(d(x2),X_45))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
opt(d(x(d(x2),X_45))) = d(X_45),
inference(resolve,[$cnf( $equal(opt(x(n(z),d(X_45))),d(X_45)) )],[refute_0_37,refute_0_46]) ).
cnf(refute_0_48,plain,
opt(d(E)) = opt(d(opt(E))),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_49,plain,
opt(d(x(n(z),E))) = opt(d(opt(x(n(z),E)))),
inference(subst,[],[refute_0_48:[bind(E,$fot(x(n(z),E)))]]) ).
cnf(refute_0_50,plain,
( opt(d(x(n(z),E))) != opt(d(opt(x(n(z),E))))
| opt(x(n(z),E)) != E
| opt(d(x(n(z),E))) = opt(d(E)) ),
introduced(tautology,[equality,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E))))) ),[1,0,0],$fot(E)]]) ).
cnf(refute_0_51,plain,
( opt(d(x(n(z),E))) != opt(d(opt(x(n(z),E))))
| opt(d(x(n(z),E))) = opt(d(E)) ),
inference(resolve,[$cnf( $equal(opt(x(n(z),E)),E) )],[refute_0_30,refute_0_50]) ).
cnf(refute_0_52,plain,
opt(d(x(n(z),E))) = opt(d(E)),
inference(resolve,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E))))) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
d(x(n(Y),X_38)) = x(d(n(Y)),d(X_38)),
inference(subst,[],[refute_0_0:[bind(F,$fot(n(Y))),bind(G,$fot(X_38))]]) ).
cnf(refute_0_54,plain,
( d(n(Y)) != n(z)
| d(x(n(Y),X_38)) != x(d(n(Y)),d(X_38))
| d(x(n(Y),X_38)) = x(n(z),d(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(n(Y),X_38)),x(d(n(Y)),d(X_38))) ),[1,0],$fot(n(z))]]) ).
cnf(refute_0_55,plain,
( d(x(n(Y),X_38)) != x(d(n(Y)),d(X_38))
| d(x(n(Y),X_38)) = x(n(z),d(X_38)) ),
inference(resolve,[$cnf( $equal(d(n(Y)),n(z)) )],[refute_0_2,refute_0_54]) ).
cnf(refute_0_56,plain,
d(x(n(Y),X_38)) = x(n(z),d(X_38)),
inference(resolve,[$cnf( $equal(d(x(n(Y),X_38)),x(d(n(Y)),d(X_38))) )],[refute_0_53,refute_0_55]) ).
cnf(refute_0_57,plain,
( d(x(d(x2),X_38)) != x(n(z),d(X_38))
| x(n(z),d(X_38)) = d(x(d(x2),X_38)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(d(x(d(x2),X_38)))),bind(Y0,$fot(x(n(z),d(X_38))))]]) ).
cnf(refute_0_58,plain,
x(n(z),d(X_38)) = d(x(d(x2),X_38)),
inference(resolve,[$cnf( $equal(d(x(d(x2),X_38)),x(n(z),d(X_38))) )],[refute_0_41,refute_0_57]) ).
cnf(refute_0_59,plain,
( d(x(n(Y),X_38)) != x(n(z),d(X_38))
| x(n(z),d(X_38)) != d(x(d(x2),X_38))
| d(x(n(Y),X_38)) = d(x(d(x2),X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(d(x(n(Y),X_38)),d(x(d(x2),X_38))) ),[0],$fot(x(n(z),d(X_38)))]]) ).
cnf(refute_0_60,plain,
( d(x(n(Y),X_38)) != x(n(z),d(X_38))
| d(x(n(Y),X_38)) = d(x(d(x2),X_38)) ),
inference(resolve,[$cnf( $equal(x(n(z),d(X_38)),d(x(d(x2),X_38))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
d(x(n(Y),X_38)) = d(x(d(x2),X_38)),
inference(resolve,[$cnf( $equal(d(x(n(Y),X_38)),x(n(z),d(X_38))) )],[refute_0_56,refute_0_60]) ).
cnf(refute_0_62,plain,
d(x(n(z),E)) = d(x(d(x2),E)),
inference(subst,[],[refute_0_61:[bind(Y,$fot(z)),bind(X_38,$fot(E))]]) ).
cnf(refute_0_63,plain,
opt(d(x(n(z),E))) = opt(d(x(n(z),E))),
introduced(tautology,[refl,[$fot(opt(d(x(n(z),E))))]]) ).
cnf(refute_0_64,plain,
( d(x(n(z),E)) != d(x(d(x2),E))
| opt(d(x(n(z),E))) != opt(d(x(n(z),E)))
| opt(d(x(n(z),E))) = opt(d(x(d(x2),E))) ),
introduced(tautology,[equality,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(x(n(z),E)))) ),[1,0],$fot(d(x(d(x2),E)))]]) ).
cnf(refute_0_65,plain,
( d(x(n(z),E)) != d(x(d(x2),E))
| opt(d(x(n(z),E))) = opt(d(x(d(x2),E))) ),
inference(resolve,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(x(n(z),E)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
opt(d(x(n(z),E))) = opt(d(x(d(x2),E))),
inference(resolve,[$cnf( $equal(d(x(n(z),E)),d(x(d(x2),E))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( opt(d(x(n(z),E))) != opt(d(E))
| opt(d(x(n(z),E))) != opt(d(x(d(x2),E)))
| opt(d(x(d(x2),E))) = opt(d(E)) ),
introduced(tautology,[equality,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(E))) ),[0],$fot(opt(d(x(d(x2),E))))]]) ).
cnf(refute_0_68,plain,
( opt(d(x(n(z),E))) != opt(d(E))
| opt(d(x(d(x2),E))) = opt(d(E)) ),
inference(resolve,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(x(d(x2),E)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
opt(d(x(d(x2),E))) = opt(d(E)),
inference(resolve,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(E))) )],[refute_0_52,refute_0_68]) ).
cnf(refute_0_70,plain,
opt(d(x(d(x2),X_45))) = opt(d(X_45)),
inference(subst,[],[refute_0_69:[bind(E,$fot(X_45))]]) ).
cnf(refute_0_71,plain,
( opt(d(x(d(x2),X_45))) != d(X_45)
| opt(d(x(d(x2),X_45))) != opt(d(X_45))
| opt(d(X_45)) = d(X_45) ),
introduced(tautology,[equality,[$cnf( $equal(opt(d(x(d(x2),X_45))),d(X_45)) ),[0],$fot(opt(d(X_45)))]]) ).
cnf(refute_0_72,plain,
( opt(d(x(d(x2),X_45))) != d(X_45)
| opt(d(X_45)) = d(X_45) ),
inference(resolve,[$cnf( $equal(opt(d(x(d(x2),X_45))),opt(d(X_45))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
opt(d(X_45)) = d(X_45),
inference(resolve,[$cnf( $equal(opt(d(x(d(x2),X_45))),d(X_45)) )],[refute_0_47,refute_0_72]) ).
cnf(refute_0_74,plain,
opt(d(d(x(x2,x2)))) = d(d(x(x2,x2))),
inference(subst,[],[refute_0_73:[bind(X_45,$fot(d(x(x2,x2))))]]) ).
cnf(refute_0_75,plain,
( opt(d(d(x(x2,x2)))) != d(d(x(x2,x2)))
| opt(d(d(x(x2,x2)))) != n(z)
| d(d(x(x2,x2))) = n(z) ),
introduced(tautology,[equality,[$cnf( $equal(opt(d(d(x(x2,x2)))),n(z)) ),[0],$fot(d(d(x(x2,x2))))]]) ).
cnf(refute_0_76,plain,
( opt(d(d(x(x2,x2)))) != n(z)
| d(d(x(x2,x2))) = n(z) ),
inference(resolve,[$cnf( $equal(opt(d(d(x(x2,x2)))),d(d(x(x2,x2)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
d(d(x(x2,x2))) = n(z),
inference(resolve,[$cnf( $equal(opt(d(d(x(x2,x2)))),n(z)) )],[refute_0_36,refute_0_76]) ).
cnf(refute_0_78,plain,
( d(d(x(x2,x2))) != n(z)
| d(d(x(x2,x2))) != x(n(z),n(z))
| n(z) = x(n(z),n(z)) ),
introduced(tautology,[equality,[$cnf( $equal(d(d(x(x2,x2))),x(n(z),n(z))) ),[0],$fot(n(z))]]) ).
cnf(refute_0_79,plain,
( d(d(x(x2,x2))) != x(n(z),n(z))
| n(z) = x(n(z),n(z)) ),
inference(resolve,[$cnf( $equal(d(d(x(x2,x2))),n(z)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
n(z) = x(n(z),n(z)),
inference(resolve,[$cnf( $equal(d(d(x(x2,x2))),x(n(z),n(z))) )],[refute_0_29,refute_0_79]) ).
cnf(refute_0_81,plain,
n(X) != x(X2,X3),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_82,plain,
n(z) != x(n(z),n(z)),
inference(subst,[],[refute_0_81:[bind(X,$fot(z)),bind(X2,$fot(n(z))),bind(X3,$fot(n(z)))]]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( $equal(n(z),x(n(z),n(z))) )],[refute_0_80,refute_0_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.15/0.33 % Computer : n011.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 09:53:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.29/0.45
%------------------------------------------------------------------------------