%------------------------------------------------------------------------------
% 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 : n001.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 07:04:31 PM UTC 2026
% Result : Unsatisfiable 0.53s 0.77s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 40
% Syntax : Number of clauses : 118 ( 65 unt; 0 nHn; 73 RR)
% Number of literals : 195 ( 194 equ; 81 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_014,axiom,
fail(Y,n(z)) = Y ).
cnf(axiom_043,axiom,
d(n(Y)) = n(z) ).
cnf(axiom_044,axiom,
d(x(F,G)) = x(d(F),d(G)) ).
cnf(axiom_046,axiom,
d(x2) = n(s(z)) ).
cnf(axiom_051,axiom,
opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ).
cnf(axiom_052,axiom,
opt(x(n(z),E)) = E ).
cnf(axiom_063,axiom,
prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ).
cnf(axiom_074,axiom,
eq2(x(X,Y),n(Z)) = bfalse ).
cnf(axiom_088,axiom,
eq3(X,X) = btrue ).
cnf(goal,negated_conjecture,
eq3(prop4(X),bfalse) != btrue ).
cnf(refute_0_0,plain,
eq3(prop4(x(n(z),x(x2,d(x2)))),bfalse) != btrue,
inference(subst,[],[goal:[bind(X,$fot(x(n(z),x(x2,d(x2)))))]]) ).
cnf(refute_0_1,plain,
prop4(x(n(z),E)) = eq2(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E))))),
inference(subst,[],[axiom_063:[bind(X,$fot(x(n(z),E)))]]) ).
cnf(refute_0_2,plain,
( opt(x(n(z),E)) != E
| prop4(x(n(z),E)) != eq2(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E)))))
| prop4(x(n(z),E)) = eq2(opt(d(x(n(z),E))),opt(d(E))) ),
introduced(tautology,[equality,[$cnf( $equal(prop4(x(n(z),E)),eq2(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E)))))) ),[1,1,0,0],$fot(E)]]) ).
cnf(refute_0_3,plain,
( prop4(x(n(z),E)) != eq2(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E)))))
| prop4(x(n(z),E)) = eq2(opt(d(x(n(z),E))),opt(d(E))) ),
inference(resolve,[$cnf( $equal(opt(x(n(z),E)),E) )],[axiom_052,refute_0_2]) ).
cnf(refute_0_4,plain,
prop4(x(n(z),E)) = eq2(opt(d(x(n(z),E))),opt(d(E))),
inference(resolve,[$cnf( $equal(prop4(x(n(z),E)),eq2(opt(d(x(n(z),E))),opt(d(opt(x(n(z),E)))))) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
d(x(n(Y),X_127)) = x(d(n(Y)),d(X_127)),
inference(subst,[],[axiom_044:[bind(F,$fot(n(Y))),bind(G,$fot(X_127))]]) ).
cnf(refute_0_6,plain,
( d(n(Y)) != n(z)
| d(x(n(Y),X_127)) != x(d(n(Y)),d(X_127))
| d(x(n(Y),X_127)) = x(n(z),d(X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(n(Y),X_127)),x(d(n(Y)),d(X_127))) ),[1,0],$fot(n(z))]]) ).
cnf(refute_0_7,plain,
( d(x(n(Y),X_127)) != x(d(n(Y)),d(X_127))
| d(x(n(Y),X_127)) = x(n(z),d(X_127)) ),
inference(resolve,[$cnf( $equal(d(n(Y)),n(z)) )],[axiom_043,refute_0_6]) ).
cnf(refute_0_8,plain,
d(x(n(Y),X_127)) = x(n(z),d(X_127)),
inference(resolve,[$cnf( $equal(d(x(n(Y),X_127)),x(d(n(Y)),d(X_127))) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
d(x(d(x2),X_127)) = x(d(d(x2)),d(X_127)),
inference(subst,[],[axiom_044:[bind(F,$fot(d(x2))),bind(G,$fot(X_127))]]) ).
cnf(refute_0_10,plain,
d(n(s(z))) = n(z),
inference(subst,[],[axiom_043:[bind(Y,$fot(s(z)))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( d(x2) != n(s(z))
| n(s(z)) = d(x2) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(d(x2))),bind(Y0,$fot(n(s(z))))]]) ).
cnf(refute_0_15,plain,
n(s(z)) = d(x2),
inference(resolve,[$cnf( $equal(d(x2),n(s(z))) )],[axiom_046,refute_0_14]) ).
cnf(refute_0_16,plain,
( d(n(s(z))) != n(z)
| n(s(z)) != d(x2)
| d(d(x2)) = n(z) ),
introduced(tautology,[equality,[$cnf( $equal(d(n(s(z))),n(z)) ),[0,0],$fot(d(x2))]]) ).
cnf(refute_0_17,plain,
( d(n(s(z))) != n(z)
| d(d(x2)) = n(z) ),
inference(resolve,[$cnf( $equal(n(s(z)),d(x2)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
d(d(x2)) = n(z),
inference(resolve,[$cnf( $equal(d(n(s(z))),n(z)) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
( d(d(x2)) != n(z)
| d(x(d(x2),X_127)) != x(d(d(x2)),d(X_127))
| d(x(d(x2),X_127)) = x(n(z),d(X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(d(x2),X_127)),x(d(d(x2)),d(X_127))) ),[1,0],$fot(n(z))]]) ).
cnf(refute_0_20,plain,
( d(x(d(x2),X_127)) != x(d(d(x2)),d(X_127))
| d(x(d(x2),X_127)) = x(n(z),d(X_127)) ),
inference(resolve,[$cnf( $equal(d(d(x2)),n(z)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
d(x(d(x2),X_127)) = x(n(z),d(X_127)),
inference(resolve,[$cnf( $equal(d(x(d(x2),X_127)),x(d(d(x2)),d(X_127))) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
( d(x(d(x2),X_127)) != x(n(z),d(X_127))
| x(n(z),d(X_127)) = d(x(d(x2),X_127)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(d(x(d(x2),X_127)))),bind(Y0,$fot(x(n(z),d(X_127))))]]) ).
cnf(refute_0_23,plain,
x(n(z),d(X_127)) = d(x(d(x2),X_127)),
inference(resolve,[$cnf( $equal(d(x(d(x2),X_127)),x(n(z),d(X_127))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( d(x(n(Y),X_127)) != x(n(z),d(X_127))
| x(n(z),d(X_127)) != d(x(d(x2),X_127))
| d(x(n(Y),X_127)) = d(x(d(x2),X_127)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(d(x(n(Y),X_127)),d(x(d(x2),X_127))) ),[0],$fot(x(n(z),d(X_127)))]]) ).
cnf(refute_0_25,plain,
( d(x(n(Y),X_127)) != x(n(z),d(X_127))
| d(x(n(Y),X_127)) = d(x(d(x2),X_127)) ),
inference(resolve,[$cnf( $equal(x(n(z),d(X_127)),d(x(d(x2),X_127))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
d(x(n(Y),X_127)) = d(x(d(x2),X_127)),
inference(resolve,[$cnf( $equal(d(x(n(Y),X_127)),x(n(z),d(X_127))) )],[refute_0_8,refute_0_25]) ).
cnf(refute_0_27,plain,
d(x(n(z),E)) = d(x(d(x2),E)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(z)),bind(X_127,$fot(E))]]) ).
cnf(refute_0_28,plain,
opt(d(x(n(z),E))) = opt(d(x(n(z),E))),
introduced(tautology,[refl,[$fot(opt(d(x(n(z),E))))]]) ).
cnf(refute_0_29,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_30,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( $equal(opt(d(x(n(z),E))),opt(d(x(n(z),E)))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
opt(d(x(n(z),E))) = opt(d(x(d(x2),E))),
inference(resolve,[$cnf( $equal(d(x(n(z),E)),d(x(d(x2),E))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
eq2(opt(d(x(n(z),E))),opt(d(E))) = eq2(opt(d(x(n(z),E))),opt(d(E))),
introduced(tautology,[refl,[$fot(eq2(opt(d(x(n(z),E))),opt(d(E))))]]) ).
cnf(refute_0_33,plain,
( eq2(opt(d(x(n(z),E))),opt(d(E))) != eq2(opt(d(x(n(z),E))),opt(d(E)))
| opt(d(x(n(z),E))) != opt(d(x(d(x2),E)))
| eq2(opt(d(x(n(z),E))),opt(d(E))) = eq2(opt(d(x(d(x2),E))),opt(d(E))) ),
introduced(tautology,[equality,[$cnf( $equal(eq2(opt(d(x(n(z),E))),opt(d(E))),eq2(opt(d(x(n(z),E))),opt(d(E)))) ),[1,0],$fot(opt(d(x(d(x2),E))))]]) ).
cnf(refute_0_34,plain,
( opt(d(x(n(z),E))) != opt(d(x(d(x2),E)))
| eq2(opt(d(x(n(z),E))),opt(d(E))) = eq2(opt(d(x(d(x2),E))),opt(d(E))) ),
inference(resolve,[$cnf( $equal(eq2(opt(d(x(n(z),E))),opt(d(E))),eq2(opt(d(x(n(z),E))),opt(d(E)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
eq2(opt(d(x(n(z),E))),opt(d(E))) = eq2(opt(d(x(d(x2),E))),opt(d(E))),
inference(resolve,[$cnf( $equal(opt(d(x(n(z),E))),opt(d(x(d(x2),E)))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( eq2(opt(d(x(n(z),E))),opt(d(E))) != eq2(opt(d(x(d(x2),E))),opt(d(E)))
| prop4(x(n(z),E)) != eq2(opt(d(x(n(z),E))),opt(d(E)))
| prop4(x(n(z),E)) = eq2(opt(d(x(d(x2),E))),opt(d(E))) ),
introduced(tautology,[equality,[$cnf( $equal(prop4(x(n(z),E)),eq2(opt(d(x(n(z),E))),opt(d(E)))) ),[1],$fot(eq2(opt(d(x(d(x2),E))),opt(d(E))))]]) ).
cnf(refute_0_37,plain,
( prop4(x(n(z),E)) != eq2(opt(d(x(n(z),E))),opt(d(E)))
| prop4(x(n(z),E)) = eq2(opt(d(x(d(x2),E))),opt(d(E))) ),
inference(resolve,[$cnf( $equal(eq2(opt(d(x(n(z),E))),opt(d(E))),eq2(opt(d(x(d(x2),E))),opt(d(E)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
prop4(x(n(z),E)) = eq2(opt(d(x(d(x2),E))),opt(d(E))),
inference(resolve,[$cnf( $equal(prop4(x(n(z),E)),eq2(opt(d(x(n(z),E))),opt(d(E)))) )],[refute_0_4,refute_0_37]) ).
cnf(refute_0_39,plain,
opt(x(n(z),d(X_128))) = d(X_128),
inference(subst,[],[axiom_052:[bind(E,$fot(d(X_128)))]]) ).
cnf(refute_0_40,plain,
d(x(d(x2),X_128)) = x(n(z),d(X_128)),
inference(subst,[],[refute_0_21:[bind(X_127,$fot(X_128))]]) ).
cnf(refute_0_41,plain,
( d(x(d(x2),X_128)) != x(n(z),d(X_128))
| x(n(z),d(X_128)) = d(x(d(x2),X_128)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(d(x(d(x2),X_128)))),bind(Y0,$fot(x(n(z),d(X_128))))]]) ).
cnf(refute_0_42,plain,
x(n(z),d(X_128)) = d(x(d(x2),X_128)),
inference(resolve,[$cnf( $equal(d(x(d(x2),X_128)),x(n(z),d(X_128))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( opt(x(n(z),d(X_128))) != d(X_128)
| x(n(z),d(X_128)) != d(x(d(x2),X_128))
| opt(d(x(d(x2),X_128))) = d(X_128) ),
introduced(tautology,[equality,[$cnf( $equal(opt(x(n(z),d(X_128))),d(X_128)) ),[0,0],$fot(d(x(d(x2),X_128)))]]) ).
cnf(refute_0_44,plain,
( opt(x(n(z),d(X_128))) != d(X_128)
| opt(d(x(d(x2),X_128))) = d(X_128) ),
inference(resolve,[$cnf( $equal(x(n(z),d(X_128)),d(x(d(x2),X_128))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
opt(d(x(d(x2),X_128))) = d(X_128),
inference(resolve,[$cnf( $equal(opt(x(n(z),d(X_128))),d(X_128)) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
opt(d(x(d(x2),E))) = d(E),
inference(subst,[],[refute_0_45:[bind(X_128,$fot(E))]]) ).
cnf(refute_0_47,plain,
eq2(opt(d(x(d(x2),E))),opt(d(E))) = eq2(opt(d(x(d(x2),E))),opt(d(E))),
introduced(tautology,[refl,[$fot(eq2(opt(d(x(d(x2),E))),opt(d(E))))]]) ).
cnf(refute_0_48,plain,
( eq2(opt(d(x(d(x2),E))),opt(d(E))) != eq2(opt(d(x(d(x2),E))),opt(d(E)))
| opt(d(x(d(x2),E))) != d(E)
| eq2(opt(d(x(d(x2),E))),opt(d(E))) = eq2(d(E),opt(d(E))) ),
introduced(tautology,[equality,[$cnf( $equal(eq2(opt(d(x(d(x2),E))),opt(d(E))),eq2(opt(d(x(d(x2),E))),opt(d(E)))) ),[1,0],$fot(d(E))]]) ).
cnf(refute_0_49,plain,
( opt(d(x(d(x2),E))) != d(E)
| eq2(opt(d(x(d(x2),E))),opt(d(E))) = eq2(d(E),opt(d(E))) ),
inference(resolve,[$cnf( $equal(eq2(opt(d(x(d(x2),E))),opt(d(E))),eq2(opt(d(x(d(x2),E))),opt(d(E)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
eq2(opt(d(x(d(x2),E))),opt(d(E))) = eq2(d(E),opt(d(E))),
inference(resolve,[$cnf( $equal(opt(d(x(d(x2),E))),d(E)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( eq2(opt(d(x(d(x2),E))),opt(d(E))) != eq2(d(E),opt(d(E)))
| prop4(x(n(z),E)) != eq2(opt(d(x(d(x2),E))),opt(d(E)))
| prop4(x(n(z),E)) = eq2(d(E),opt(d(E))) ),
introduced(tautology,[equality,[$cnf( $equal(prop4(x(n(z),E)),eq2(opt(d(x(d(x2),E))),opt(d(E)))) ),[1],$fot(eq2(d(E),opt(d(E))))]]) ).
cnf(refute_0_52,plain,
( prop4(x(n(z),E)) != eq2(opt(d(x(d(x2),E))),opt(d(E)))
| prop4(x(n(z),E)) = eq2(d(E),opt(d(E))) ),
inference(resolve,[$cnf( $equal(eq2(opt(d(x(d(x2),E))),opt(d(E))),eq2(d(E),opt(d(E)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
prop4(x(n(z),E)) = eq2(d(E),opt(d(E))),
inference(resolve,[$cnf( $equal(prop4(x(n(z),E)),eq2(opt(d(x(d(x2),E))),opt(d(E)))) )],[refute_0_38,refute_0_52]) ).
cnf(refute_0_54,plain,
prop4(x(n(z),x(x2,d(x2)))) = eq2(d(x(x2,d(x2))),opt(d(x(x2,d(x2))))),
inference(subst,[],[refute_0_53:[bind(E,$fot(x(x2,d(x2))))]]) ).
cnf(refute_0_55,plain,
opt(x(n(s(z)),X_83)) = fail(n(s(z)),X_83),
inference(subst,[],[axiom_051:[bind(E,$fot(X_83)),bind(X4,$fot(z))]]) ).
cnf(refute_0_56,plain,
( n(s(z)) != d(x2)
| opt(x(n(s(z)),X_83)) != fail(n(s(z)),X_83)
| opt(x(d(x2),X_83)) = fail(n(s(z)),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(opt(x(n(s(z)),X_83)),fail(n(s(z)),X_83)) ),[0,0,0],$fot(d(x2))]]) ).
cnf(refute_0_57,plain,
( opt(x(n(s(z)),X_83)) != fail(n(s(z)),X_83)
| opt(x(d(x2),X_83)) = fail(n(s(z)),X_83) ),
inference(resolve,[$cnf( $equal(n(s(z)),d(x2)) )],[refute_0_15,refute_0_56]) ).
cnf(refute_0_58,plain,
opt(x(d(x2),X_83)) = fail(n(s(z)),X_83),
inference(resolve,[$cnf( $equal(opt(x(n(s(z)),X_83)),fail(n(s(z)),X_83)) )],[refute_0_55,refute_0_57]) ).
cnf(refute_0_59,plain,
fail(n(s(z)),X_83) = fail(n(s(z)),X_83),
introduced(tautology,[refl,[$fot(fail(n(s(z)),X_83))]]) ).
cnf(refute_0_60,plain,
( fail(n(s(z)),X_83) != fail(n(s(z)),X_83)
| n(s(z)) != d(x2)
| fail(n(s(z)),X_83) = fail(d(x2),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(fail(n(s(z)),X_83),fail(n(s(z)),X_83)) ),[1,0],$fot(d(x2))]]) ).
cnf(refute_0_61,plain,
( n(s(z)) != d(x2)
| fail(n(s(z)),X_83) = fail(d(x2),X_83) ),
inference(resolve,[$cnf( $equal(fail(n(s(z)),X_83),fail(n(s(z)),X_83)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
fail(n(s(z)),X_83) = fail(d(x2),X_83),
inference(resolve,[$cnf( $equal(n(s(z)),d(x2)) )],[refute_0_15,refute_0_61]) ).
cnf(refute_0_63,plain,
( fail(n(s(z)),X_83) != fail(d(x2),X_83)
| opt(x(d(x2),X_83)) != fail(n(s(z)),X_83)
| opt(x(d(x2),X_83)) = fail(d(x2),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(opt(x(d(x2),X_83)),fail(n(s(z)),X_83)) ),[1],$fot(fail(d(x2),X_83))]]) ).
cnf(refute_0_64,plain,
( opt(x(d(x2),X_83)) != fail(n(s(z)),X_83)
| opt(x(d(x2),X_83)) = fail(d(x2),X_83) ),
inference(resolve,[$cnf( $equal(fail(n(s(z)),X_83),fail(d(x2),X_83)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
opt(x(d(x2),X_83)) = fail(d(x2),X_83),
inference(resolve,[$cnf( $equal(opt(x(d(x2),X_83)),fail(n(s(z)),X_83)) )],[refute_0_58,refute_0_64]) ).
cnf(refute_0_66,plain,
opt(x(d(x2),n(z))) = fail(d(x2),n(z)),
inference(subst,[],[refute_0_65:[bind(X_83,$fot(n(z)))]]) ).
cnf(refute_0_67,plain,
d(x(X_126,d(x2))) = x(d(X_126),d(d(x2))),
inference(subst,[],[axiom_044:[bind(F,$fot(X_126)),bind(G,$fot(d(x2)))]]) ).
cnf(refute_0_68,plain,
( d(d(x2)) != n(z)
| d(x(X_126,d(x2))) != x(d(X_126),d(d(x2)))
| d(x(X_126,d(x2))) = x(d(X_126),n(z)) ),
introduced(tautology,[equality,[$cnf( $equal(d(x(X_126,d(x2))),x(d(X_126),d(d(x2)))) ),[1,1],$fot(n(z))]]) ).
cnf(refute_0_69,plain,
( d(x(X_126,d(x2))) != x(d(X_126),d(d(x2)))
| d(x(X_126,d(x2))) = x(d(X_126),n(z)) ),
inference(resolve,[$cnf( $equal(d(d(x2)),n(z)) )],[refute_0_18,refute_0_68]) ).
cnf(refute_0_70,plain,
d(x(X_126,d(x2))) = x(d(X_126),n(z)),
inference(resolve,[$cnf( $equal(d(x(X_126,d(x2))),x(d(X_126),d(d(x2)))) )],[refute_0_67,refute_0_69]) ).
cnf(refute_0_71,plain,
d(x(x2,d(x2))) = x(d(x2),n(z)),
inference(subst,[],[refute_0_70:[bind(X_126,$fot(x2))]]) ).
cnf(refute_0_72,plain,
( d(x(x2,d(x2))) != x(d(x2),n(z))
| x(d(x2),n(z)) = d(x(x2,d(x2))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(d(x(x2,d(x2))))),bind(Y0,$fot(x(d(x2),n(z))))]]) ).
cnf(refute_0_73,plain,
x(d(x2),n(z)) = d(x(x2,d(x2))),
inference(resolve,[$cnf( $equal(d(x(x2,d(x2))),x(d(x2),n(z))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( opt(x(d(x2),n(z))) != fail(d(x2),n(z))
| x(d(x2),n(z)) != d(x(x2,d(x2)))
| opt(d(x(x2,d(x2)))) = fail(d(x2),n(z)) ),
introduced(tautology,[equality,[$cnf( $equal(opt(x(d(x2),n(z))),fail(d(x2),n(z))) ),[0,0],$fot(d(x(x2,d(x2))))]]) ).
cnf(refute_0_75,plain,
( opt(x(d(x2),n(z))) != fail(d(x2),n(z))
| opt(d(x(x2,d(x2)))) = fail(d(x2),n(z)) ),
inference(resolve,[$cnf( $equal(x(d(x2),n(z)),d(x(x2,d(x2)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
opt(d(x(x2,d(x2)))) = fail(d(x2),n(z)),
inference(resolve,[$cnf( $equal(opt(x(d(x2),n(z))),fail(d(x2),n(z))) )],[refute_0_66,refute_0_75]) ).
cnf(refute_0_77,plain,
fail(d(x2),n(z)) = d(x2),
inference(subst,[],[axiom_014:[bind(Y,$fot(d(x2)))]]) ).
cnf(refute_0_78,plain,
( fail(d(x2),n(z)) != d(x2)
| opt(d(x(x2,d(x2)))) != fail(d(x2),n(z))
| opt(d(x(x2,d(x2)))) = d(x2) ),
introduced(tautology,[equality,[$cnf( $equal(opt(d(x(x2,d(x2)))),fail(d(x2),n(z))) ),[1],$fot(d(x2))]]) ).
cnf(refute_0_79,plain,
( opt(d(x(x2,d(x2)))) != fail(d(x2),n(z))
| opt(d(x(x2,d(x2)))) = d(x2) ),
inference(resolve,[$cnf( $equal(fail(d(x2),n(z)),d(x2)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
opt(d(x(x2,d(x2)))) = d(x2),
inference(resolve,[$cnf( $equal(opt(d(x(x2,d(x2)))),fail(d(x2),n(z))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( opt(d(x(x2,d(x2)))) != d(x2)
| prop4(x(n(z),x(x2,d(x2)))) != eq2(d(x(x2,d(x2))),opt(d(x(x2,d(x2)))))
| prop4(x(n(z),x(x2,d(x2)))) = eq2(d(x(x2,d(x2))),d(x2)) ),
introduced(tautology,[equality,[$cnf( $equal(prop4(x(n(z),x(x2,d(x2)))),eq2(d(x(x2,d(x2))),opt(d(x(x2,d(x2)))))) ),[1,1],$fot(d(x2))]]) ).
cnf(refute_0_82,plain,
( prop4(x(n(z),x(x2,d(x2)))) != eq2(d(x(x2,d(x2))),opt(d(x(x2,d(x2)))))
| prop4(x(n(z),x(x2,d(x2)))) = eq2(d(x(x2,d(x2))),d(x2)) ),
inference(resolve,[$cnf( $equal(opt(d(x(x2,d(x2)))),d(x2)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
prop4(x(n(z),x(x2,d(x2)))) = eq2(d(x(x2,d(x2))),d(x2)),
inference(resolve,[$cnf( $equal(prop4(x(n(z),x(x2,d(x2)))),eq2(d(x(x2,d(x2))),opt(d(x(x2,d(x2)))))) )],[refute_0_54,refute_0_82]) ).
cnf(refute_0_84,plain,
eq2(x(X_66,X_67),n(s(z))) = bfalse,
inference(subst,[],[axiom_074:[bind(X,$fot(X_66)),bind(Y,$fot(X_67)),bind(Z,$fot(s(z)))]]) ).
cnf(refute_0_85,plain,
( eq2(x(X_66,X_67),n(s(z))) != bfalse
| n(s(z)) != d(x2)
| eq2(x(X_66,X_67),d(x2)) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(eq2(x(X_66,X_67),n(s(z))),bfalse) ),[0,1],$fot(d(x2))]]) ).
cnf(refute_0_86,plain,
( eq2(x(X_66,X_67),n(s(z))) != bfalse
| eq2(x(X_66,X_67),d(x2)) = bfalse ),
inference(resolve,[$cnf( $equal(n(s(z)),d(x2)) )],[refute_0_15,refute_0_85]) ).
cnf(refute_0_87,plain,
eq2(x(X_66,X_67),d(x2)) = bfalse,
inference(resolve,[$cnf( $equal(eq2(x(X_66,X_67),n(s(z))),bfalse) )],[refute_0_84,refute_0_86]) ).
cnf(refute_0_88,plain,
eq2(x(d(X_126),d(X_127)),d(x2)) = bfalse,
inference(subst,[],[refute_0_87:[bind(X_66,$fot(d(X_126))),bind(X_67,$fot(d(X_127)))]]) ).
cnf(refute_0_89,plain,
d(x(X_126,X_127)) = x(d(X_126),d(X_127)),
inference(subst,[],[axiom_044:[bind(F,$fot(X_126)),bind(G,$fot(X_127))]]) ).
cnf(refute_0_90,plain,
( d(x(X_126,X_127)) != x(d(X_126),d(X_127))
| x(d(X_126),d(X_127)) = d(x(X_126,X_127)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(d(x(X_126,X_127)))),bind(Y0,$fot(x(d(X_126),d(X_127))))]]) ).
cnf(refute_0_91,plain,
x(d(X_126),d(X_127)) = d(x(X_126,X_127)),
inference(resolve,[$cnf( $equal(d(x(X_126,X_127)),x(d(X_126),d(X_127))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( eq2(x(d(X_126),d(X_127)),d(x2)) != bfalse
| x(d(X_126),d(X_127)) != d(x(X_126,X_127))
| eq2(d(x(X_126,X_127)),d(x2)) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(eq2(x(d(X_126),d(X_127)),d(x2)),bfalse) ),[0,0],$fot(d(x(X_126,X_127)))]]) ).
cnf(refute_0_93,plain,
( eq2(x(d(X_126),d(X_127)),d(x2)) != bfalse
| eq2(d(x(X_126,X_127)),d(x2)) = bfalse ),
inference(resolve,[$cnf( $equal(x(d(X_126),d(X_127)),d(x(X_126,X_127))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
eq2(d(x(X_126,X_127)),d(x2)) = bfalse,
inference(resolve,[$cnf( $equal(eq2(x(d(X_126),d(X_127)),d(x2)),bfalse) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
eq2(d(x(x2,d(x2))),d(x2)) = bfalse,
inference(subst,[],[refute_0_94:[bind(X_126,$fot(x2)),bind(X_127,$fot(d(x2)))]]) ).
cnf(refute_0_96,plain,
( eq2(d(x(x2,d(x2))),d(x2)) != bfalse
| prop4(x(n(z),x(x2,d(x2)))) != eq2(d(x(x2,d(x2))),d(x2))
| prop4(x(n(z),x(x2,d(x2)))) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(prop4(x(n(z),x(x2,d(x2)))),eq2(d(x(x2,d(x2))),d(x2))) ),[1],$fot(bfalse)]]) ).
cnf(refute_0_97,plain,
( prop4(x(n(z),x(x2,d(x2)))) != eq2(d(x(x2,d(x2))),d(x2))
| prop4(x(n(z),x(x2,d(x2)))) = bfalse ),
inference(resolve,[$cnf( $equal(eq2(d(x(x2,d(x2))),d(x2)),bfalse) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
prop4(x(n(z),x(x2,d(x2)))) = bfalse,
inference(resolve,[$cnf( $equal(prop4(x(n(z),x(x2,d(x2)))),eq2(d(x(x2,d(x2))),d(x2))) )],[refute_0_83,refute_0_97]) ).
cnf(refute_0_99,plain,
( eq3(bfalse,bfalse) != btrue
| prop4(x(n(z),x(x2,d(x2)))) != bfalse
| eq3(prop4(x(n(z),x(x2,d(x2)))),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( ~ $equal(eq3(prop4(x(n(z),x(x2,d(x2)))),bfalse),btrue) ),[0,0],$fot(bfalse)]]) ).
cnf(refute_0_100,plain,
( eq3(bfalse,bfalse) != btrue
| eq3(prop4(x(n(z),x(x2,d(x2)))),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(prop4(x(n(z),x(x2,d(x2)))),bfalse) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
eq3(bfalse,bfalse) != btrue,
inference(resolve,[$cnf( $equal(eq3(prop4(x(n(z),x(x2,d(x2)))),bfalse),btrue) )],[refute_0_100,refute_0_0]) ).
cnf(refute_0_102,plain,
eq3(bfalse,bfalse) = btrue,
inference(subst,[],[axiom_088:[bind(X,$fot(bfalse))]]) ).
cnf(refute_0_103,plain,
( btrue != btrue
| eq3(bfalse,bfalse) != btrue
| eq3(bfalse,bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( $equal(eq3(bfalse,bfalse),btrue) ),[1],$fot(btrue)]]) ).
cnf(refute_0_104,plain,
( btrue != btrue
| eq3(bfalse,bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq3(bfalse,bfalse),btrue) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
btrue != btrue,
inference(resolve,[$cnf( $equal(eq3(bfalse,bfalse),btrue) )],[refute_0_104,refute_0_101]) ).
cnf(refute_0_106,plain,
btrue = btrue,
introduced(tautology,[refl,[$fot(btrue)]]) ).
cnf(refute_0_107,plain,
$false,
inference(resolve,[$cnf( $equal(btrue,btrue) )],[refute_0_106,refute_0_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX190-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 09:57:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.53/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.77
% 0.53/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.53/0.79
%------------------------------------------------------------------------------