%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 0.19s 0.44s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 36
% Syntax : Number of formulae : 129 ( 81 unt; 0 def)
% Number of atoms : 200 ( 199 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 151 ( 80 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 106 ( 3 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X] : proj1S(s(X)) = X ).
fof(axiom_002,axiom,
! [X] : z != s(X) ).
fof(axiom_003,axiom,
! [Y] : x2(z,Y) = Y ).
fof(axiom_004,axiom,
! [Y,N] : x2(s(N),Y) = s(x2(N,Y)) ).
fof(axiom_005,axiom,
! [Y] : x22(z,Y) = z ).
fof(axiom_006,axiom,
! [Y,N] : x22(s(N),Y) = x2(Y,x22(N,Y)) ).
fof(goal_007,conjecture,
? [X] : x22(X,X) != X ).
fof(subgoal_0,plain,
? [X] : x22(X,X) != X,
inference(strip,[],[goal_007]) ).
fof(negate_0_0,plain,
~ ? [X] : x22(X,X) != X,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : proj1S(s(X)) = X,
inference(canonicalize,[],[axiom_001]) ).
fof(normalize_0_1,plain,
! [X] : proj1S(s(X)) = X,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [N,Y] : x2(s(N),Y) = s(x2(N,Y)),
inference(canonicalize,[],[axiom_004]) ).
fof(normalize_0_3,plain,
! [N,Y] : x2(s(N),Y) = s(x2(N,Y)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [N,Y] : x22(s(N),Y) = x2(Y,x22(N,Y)),
inference(canonicalize,[],[axiom_006]) ).
fof(normalize_0_5,plain,
! [N,Y] : x22(s(N),Y) = x2(Y,x22(N,Y)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y] : x22(z,Y) = z,
inference(canonicalize,[],[axiom_005]) ).
fof(normalize_0_7,plain,
! [Y] : x22(z,Y) = z,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y] : x2(z,Y) = Y,
inference(canonicalize,[],[axiom_003]) ).
fof(normalize_0_9,plain,
! [Y] : x2(z,Y) = Y,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] : x22(X,X) = X,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
! [X] : x22(X,X) = X,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : z != s(X),
inference(canonicalize,[],[axiom_002]) ).
fof(normalize_0_13,plain,
! [X] : z != s(X),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
proj1S(s(X)) = X,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
proj1S(s(s(s(z)))) = s(s(z)),
inference(subst,[],[refute_0_0:[bind(X,$fot(s(s(z))))]]) ).
cnf(refute_0_2,plain,
x2(s(N),Y) = s(x2(N,Y)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
x2(s(N),s(x2(s(N),z))) = s(x2(N,s(x2(s(N),z)))),
inference(subst,[],[refute_0_2:[bind(Y,$fot(s(x2(s(N),z))))]]) ).
cnf(refute_0_4,plain,
proj1S(s(x2(X_17,s(x2(X_17,z))))) = x2(X_17,s(x2(X_17,z))),
inference(subst,[],[refute_0_0:[bind(X,$fot(x2(X_17,s(x2(X_17,z)))))]]) ).
cnf(refute_0_5,plain,
x22(s(N),Y) = x2(Y,x22(N,Y)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
x22(s(s(z)),Y) = x2(Y,x22(s(z),Y)),
inference(subst,[],[refute_0_5:[bind(N,$fot(s(z)))]]) ).
cnf(refute_0_7,plain,
x22(s(z),X_6) = x2(X_6,x22(z,X_6)),
inference(subst,[],[refute_0_5:[bind(N,$fot(z)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_8,plain,
x22(z,Y) = z,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
x22(z,X_6) = z,
inference(subst,[],[refute_0_8:[bind(Y,$fot(X_6))]]) ).
cnf(refute_0_10,plain,
( x22(s(z),X_6) != x2(X_6,x22(z,X_6))
| x22(z,X_6) != z
| x22(s(z),X_6) = x2(X_6,z) ),
introduced(tautology,[equality,[$cnf( $equal(x22(s(z),X_6),x2(X_6,x22(z,X_6))) ),[1,1],$fot(z)]]) ).
cnf(refute_0_11,plain,
( x22(s(z),X_6) != x2(X_6,x22(z,X_6))
| x22(s(z),X_6) = x2(X_6,z) ),
inference(resolve,[$cnf( $equal(x22(z,X_6),z) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
x22(s(z),X_6) = x2(X_6,z),
inference(resolve,[$cnf( $equal(x22(s(z),X_6),x2(X_6,x22(z,X_6))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
x22(s(z),Y) = x2(Y,z),
inference(subst,[],[refute_0_12:[bind(X_6,$fot(Y))]]) ).
cnf(refute_0_14,plain,
( x22(s(s(z)),Y) != x2(Y,x22(s(z),Y))
| x22(s(z),Y) != x2(Y,z)
| x22(s(s(z)),Y) = x2(Y,x2(Y,z)) ),
introduced(tautology,[equality,[$cnf( $equal(x22(s(s(z)),Y),x2(Y,x22(s(z),Y))) ),[1,1],$fot(x2(Y,z))]]) ).
cnf(refute_0_15,plain,
( x22(s(s(z)),Y) != x2(Y,x22(s(z),Y))
| x22(s(s(z)),Y) = x2(Y,x2(Y,z)) ),
inference(resolve,[$cnf( $equal(x22(s(z),Y),x2(Y,z)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
x22(s(s(z)),Y) = x2(Y,x2(Y,z)),
inference(resolve,[$cnf( $equal(x22(s(s(z)),Y),x2(Y,x22(s(z),Y))) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
x22(s(s(z)),s(X_12)) = x2(s(X_12),x2(s(X_12),z)),
inference(subst,[],[refute_0_16:[bind(Y,$fot(s(X_12)))]]) ).
cnf(refute_0_18,plain,
x2(s(X_12),x2(s(X_12),z)) = s(x2(X_12,x2(s(X_12),z))),
inference(subst,[],[refute_0_2:[bind(N,$fot(X_12)),bind(Y,$fot(x2(s(X_12),z)))]]) ).
cnf(refute_0_19,plain,
( x2(s(X_12),x2(s(X_12),z)) != s(x2(X_12,x2(s(X_12),z)))
| x22(s(s(z)),s(X_12)) != x2(s(X_12),x2(s(X_12),z))
| x22(s(s(z)),s(X_12)) = s(x2(X_12,x2(s(X_12),z))) ),
introduced(tautology,[equality,[$cnf( $equal(x22(s(s(z)),s(X_12)),x2(s(X_12),x2(s(X_12),z))) ),[1],$fot(s(x2(X_12,x2(s(X_12),z))))]]) ).
cnf(refute_0_20,plain,
( x22(s(s(z)),s(X_12)) != x2(s(X_12),x2(s(X_12),z))
| x22(s(s(z)),s(X_12)) = s(x2(X_12,x2(s(X_12),z))) ),
inference(resolve,[$cnf( $equal(x2(s(X_12),x2(s(X_12),z)),s(x2(X_12,x2(s(X_12),z)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
x22(s(s(z)),s(X_12)) = s(x2(X_12,x2(s(X_12),z))),
inference(resolve,[$cnf( $equal(x22(s(s(z)),s(X_12)),x2(s(X_12),x2(s(X_12),z))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
x2(s(X_12),z) = s(x2(X_12,z)),
inference(subst,[],[refute_0_2:[bind(N,$fot(X_12)),bind(Y,$fot(z))]]) ).
cnf(refute_0_23,plain,
x2(X_12,x2(s(X_12),z)) = x2(X_12,x2(s(X_12),z)),
introduced(tautology,[refl,[$fot(x2(X_12,x2(s(X_12),z)))]]) ).
cnf(refute_0_24,plain,
( x2(X_12,x2(s(X_12),z)) != x2(X_12,x2(s(X_12),z))
| x2(s(X_12),z) != s(x2(X_12,z))
| x2(X_12,x2(s(X_12),z)) = x2(X_12,s(x2(X_12,z))) ),
introduced(tautology,[equality,[$cnf( $equal(x2(X_12,x2(s(X_12),z)),x2(X_12,x2(s(X_12),z))) ),[1,1],$fot(s(x2(X_12,z)))]]) ).
cnf(refute_0_25,plain,
( x2(s(X_12),z) != s(x2(X_12,z))
| x2(X_12,x2(s(X_12),z)) = x2(X_12,s(x2(X_12,z))) ),
inference(resolve,[$cnf( $equal(x2(X_12,x2(s(X_12),z)),x2(X_12,x2(s(X_12),z))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
x2(X_12,x2(s(X_12),z)) = x2(X_12,s(x2(X_12,z))),
inference(resolve,[$cnf( $equal(x2(s(X_12),z),s(x2(X_12,z))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
s(x2(X_12,x2(s(X_12),z))) = s(x2(X_12,x2(s(X_12),z))),
introduced(tautology,[refl,[$fot(s(x2(X_12,x2(s(X_12),z))))]]) ).
cnf(refute_0_28,plain,
( s(x2(X_12,x2(s(X_12),z))) != s(x2(X_12,x2(s(X_12),z)))
| x2(X_12,x2(s(X_12),z)) != x2(X_12,s(x2(X_12,z)))
| s(x2(X_12,x2(s(X_12),z))) = s(x2(X_12,s(x2(X_12,z)))) ),
introduced(tautology,[equality,[$cnf( $equal(s(x2(X_12,x2(s(X_12),z))),s(x2(X_12,x2(s(X_12),z)))) ),[1,0],$fot(x2(X_12,s(x2(X_12,z))))]]) ).
cnf(refute_0_29,plain,
( x2(X_12,x2(s(X_12),z)) != x2(X_12,s(x2(X_12,z)))
| s(x2(X_12,x2(s(X_12),z))) = s(x2(X_12,s(x2(X_12,z)))) ),
inference(resolve,[$cnf( $equal(s(x2(X_12,x2(s(X_12),z))),s(x2(X_12,x2(s(X_12),z)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
s(x2(X_12,x2(s(X_12),z))) = s(x2(X_12,s(x2(X_12,z)))),
inference(resolve,[$cnf( $equal(x2(X_12,x2(s(X_12),z)),x2(X_12,s(x2(X_12,z)))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( s(x2(X_12,x2(s(X_12),z))) != s(x2(X_12,s(x2(X_12,z))))
| x22(s(s(z)),s(X_12)) != s(x2(X_12,x2(s(X_12),z)))
| x22(s(s(z)),s(X_12)) = s(x2(X_12,s(x2(X_12,z)))) ),
introduced(tautology,[equality,[$cnf( $equal(x22(s(s(z)),s(X_12)),s(x2(X_12,x2(s(X_12),z)))) ),[1],$fot(s(x2(X_12,s(x2(X_12,z)))))]]) ).
cnf(refute_0_32,plain,
( x22(s(s(z)),s(X_12)) != s(x2(X_12,x2(s(X_12),z)))
| x22(s(s(z)),s(X_12)) = s(x2(X_12,s(x2(X_12,z)))) ),
inference(resolve,[$cnf( $equal(s(x2(X_12,x2(s(X_12),z))),s(x2(X_12,s(x2(X_12,z))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
x22(s(s(z)),s(X_12)) = s(x2(X_12,s(x2(X_12,z)))),
inference(resolve,[$cnf( $equal(x22(s(s(z)),s(X_12)),s(x2(X_12,x2(s(X_12),z)))) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
x22(s(s(z)),s(X_17)) = s(x2(X_17,s(x2(X_17,z)))),
inference(subst,[],[refute_0_33:[bind(X_12,$fot(X_17))]]) ).
cnf(refute_0_35,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_36,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_37,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( x22(s(s(z)),s(X_17)) != s(x2(X_17,s(x2(X_17,z))))
| s(x2(X_17,s(x2(X_17,z)))) = x22(s(s(z)),s(X_17)) ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(x22(s(s(z)),s(X_17)))),bind(Y0,$fot(s(x2(X_17,s(x2(X_17,z))))))]]) ).
cnf(refute_0_39,plain,
s(x2(X_17,s(x2(X_17,z)))) = x22(s(s(z)),s(X_17)),
inference(resolve,[$cnf( $equal(x22(s(s(z)),s(X_17)),s(x2(X_17,s(x2(X_17,z))))) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
( proj1S(s(x2(X_17,s(x2(X_17,z))))) != x2(X_17,s(x2(X_17,z)))
| s(x2(X_17,s(x2(X_17,z)))) != x22(s(s(z)),s(X_17))
| proj1S(x22(s(s(z)),s(X_17))) = x2(X_17,s(x2(X_17,z))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1S(s(x2(X_17,s(x2(X_17,z))))),x2(X_17,s(x2(X_17,z)))) ),[0,0],$fot(x22(s(s(z)),s(X_17)))]]) ).
cnf(refute_0_41,plain,
( proj1S(s(x2(X_17,s(x2(X_17,z))))) != x2(X_17,s(x2(X_17,z)))
| proj1S(x22(s(s(z)),s(X_17))) = x2(X_17,s(x2(X_17,z))) ),
inference(resolve,[$cnf( $equal(s(x2(X_17,s(x2(X_17,z)))),x22(s(s(z)),s(X_17))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
proj1S(x22(s(s(z)),s(X_17))) = x2(X_17,s(x2(X_17,z))),
inference(resolve,[$cnf( $equal(proj1S(s(x2(X_17,s(x2(X_17,z))))),x2(X_17,s(x2(X_17,z)))) )],[refute_0_4,refute_0_41]) ).
cnf(refute_0_43,plain,
proj1S(x22(s(s(z)),s(s(N)))) = x2(s(N),s(x2(s(N),z))),
inference(subst,[],[refute_0_42:[bind(X_17,$fot(s(N)))]]) ).
cnf(refute_0_44,plain,
( proj1S(x22(s(s(z)),s(s(N)))) != x2(s(N),s(x2(s(N),z)))
| x2(s(N),s(x2(s(N),z))) = proj1S(x22(s(s(z)),s(s(N)))) ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(proj1S(x22(s(s(z)),s(s(N)))))),bind(Y0,$fot(x2(s(N),s(x2(s(N),z)))))]]) ).
cnf(refute_0_45,plain,
x2(s(N),s(x2(s(N),z))) = proj1S(x22(s(s(z)),s(s(N)))),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(N)))),x2(s(N),s(x2(s(N),z)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( x2(s(N),s(x2(s(N),z))) != proj1S(x22(s(s(z)),s(s(N))))
| x2(s(N),s(x2(s(N),z))) != s(x2(N,s(x2(s(N),z))))
| proj1S(x22(s(s(z)),s(s(N)))) = s(x2(N,s(x2(s(N),z)))) ),
introduced(tautology,[equality,[$cnf( $equal(x2(s(N),s(x2(s(N),z))),s(x2(N,s(x2(s(N),z))))) ),[0],$fot(proj1S(x22(s(s(z)),s(s(N)))))]]) ).
cnf(refute_0_47,plain,
( x2(s(N),s(x2(s(N),z))) != s(x2(N,s(x2(s(N),z))))
| proj1S(x22(s(s(z)),s(s(N)))) = s(x2(N,s(x2(s(N),z)))) ),
inference(resolve,[$cnf( $equal(x2(s(N),s(x2(s(N),z))),proj1S(x22(s(s(z)),s(s(N))))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
proj1S(x22(s(s(z)),s(s(N)))) = s(x2(N,s(x2(s(N),z)))),
inference(resolve,[$cnf( $equal(x2(s(N),s(x2(s(N),z))),s(x2(N,s(x2(s(N),z))))) )],[refute_0_3,refute_0_47]) ).
cnf(refute_0_49,plain,
x2(s(N),z) = s(x2(N,z)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(z))]]) ).
cnf(refute_0_50,plain,
s(x2(s(N),z)) = s(x2(s(N),z)),
introduced(tautology,[refl,[$fot(s(x2(s(N),z)))]]) ).
cnf(refute_0_51,plain,
( s(x2(s(N),z)) != s(x2(s(N),z))
| x2(s(N),z) != s(x2(N,z))
| s(x2(s(N),z)) = s(s(x2(N,z))) ),
introduced(tautology,[equality,[$cnf( $equal(s(x2(s(N),z)),s(x2(s(N),z))) ),[1,0],$fot(s(x2(N,z)))]]) ).
cnf(refute_0_52,plain,
( x2(s(N),z) != s(x2(N,z))
| s(x2(s(N),z)) = s(s(x2(N,z))) ),
inference(resolve,[$cnf( $equal(s(x2(s(N),z)),s(x2(s(N),z))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
s(x2(s(N),z)) = s(s(x2(N,z))),
inference(resolve,[$cnf( $equal(x2(s(N),z),s(x2(N,z))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
x2(N,s(x2(s(N),z))) = x2(N,s(x2(s(N),z))),
introduced(tautology,[refl,[$fot(x2(N,s(x2(s(N),z))))]]) ).
cnf(refute_0_55,plain,
( s(x2(s(N),z)) != s(s(x2(N,z)))
| x2(N,s(x2(s(N),z))) != x2(N,s(x2(s(N),z)))
| x2(N,s(x2(s(N),z))) = x2(N,s(s(x2(N,z)))) ),
introduced(tautology,[equality,[$cnf( $equal(x2(N,s(x2(s(N),z))),x2(N,s(x2(s(N),z)))) ),[1,1],$fot(s(s(x2(N,z))))]]) ).
cnf(refute_0_56,plain,
( s(x2(s(N),z)) != s(s(x2(N,z)))
| x2(N,s(x2(s(N),z))) = x2(N,s(s(x2(N,z)))) ),
inference(resolve,[$cnf( $equal(x2(N,s(x2(s(N),z))),x2(N,s(x2(s(N),z)))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
x2(N,s(x2(s(N),z))) = x2(N,s(s(x2(N,z)))),
inference(resolve,[$cnf( $equal(s(x2(s(N),z)),s(s(x2(N,z)))) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
s(x2(N,s(x2(s(N),z)))) = s(x2(N,s(x2(s(N),z)))),
introduced(tautology,[refl,[$fot(s(x2(N,s(x2(s(N),z)))))]]) ).
cnf(refute_0_59,plain,
( s(x2(N,s(x2(s(N),z)))) != s(x2(N,s(x2(s(N),z))))
| x2(N,s(x2(s(N),z))) != x2(N,s(s(x2(N,z))))
| s(x2(N,s(x2(s(N),z)))) = s(x2(N,s(s(x2(N,z))))) ),
introduced(tautology,[equality,[$cnf( $equal(s(x2(N,s(x2(s(N),z)))),s(x2(N,s(x2(s(N),z))))) ),[1,0],$fot(x2(N,s(s(x2(N,z)))))]]) ).
cnf(refute_0_60,plain,
( x2(N,s(x2(s(N),z))) != x2(N,s(s(x2(N,z))))
| s(x2(N,s(x2(s(N),z)))) = s(x2(N,s(s(x2(N,z))))) ),
inference(resolve,[$cnf( $equal(s(x2(N,s(x2(s(N),z)))),s(x2(N,s(x2(s(N),z))))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
s(x2(N,s(x2(s(N),z)))) = s(x2(N,s(s(x2(N,z))))),
inference(resolve,[$cnf( $equal(x2(N,s(x2(s(N),z))),x2(N,s(s(x2(N,z))))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( proj1S(x22(s(s(z)),s(s(N)))) != s(x2(N,s(x2(s(N),z))))
| s(x2(N,s(x2(s(N),z)))) != s(x2(N,s(s(x2(N,z)))))
| proj1S(x22(s(s(z)),s(s(N)))) = s(x2(N,s(s(x2(N,z))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(proj1S(x22(s(s(z)),s(s(N)))),s(x2(N,s(s(x2(N,z)))))) ),[0],$fot(s(x2(N,s(x2(s(N),z)))))]]) ).
cnf(refute_0_63,plain,
( proj1S(x22(s(s(z)),s(s(N)))) != s(x2(N,s(x2(s(N),z))))
| proj1S(x22(s(s(z)),s(s(N)))) = s(x2(N,s(s(x2(N,z))))) ),
inference(resolve,[$cnf( $equal(s(x2(N,s(x2(s(N),z)))),s(x2(N,s(s(x2(N,z)))))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
proj1S(x22(s(s(z)),s(s(N)))) = s(x2(N,s(s(x2(N,z))))),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(N)))),s(x2(N,s(x2(s(N),z))))) )],[refute_0_48,refute_0_63]) ).
cnf(refute_0_65,plain,
proj1S(x22(s(s(z)),s(s(z)))) = s(x2(z,s(s(x2(z,z))))),
inference(subst,[],[refute_0_64:[bind(N,$fot(z))]]) ).
cnf(refute_0_66,plain,
x2(z,Y) = Y,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_67,plain,
x2(z,z) = z,
inference(subst,[],[refute_0_66:[bind(Y,$fot(z))]]) ).
cnf(refute_0_68,plain,
( proj1S(x22(s(s(z)),s(s(z)))) != s(x2(z,s(s(x2(z,z)))))
| x2(z,z) != z
| proj1S(x22(s(s(z)),s(s(z)))) = s(x2(z,s(s(z)))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),s(x2(z,s(s(x2(z,z)))))) ),[1,0,1,0,0],$fot(z)]]) ).
cnf(refute_0_69,plain,
( proj1S(x22(s(s(z)),s(s(z)))) != s(x2(z,s(s(x2(z,z)))))
| proj1S(x22(s(s(z)),s(s(z)))) = s(x2(z,s(s(z)))) ),
inference(resolve,[$cnf( $equal(x2(z,z),z) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
proj1S(x22(s(s(z)),s(s(z)))) = s(x2(z,s(s(z)))),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),s(x2(z,s(s(x2(z,z)))))) )],[refute_0_65,refute_0_69]) ).
cnf(refute_0_71,plain,
proj1S(s(s(z))) = s(z),
inference(subst,[],[refute_0_0:[bind(X,$fot(s(z)))]]) ).
cnf(refute_0_72,plain,
x22(X,X) = X,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_73,plain,
x22(s(s(z)),s(s(z))) = s(s(z)),
inference(subst,[],[refute_0_72:[bind(X,$fot(s(s(z))))]]) ).
cnf(refute_0_74,plain,
proj1S(x22(s(s(z)),s(s(z)))) = proj1S(x22(s(s(z)),s(s(z)))),
introduced(tautology,[refl,[$fot(proj1S(x22(s(s(z)),s(s(z)))))]]) ).
cnf(refute_0_75,plain,
( proj1S(x22(s(s(z)),s(s(z)))) != proj1S(x22(s(s(z)),s(s(z))))
| x22(s(s(z)),s(s(z))) != s(s(z))
| proj1S(x22(s(s(z)),s(s(z)))) = proj1S(s(s(z))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),proj1S(x22(s(s(z)),s(s(z))))) ),[1,0],$fot(s(s(z)))]]) ).
cnf(refute_0_76,plain,
( x22(s(s(z)),s(s(z))) != s(s(z))
| proj1S(x22(s(s(z)),s(s(z)))) = proj1S(s(s(z))) ),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),proj1S(x22(s(s(z)),s(s(z))))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
proj1S(x22(s(s(z)),s(s(z)))) = proj1S(s(s(z))),
inference(resolve,[$cnf( $equal(x22(s(s(z)),s(s(z))),s(s(z))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_79,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_37,refute_0_78]) ).
cnf(refute_0_80,plain,
( proj1S(s(s(z))) != s(z)
| proj1S(x22(s(s(z)),s(s(z)))) != proj1S(s(s(z)))
| proj1S(x22(s(s(z)),s(s(z)))) = s(z) ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(proj1S(x22(s(s(z)),s(s(z)))))),bind(Y0,$fot(proj1S(s(s(z))))),bind(Z,$fot(s(z)))]]) ).
cnf(refute_0_81,plain,
( proj1S(s(s(z))) != s(z)
| proj1S(x22(s(s(z)),s(s(z)))) = s(z) ),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),proj1S(s(s(z)))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
proj1S(x22(s(s(z)),s(s(z)))) = s(z),
inference(resolve,[$cnf( $equal(proj1S(s(s(z))),s(z)) )],[refute_0_71,refute_0_81]) ).
cnf(refute_0_83,plain,
( proj1S(x22(s(s(z)),s(s(z)))) != s(x2(z,s(s(z))))
| proj1S(x22(s(s(z)),s(s(z)))) != s(z)
| s(z) = s(x2(z,s(s(z)))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),s(x2(z,s(s(z))))) ),[0],$fot(s(z))]]) ).
cnf(refute_0_84,plain,
( proj1S(x22(s(s(z)),s(s(z)))) != s(x2(z,s(s(z))))
| s(z) = s(x2(z,s(s(z)))) ),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),s(z)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
x2(z,s(s(z))) = s(s(z)),
inference(subst,[],[refute_0_66:[bind(Y,$fot(s(s(z))))]]) ).
cnf(refute_0_86,plain,
s(x2(z,s(s(z)))) = s(x2(z,s(s(z)))),
introduced(tautology,[refl,[$fot(s(x2(z,s(s(z)))))]]) ).
cnf(refute_0_87,plain,
( s(x2(z,s(s(z)))) != s(x2(z,s(s(z))))
| x2(z,s(s(z))) != s(s(z))
| s(x2(z,s(s(z)))) = s(s(s(z))) ),
introduced(tautology,[equality,[$cnf( $equal(s(x2(z,s(s(z)))),s(x2(z,s(s(z))))) ),[1,0],$fot(s(s(z)))]]) ).
cnf(refute_0_88,plain,
( x2(z,s(s(z))) != s(s(z))
| s(x2(z,s(s(z)))) = s(s(s(z))) ),
inference(resolve,[$cnf( $equal(s(x2(z,s(s(z)))),s(x2(z,s(s(z))))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
s(x2(z,s(s(z)))) = s(s(s(z))),
inference(resolve,[$cnf( $equal(x2(z,s(s(z))),s(s(z))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( s(x2(z,s(s(z)))) != s(s(s(z)))
| s(z) != s(x2(z,s(s(z))))
| s(z) = s(s(s(z))) ),
introduced(tautology,[equality,[$cnf( $equal(s(z),s(x2(z,s(s(z))))) ),[1],$fot(s(s(s(z))))]]) ).
cnf(refute_0_91,plain,
( s(z) != s(x2(z,s(s(z))))
| s(z) = s(s(s(z))) ),
inference(resolve,[$cnf( $equal(s(x2(z,s(s(z)))),s(s(s(z)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( proj1S(x22(s(s(z)),s(s(z)))) != s(x2(z,s(s(z))))
| s(z) = s(s(s(z))) ),
inference(resolve,[$cnf( $equal(s(z),s(x2(z,s(s(z))))) )],[refute_0_84,refute_0_91]) ).
cnf(refute_0_93,plain,
s(z) = s(s(s(z))),
inference(resolve,[$cnf( $equal(proj1S(x22(s(s(z)),s(s(z)))),s(x2(z,s(s(z))))) )],[refute_0_70,refute_0_92]) ).
cnf(refute_0_94,plain,
( s(z) != s(s(s(z)))
| s(s(s(z))) = s(z) ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(s(z))),bind(Y0,$fot(s(s(s(z)))))]]) ).
cnf(refute_0_95,plain,
s(s(s(z))) = s(z),
inference(resolve,[$cnf( $equal(s(z),s(s(s(z)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( proj1S(s(s(s(z)))) != s(s(z))
| s(s(s(z))) != s(z)
| proj1S(s(z)) = s(s(z)) ),
introduced(tautology,[equality,[$cnf( $equal(proj1S(s(s(s(z)))),s(s(z))) ),[0,0],$fot(s(z))]]) ).
cnf(refute_0_97,plain,
( proj1S(s(s(s(z)))) != s(s(z))
| proj1S(s(z)) = s(s(z)) ),
inference(resolve,[$cnf( $equal(s(s(s(z))),s(z)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
proj1S(s(z)) = s(s(z)),
inference(resolve,[$cnf( $equal(proj1S(s(s(s(z)))),s(s(z))) )],[refute_0_1,refute_0_97]) ).
cnf(refute_0_99,plain,
proj1S(s(z)) = z,
inference(subst,[],[refute_0_0:[bind(X,$fot(z))]]) ).
cnf(refute_0_100,plain,
( proj1S(s(z)) != s(s(z))
| proj1S(s(z)) != z
| z = s(s(z)) ),
introduced(tautology,[equality,[$cnf( $equal(proj1S(s(z)),s(s(z))) ),[0],$fot(z)]]) ).
cnf(refute_0_101,plain,
( proj1S(s(z)) != s(s(z))
| z = s(s(z)) ),
inference(resolve,[$cnf( $equal(proj1S(s(z)),z) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
z = s(s(z)),
inference(resolve,[$cnf( $equal(proj1S(s(z)),s(s(z))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
z != s(X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_104,plain,
z != s(s(z)),
inference(subst,[],[refute_0_103:[bind(X,$fot(s(z)))]]) ).
cnf(refute_0_105,plain,
$false,
inference(resolve,[$cnf( $equal(z,s(s(z))) )],[refute_0_102,refute_0_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX204+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 : n016.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 11:28:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.30/0.46
%------------------------------------------------------------------------------