Metis---2.4.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWX203-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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   : Unsatisfiable 7.96s 8.19s
% Output   : CNFRefutation 8.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :  123
% Syntax   : Number of clauses     :  471 ( 256 unt;   0 nHn; 237 RR)
%            Number of literals    :  792 ( 791 equ; 325 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   4 con; 0-3 aty)
%            Number of variables   :  770 (  60 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_001,axiom,
    aux(Y,Xs,bfalse) = unique(Xs) ).

cnf(axiom_003,axiom,
    orb(bfalse,Q) = Q ).

cnf(axiom_004,axiom,
    leqNat(z,Y) = btrue ).

cnf(axiom_005,axiom,
    leqNat(s(Z),z) = bfalse ).

cnf(axiom_006,axiom,
    leqNat(s(Z),s(M)) = leqNat(Z,M) ).

cnf(axiom_007,axiom,
    lengthNat(nil) = z ).

cnf(axiom_008,axiom,
    lengthNat(cons(Y,Xs)) = s(lengthNat(Xs)) ).

cnf(axiom_009,axiom,
    impl(btrue,Q) = Q ).

cnf(axiom_011,axiom,
    elemNat(X,nil) = bfalse ).

cnf(axiom_012,axiom,
    elemNat(X,cons(Z,Xs)) = orb(eq(X,Z),elemNat(X,Xs)) ).

cnf(axiom_013,axiom,
    unique(nil) = btrue ).

cnf(axiom_014,axiom,
    unique(cons(Y,Xs)) = aux(Y,Xs,elemNat(Y,Xs)) ).

cnf(axiom_015,axiom,
    append(nil,Y) = Y ).

cnf(axiom_016,axiom,
    append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)) ).

cnf(axiom_017,axiom,
    rev(nil) = nil ).

cnf(axiom_018,axiom,
    rev(cons(Y,Xs)) = append(rev(Xs),cons(Y,nil)) ).

cnf(axiom_019,axiom,
    andb(btrue,Q) = Q ).

cnf(axiom_022,axiom,
    sorted(cons(Y,nil)) = btrue ).

cnf(axiom_023,axiom,
    sorted(cons(Y,cons(Y2,Xs))) = andb(leqNat(Y,Y2),sorted(cons(Y2,Xs))) ).

cnf(axiom_024,axiom,
    psorted_rev(X) = impl(eq2(sorted(rev(X)),btrue),impl(eq2(unique(X),btrue),eq2(leqNat(lengthNat(X),s(s(s(z)))),btrue))) ).

cnf(axiom_025,axiom,
    eq2(bfalse,btrue) = bfalse ).

cnf(axiom_027,axiom,
    eq(s(X),s(Y)) = eq(X,Y) ).

cnf(axiom_029,axiom,
    eq(s(X),z) = bfalse ).

cnf(axiom_031,axiom,
    eq2(X,X) = btrue ).

cnf(goal,negated_conjecture,
    eq2(psorted_rev(X),bfalse) != btrue ).

cnf(refute_0_0,plain,
    eq2(psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse) != btrue,
    inference(subst,[],[goal:[bind(X,$fot(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))))]]) ).

cnf(refute_0_1,plain,
    psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
    inference(subst,[],[axiom_024:[bind(X,$fot(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))))]]) ).

cnf(refute_0_2,plain,
    unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))) = aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307)))),
    inference(subst,[],[axiom_014:[bind(Xs,$fot(cons(X_305,cons(s(z),X_307)))),bind(Y,$fot(s(s(X_306))))]]) ).

cnf(refute_0_3,plain,
    elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),cons(s(z),X_107))),
    inference(subst,[],[axiom_012:[bind(X,$fot(s(s(X_106)))),bind(Xs,$fot(cons(s(z),X_107)))]]) ).

cnf(refute_0_4,plain,
    elemNat(s(X),cons(s(Y),X_44)) = orb(eq(s(X),s(Y)),elemNat(s(X),X_44)),
    inference(subst,[],[axiom_012:[bind(X,$fot(s(X))),bind(Xs,$fot(X_44)),bind(Z,$fot(s(Y)))]]) ).

cnf(refute_0_5,plain,
    ( elemNat(s(X),cons(s(Y),X_44)) != orb(eq(s(X),s(Y)),elemNat(s(X),X_44))
    | eq(s(X),s(Y)) != eq(X,Y)
    | elemNat(s(X),cons(s(Y),X_44)) = orb(eq(X,Y),elemNat(s(X),X_44)) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(s(X),cons(s(Y),X_44)),orb(eq(s(X),s(Y)),elemNat(s(X),X_44))) ),[1,0],$fot(eq(X,Y))]]) ).

cnf(refute_0_6,plain,
    ( elemNat(s(X),cons(s(Y),X_44)) != orb(eq(s(X),s(Y)),elemNat(s(X),X_44))
    | elemNat(s(X),cons(s(Y),X_44)) = orb(eq(X,Y),elemNat(s(X),X_44)) ),
    inference(resolve,[$cnf( $equal(eq(s(X),s(Y)),eq(X,Y)) )],[axiom_027,refute_0_5]) ).

cnf(refute_0_7,plain,
    elemNat(s(X),cons(s(Y),X_44)) = orb(eq(X,Y),elemNat(s(X),X_44)),
    inference(resolve,[$cnf( $equal(elemNat(s(X),cons(s(Y),X_44)),orb(eq(s(X),s(Y)),elemNat(s(X),X_44))) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    elemNat(s(s(X)),cons(s(z),X_105)) = orb(eq(s(X),z),elemNat(s(s(X)),X_105)),
    inference(subst,[],[refute_0_7:[bind(X,$fot(s(X))),bind(Y,$fot(z)),bind(X_44,$fot(X_105))]]) ).

cnf(refute_0_9,plain,
    ( elemNat(s(s(X)),cons(s(z),X_105)) != orb(eq(s(X),z),elemNat(s(s(X)),X_105))
    | eq(s(X),z) != bfalse
    | elemNat(s(s(X)),cons(s(z),X_105)) = orb(bfalse,elemNat(s(s(X)),X_105)) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(s(s(X)),cons(s(z),X_105)),orb(eq(s(X),z),elemNat(s(s(X)),X_105))) ),[1,0],$fot(bfalse)]]) ).

cnf(refute_0_10,plain,
    ( elemNat(s(s(X)),cons(s(z),X_105)) != orb(eq(s(X),z),elemNat(s(s(X)),X_105))
    | elemNat(s(s(X)),cons(s(z),X_105)) = orb(bfalse,elemNat(s(s(X)),X_105)) ),
    inference(resolve,[$cnf( $equal(eq(s(X),z),bfalse) )],[axiom_029,refute_0_9]) ).

cnf(refute_0_11,plain,
    elemNat(s(s(X)),cons(s(z),X_105)) = orb(bfalse,elemNat(s(s(X)),X_105)),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X)),cons(s(z),X_105)),orb(eq(s(X),z),elemNat(s(s(X)),X_105))) )],[refute_0_8,refute_0_10]) ).

cnf(refute_0_12,plain,
    orb(bfalse,elemNat(s(s(X)),X_105)) = elemNat(s(s(X)),X_105),
    inference(subst,[],[axiom_003:[bind(Q,$fot(elemNat(s(s(X)),X_105)))]]) ).

cnf(refute_0_13,plain,
    ( elemNat(s(s(X)),cons(s(z),X_105)) != orb(bfalse,elemNat(s(s(X)),X_105))
    | orb(bfalse,elemNat(s(s(X)),X_105)) != elemNat(s(s(X)),X_105)
    | elemNat(s(s(X)),cons(s(z),X_105)) = elemNat(s(s(X)),X_105) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(elemNat(s(s(X)),cons(s(z),X_105)),elemNat(s(s(X)),X_105)) ),[0],$fot(orb(bfalse,elemNat(s(s(X)),X_105)))]]) ).

cnf(refute_0_14,plain,
    ( elemNat(s(s(X)),cons(s(z),X_105)) != orb(bfalse,elemNat(s(s(X)),X_105))
    | elemNat(s(s(X)),cons(s(z),X_105)) = elemNat(s(s(X)),X_105) ),
    inference(resolve,[$cnf( $equal(orb(bfalse,elemNat(s(s(X)),X_105)),elemNat(s(s(X)),X_105)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    elemNat(s(s(X)),cons(s(z),X_105)) = elemNat(s(s(X)),X_105),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X)),cons(s(z),X_105)),orb(bfalse,elemNat(s(s(X)),X_105))) )],[refute_0_11,refute_0_14]) ).

cnf(refute_0_16,plain,
    elemNat(s(s(X_106)),cons(s(z),X_107)) = elemNat(s(s(X_106)),X_107),
    inference(subst,[],[refute_0_15:[bind(X,$fot(X_106)),bind(X_105,$fot(X_107))]]) ).

cnf(refute_0_17,plain,
    ( elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) != orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),cons(s(z),X_107)))
    | elemNat(s(s(X_106)),cons(s(z),X_107)) != elemNat(s(s(X_106)),X_107)
    | elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))),orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),cons(s(z),X_107)))) ),[1,1],$fot(elemNat(s(s(X_106)),X_107))]]) ).

cnf(refute_0_18,plain,
    ( elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) != orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),cons(s(z),X_107)))
    | elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)) ),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X_106)),cons(s(z),X_107)),elemNat(s(s(X_106)),X_107)) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))),orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),cons(s(z),X_107)))) )],[refute_0_3,refute_0_18]) ).

cnf(refute_0_20,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_21,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_22,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( elemNat(X,cons(Z,Xs)) != orb(eq(X,Z),elemNat(X,Xs))
    | orb(eq(X,Z),elemNat(X,Xs)) = elemNat(X,cons(Z,Xs)) ),
    inference(subst,[],[refute_0_22:[bind(X0,$fot(elemNat(X,cons(Z,Xs)))),bind(Y0,$fot(orb(eq(X,Z),elemNat(X,Xs))))]]) ).

cnf(refute_0_24,plain,
    orb(eq(X,Z),elemNat(X,Xs)) = elemNat(X,cons(Z,Xs)),
    inference(resolve,[$cnf( $equal(elemNat(X,cons(Z,Xs)),orb(eq(X,Z),elemNat(X,Xs))) )],[axiom_012,refute_0_23]) ).

cnf(refute_0_25,plain,
    orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)) = elemNat(s(s(X_106)),cons(Z,X_107)),
    inference(subst,[],[refute_0_24:[bind(X,$fot(s(s(X_106)))),bind(Xs,$fot(X_107))]]) ).

cnf(refute_0_26,plain,
    ( elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) != orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107))
    | orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)) != elemNat(s(s(X_106)),cons(Z,X_107))
    | elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = elemNat(s(s(X_106)),cons(Z,X_107)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))),elemNat(s(s(X_106)),cons(Z,X_107))) ),[0],$fot(orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)))]]) ).

cnf(refute_0_27,plain,
    ( elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) != orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107))
    | elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = elemNat(s(s(X_106)),cons(Z,X_107)) ),
    inference(resolve,[$cnf( $equal(orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107)),elemNat(s(s(X_106)),cons(Z,X_107))) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))) = elemNat(s(s(X_106)),cons(Z,X_107)),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X_106)),cons(Z,cons(s(z),X_107))),orb(eq(s(s(X_106)),Z),elemNat(s(s(X_106)),X_107))) )],[refute_0_19,refute_0_27]) ).

cnf(refute_0_29,plain,
    elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))) = elemNat(s(s(X_306)),cons(X_305,X_307)),
    inference(subst,[],[refute_0_28:[bind(Z,$fot(X_305)),bind(X_106,$fot(X_306)),bind(X_107,$fot(X_307))]]) ).

cnf(refute_0_30,plain,
    ( elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))) != elemNat(s(s(X_306)),cons(X_305,X_307))
    | unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))) != aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))))
    | unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))) = aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,X_307))) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))),aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))))) ),[1,2],$fot(elemNat(s(s(X_306)),cons(X_305,X_307)))]]) ).

cnf(refute_0_31,plain,
    ( unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))) != aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))))
    | unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))) = aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,X_307))) ),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))),elemNat(s(s(X_306)),cons(X_305,X_307))) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))) = aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,X_307))),
    inference(resolve,[$cnf( $equal(unique(cons(s(s(X_306)),cons(X_305,cons(s(z),X_307)))),aux(s(s(X_306)),cons(X_305,cons(s(z),X_307)),elemNat(s(s(X_306)),cons(X_305,cons(s(z),X_307))))) )],[refute_0_2,refute_0_31]) ).

cnf(refute_0_33,plain,
    unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))) = aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57)))),
    inference(subst,[],[refute_0_32:[bind(X_305,$fot(X_1037)),bind(X_306,$fot(X_1038)),bind(X_307,$fot(cons(z,X_57)))]]) ).

cnf(refute_0_34,plain,
    elemNat(s(X_56),cons(Z,cons(z,X_57))) = orb(eq(s(X_56),Z),elemNat(s(X_56),cons(z,X_57))),
    inference(subst,[],[axiom_012:[bind(X,$fot(s(X_56))),bind(Xs,$fot(cons(z,X_57)))]]) ).

cnf(refute_0_35,plain,
    elemNat(s(X),cons(z,X_44)) = orb(eq(s(X),z),elemNat(s(X),X_44)),
    inference(subst,[],[axiom_012:[bind(X,$fot(s(X))),bind(Xs,$fot(X_44)),bind(Z,$fot(z))]]) ).

cnf(refute_0_36,plain,
    ( elemNat(s(X),cons(z,X_44)) != orb(eq(s(X),z),elemNat(s(X),X_44))
    | eq(s(X),z) != bfalse
    | elemNat(s(X),cons(z,X_44)) = orb(bfalse,elemNat(s(X),X_44)) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(s(X),cons(z,X_44)),orb(eq(s(X),z),elemNat(s(X),X_44))) ),[1,0],$fot(bfalse)]]) ).

cnf(refute_0_37,plain,
    ( elemNat(s(X),cons(z,X_44)) != orb(eq(s(X),z),elemNat(s(X),X_44))
    | elemNat(s(X),cons(z,X_44)) = orb(bfalse,elemNat(s(X),X_44)) ),
    inference(resolve,[$cnf( $equal(eq(s(X),z),bfalse) )],[axiom_029,refute_0_36]) ).

cnf(refute_0_38,plain,
    elemNat(s(X),cons(z,X_44)) = orb(bfalse,elemNat(s(X),X_44)),
    inference(resolve,[$cnf( $equal(elemNat(s(X),cons(z,X_44)),orb(eq(s(X),z),elemNat(s(X),X_44))) )],[refute_0_35,refute_0_37]) ).

cnf(refute_0_39,plain,
    orb(bfalse,elemNat(s(X),X_44)) = elemNat(s(X),X_44),
    inference(subst,[],[axiom_003:[bind(Q,$fot(elemNat(s(X),X_44)))]]) ).

cnf(refute_0_40,plain,
    ( elemNat(s(X),cons(z,X_44)) != orb(bfalse,elemNat(s(X),X_44))
    | orb(bfalse,elemNat(s(X),X_44)) != elemNat(s(X),X_44)
    | elemNat(s(X),cons(z,X_44)) = elemNat(s(X),X_44) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(elemNat(s(X),cons(z,X_44)),elemNat(s(X),X_44)) ),[0],$fot(orb(bfalse,elemNat(s(X),X_44)))]]) ).

cnf(refute_0_41,plain,
    ( elemNat(s(X),cons(z,X_44)) != orb(bfalse,elemNat(s(X),X_44))
    | elemNat(s(X),cons(z,X_44)) = elemNat(s(X),X_44) ),
    inference(resolve,[$cnf( $equal(orb(bfalse,elemNat(s(X),X_44)),elemNat(s(X),X_44)) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    elemNat(s(X),cons(z,X_44)) = elemNat(s(X),X_44),
    inference(resolve,[$cnf( $equal(elemNat(s(X),cons(z,X_44)),orb(bfalse,elemNat(s(X),X_44))) )],[refute_0_38,refute_0_41]) ).

cnf(refute_0_43,plain,
    elemNat(s(X_56),cons(z,X_57)) = elemNat(s(X_56),X_57),
    inference(subst,[],[refute_0_42:[bind(X,$fot(X_56)),bind(X_44,$fot(X_57))]]) ).

cnf(refute_0_44,plain,
    ( elemNat(s(X_56),cons(Z,cons(z,X_57))) != orb(eq(s(X_56),Z),elemNat(s(X_56),cons(z,X_57)))
    | elemNat(s(X_56),cons(z,X_57)) != elemNat(s(X_56),X_57)
    | elemNat(s(X_56),cons(Z,cons(z,X_57))) = orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(s(X_56),cons(Z,cons(z,X_57))),orb(eq(s(X_56),Z),elemNat(s(X_56),cons(z,X_57)))) ),[1,1],$fot(elemNat(s(X_56),X_57))]]) ).

cnf(refute_0_45,plain,
    ( elemNat(s(X_56),cons(Z,cons(z,X_57))) != orb(eq(s(X_56),Z),elemNat(s(X_56),cons(z,X_57)))
    | elemNat(s(X_56),cons(Z,cons(z,X_57))) = orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)) ),
    inference(resolve,[$cnf( $equal(elemNat(s(X_56),cons(z,X_57)),elemNat(s(X_56),X_57)) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    elemNat(s(X_56),cons(Z,cons(z,X_57))) = orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)),
    inference(resolve,[$cnf( $equal(elemNat(s(X_56),cons(Z,cons(z,X_57))),orb(eq(s(X_56),Z),elemNat(s(X_56),cons(z,X_57)))) )],[refute_0_34,refute_0_45]) ).

cnf(refute_0_47,plain,
    orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)) = elemNat(s(X_56),cons(Z,X_57)),
    inference(subst,[],[refute_0_24:[bind(X,$fot(s(X_56))),bind(Xs,$fot(X_57))]]) ).

cnf(refute_0_48,plain,
    ( elemNat(s(X_56),cons(Z,cons(z,X_57))) != orb(eq(s(X_56),Z),elemNat(s(X_56),X_57))
    | orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)) != elemNat(s(X_56),cons(Z,X_57))
    | elemNat(s(X_56),cons(Z,cons(z,X_57))) = elemNat(s(X_56),cons(Z,X_57)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(elemNat(s(X_56),cons(Z,cons(z,X_57))),elemNat(s(X_56),cons(Z,X_57))) ),[0],$fot(orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)))]]) ).

cnf(refute_0_49,plain,
    ( elemNat(s(X_56),cons(Z,cons(z,X_57))) != orb(eq(s(X_56),Z),elemNat(s(X_56),X_57))
    | elemNat(s(X_56),cons(Z,cons(z,X_57))) = elemNat(s(X_56),cons(Z,X_57)) ),
    inference(resolve,[$cnf( $equal(orb(eq(s(X_56),Z),elemNat(s(X_56),X_57)),elemNat(s(X_56),cons(Z,X_57))) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    elemNat(s(X_56),cons(Z,cons(z,X_57))) = elemNat(s(X_56),cons(Z,X_57)),
    inference(resolve,[$cnf( $equal(elemNat(s(X_56),cons(Z,cons(z,X_57))),orb(eq(s(X_56),Z),elemNat(s(X_56),X_57))) )],[refute_0_46,refute_0_49]) ).

cnf(refute_0_51,plain,
    elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))) = elemNat(s(s(X_1038)),cons(X_1037,X_57)),
    inference(subst,[],[refute_0_50:[bind(Z,$fot(X_1037)),bind(X_56,$fot(s(X_1038)))]]) ).

cnf(refute_0_52,plain,
    ( elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))) != elemNat(s(s(X_1038)),cons(X_1037,X_57))
    | unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))) != aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))))
    | unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))) = aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,X_57))) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))),aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))))) ),[1,2],$fot(elemNat(s(s(X_1038)),cons(X_1037,X_57)))]]) ).

cnf(refute_0_53,plain,
    ( unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))) != aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))))
    | unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))) = aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,X_57))) ),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,X_57))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))) = aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,X_57))),
    inference(resolve,[$cnf( $equal(unique(cons(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))))),aux(s(s(X_1038)),cons(X_1037,cons(s(z),cons(z,X_57))),elemNat(s(s(X_1038)),cons(X_1037,cons(z,X_57))))) )],[refute_0_33,refute_0_53]) ).

cnf(refute_0_55,plain,
    unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))) = aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(s(X_3133)),cons(s(Y),nil))),
    inference(subst,[],[refute_0_54:[bind(X_1037,$fot(s(Y))),bind(X_1038,$fot(X_3133)),bind(X_57,$fot(nil))]]) ).

cnf(refute_0_56,plain,
    elemNat(X_43,cons(X_45,nil)) = orb(eq(X_43,X_45),elemNat(X_43,nil)),
    inference(subst,[],[axiom_012:[bind(X,$fot(X_43)),bind(Xs,$fot(nil)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_57,plain,
    elemNat(X_43,nil) = bfalse,
    inference(subst,[],[axiom_011:[bind(X,$fot(X_43))]]) ).

cnf(refute_0_58,plain,
    ( elemNat(X_43,cons(X_45,nil)) != orb(eq(X_43,X_45),elemNat(X_43,nil))
    | elemNat(X_43,nil) != bfalse
    | elemNat(X_43,cons(X_45,nil)) = orb(eq(X_43,X_45),bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(X_43,cons(X_45,nil)),orb(eq(X_43,X_45),elemNat(X_43,nil))) ),[1,1],$fot(bfalse)]]) ).

cnf(refute_0_59,plain,
    ( elemNat(X_43,cons(X_45,nil)) != orb(eq(X_43,X_45),elemNat(X_43,nil))
    | elemNat(X_43,cons(X_45,nil)) = orb(eq(X_43,X_45),bfalse) ),
    inference(resolve,[$cnf( $equal(elemNat(X_43,nil),bfalse) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    elemNat(X_43,cons(X_45,nil)) = orb(eq(X_43,X_45),bfalse),
    inference(resolve,[$cnf( $equal(elemNat(X_43,cons(X_45,nil)),orb(eq(X_43,X_45),elemNat(X_43,nil))) )],[refute_0_56,refute_0_59]) ).

cnf(refute_0_61,plain,
    elemNat(s(X),cons(s(Y),nil)) = orb(eq(s(X),s(Y)),bfalse),
    inference(subst,[],[refute_0_60:[bind(X_43,$fot(s(X))),bind(X_45,$fot(s(Y)))]]) ).

cnf(refute_0_62,plain,
    ( elemNat(s(X),cons(s(Y),nil)) != orb(eq(s(X),s(Y)),bfalse)
    | eq(s(X),s(Y)) != eq(X,Y)
    | elemNat(s(X),cons(s(Y),nil)) = orb(eq(X,Y),bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(elemNat(s(X),cons(s(Y),nil)),orb(eq(s(X),s(Y)),bfalse)) ),[1,0],$fot(eq(X,Y))]]) ).

cnf(refute_0_63,plain,
    ( elemNat(s(X),cons(s(Y),nil)) != orb(eq(s(X),s(Y)),bfalse)
    | elemNat(s(X),cons(s(Y),nil)) = orb(eq(X,Y),bfalse) ),
    inference(resolve,[$cnf( $equal(eq(s(X),s(Y)),eq(X,Y)) )],[axiom_027,refute_0_62]) ).

cnf(refute_0_64,plain,
    elemNat(s(X),cons(s(Y),nil)) = orb(eq(X,Y),bfalse),
    inference(resolve,[$cnf( $equal(elemNat(s(X),cons(s(Y),nil)),orb(eq(s(X),s(Y)),bfalse)) )],[refute_0_61,refute_0_63]) ).

cnf(refute_0_65,plain,
    ( elemNat(X_43,cons(X_45,nil)) != orb(eq(X_43,X_45),bfalse)
    | orb(eq(X_43,X_45),bfalse) = elemNat(X_43,cons(X_45,nil)) ),
    inference(subst,[],[refute_0_22:[bind(X0,$fot(elemNat(X_43,cons(X_45,nil)))),bind(Y0,$fot(orb(eq(X_43,X_45),bfalse)))]]) ).

cnf(refute_0_66,plain,
    orb(eq(X_43,X_45),bfalse) = elemNat(X_43,cons(X_45,nil)),
    inference(resolve,[$cnf( $equal(elemNat(X_43,cons(X_45,nil)),orb(eq(X_43,X_45),bfalse)) )],[refute_0_60,refute_0_65]) ).

cnf(refute_0_67,plain,
    orb(eq(X,Y),bfalse) = elemNat(X,cons(Y,nil)),
    inference(subst,[],[refute_0_66:[bind(X_43,$fot(X)),bind(X_45,$fot(Y))]]) ).

cnf(refute_0_68,plain,
    ( elemNat(s(X),cons(s(Y),nil)) != orb(eq(X,Y),bfalse)
    | orb(eq(X,Y),bfalse) != elemNat(X,cons(Y,nil))
    | elemNat(s(X),cons(s(Y),nil)) = elemNat(X,cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(elemNat(s(X),cons(s(Y),nil)),elemNat(X,cons(Y,nil))) ),[0],$fot(orb(eq(X,Y),bfalse))]]) ).

cnf(refute_0_69,plain,
    ( elemNat(s(X),cons(s(Y),nil)) != orb(eq(X,Y),bfalse)
    | elemNat(s(X),cons(s(Y),nil)) = elemNat(X,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(orb(eq(X,Y),bfalse),elemNat(X,cons(Y,nil))) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    elemNat(s(X),cons(s(Y),nil)) = elemNat(X,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(elemNat(s(X),cons(s(Y),nil)),orb(eq(X,Y),bfalse)) )],[refute_0_64,refute_0_69]) ).

cnf(refute_0_71,plain,
    elemNat(s(s(X_3133)),cons(s(Y),nil)) = elemNat(s(X_3133),cons(Y,nil)),
    inference(subst,[],[refute_0_70:[bind(X,$fot(s(X_3133)))]]) ).

cnf(refute_0_72,plain,
    ( elemNat(s(s(X_3133)),cons(s(Y),nil)) != elemNat(s(X_3133),cons(Y,nil))
    | unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))) != aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(s(X_3133)),cons(s(Y),nil)))
    | unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))) = aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(X_3133),cons(Y,nil))) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))),aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(s(X_3133)),cons(s(Y),nil)))) ),[1,2],$fot(elemNat(s(X_3133),cons(Y,nil)))]]) ).

cnf(refute_0_73,plain,
    ( unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))) != aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(s(X_3133)),cons(s(Y),nil)))
    | unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))) = aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(X_3133),cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X_3133)),cons(s(Y),nil)),elemNat(s(X_3133),cons(Y,nil))) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))) = aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(X_3133),cons(Y,nil))),
    inference(resolve,[$cnf( $equal(unique(cons(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))))),aux(s(s(X_3133)),cons(s(Y),cons(s(z),cons(z,nil))),elemNat(s(s(X_3133)),cons(s(Y),nil)))) )],[refute_0_55,refute_0_73]) ).

cnf(refute_0_75,plain,
    unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),cons(s(z),nil))),
    inference(subst,[],[refute_0_74:[bind(Y,$fot(s(z))),bind(X_3133,$fot(s(X)))]]) ).

cnf(refute_0_76,plain,
    elemNat(s(s(X)),cons(s(z),nil)) = elemNat(s(s(X)),nil),
    inference(subst,[],[refute_0_15:[bind(X_105,$fot(nil))]]) ).

cnf(refute_0_77,plain,
    ( elemNat(s(s(X)),cons(s(z),nil)) != elemNat(s(s(X)),nil)
    | unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),cons(s(z),nil)))
    | unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),cons(s(z),nil)))) ),[1,2],$fot(elemNat(s(s(X)),nil))]]) ).

cnf(refute_0_78,plain,
    ( unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),cons(s(z),nil)))
    | unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) ),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X)),cons(s(z),nil)),elemNat(s(s(X)),nil)) )],[refute_0_76,refute_0_77]) ).

cnf(refute_0_79,plain,
    unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)),
    inference(resolve,[$cnf( $equal(unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),cons(s(z),nil)))) )],[refute_0_75,refute_0_78]) ).

cnf(refute_0_80,plain,
    unique(cons(s(X_131),cons(X_130,cons(z,X_132)))) = aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,cons(z,X_132)))),
    inference(subst,[],[axiom_014:[bind(Xs,$fot(cons(X_130,cons(z,X_132)))),bind(Y,$fot(s(X_131)))]]) ).

cnf(refute_0_81,plain,
    elemNat(s(X_131),cons(X_130,cons(z,X_132))) = elemNat(s(X_131),cons(X_130,X_132)),
    inference(subst,[],[refute_0_50:[bind(Z,$fot(X_130)),bind(X_56,$fot(X_131)),bind(X_57,$fot(X_132))]]) ).

cnf(refute_0_82,plain,
    ( elemNat(s(X_131),cons(X_130,cons(z,X_132))) != elemNat(s(X_131),cons(X_130,X_132))
    | unique(cons(s(X_131),cons(X_130,cons(z,X_132)))) != aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,cons(z,X_132))))
    | unique(cons(s(X_131),cons(X_130,cons(z,X_132)))) = aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(X_131),cons(X_130,cons(z,X_132)))),aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,cons(z,X_132))))) ),[1,2],$fot(elemNat(s(X_131),cons(X_130,X_132)))]]) ).

cnf(refute_0_83,plain,
    ( unique(cons(s(X_131),cons(X_130,cons(z,X_132)))) != aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,cons(z,X_132))))
    | unique(cons(s(X_131),cons(X_130,cons(z,X_132)))) = aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,X_132))) ),
    inference(resolve,[$cnf( $equal(elemNat(s(X_131),cons(X_130,cons(z,X_132))),elemNat(s(X_131),cons(X_130,X_132))) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    unique(cons(s(X_131),cons(X_130,cons(z,X_132)))) = aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,X_132))),
    inference(resolve,[$cnf( $equal(unique(cons(s(X_131),cons(X_130,cons(z,X_132)))),aux(s(X_131),cons(X_130,cons(z,X_132)),elemNat(s(X_131),cons(X_130,cons(z,X_132))))) )],[refute_0_80,refute_0_83]) ).

cnf(refute_0_85,plain,
    unique(cons(s(X_276),cons(s(Y),cons(z,nil)))) = aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(s(X_276),cons(s(Y),nil))),
    inference(subst,[],[refute_0_84:[bind(X_130,$fot(s(Y))),bind(X_131,$fot(X_276)),bind(X_132,$fot(nil))]]) ).

cnf(refute_0_86,plain,
    elemNat(s(X_276),cons(s(Y),nil)) = elemNat(X_276,cons(Y,nil)),
    inference(subst,[],[refute_0_70:[bind(X,$fot(X_276))]]) ).

cnf(refute_0_87,plain,
    ( elemNat(s(X_276),cons(s(Y),nil)) != elemNat(X_276,cons(Y,nil))
    | unique(cons(s(X_276),cons(s(Y),cons(z,nil)))) != aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(s(X_276),cons(s(Y),nil)))
    | unique(cons(s(X_276),cons(s(Y),cons(z,nil)))) = aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(X_276,cons(Y,nil))) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(X_276),cons(s(Y),cons(z,nil)))),aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(s(X_276),cons(s(Y),nil)))) ),[1,2],$fot(elemNat(X_276,cons(Y,nil)))]]) ).

cnf(refute_0_88,plain,
    ( unique(cons(s(X_276),cons(s(Y),cons(z,nil)))) != aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(s(X_276),cons(s(Y),nil)))
    | unique(cons(s(X_276),cons(s(Y),cons(z,nil)))) = aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(X_276,cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(elemNat(s(X_276),cons(s(Y),nil)),elemNat(X_276,cons(Y,nil))) )],[refute_0_86,refute_0_87]) ).

cnf(refute_0_89,plain,
    unique(cons(s(X_276),cons(s(Y),cons(z,nil)))) = aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(X_276,cons(Y,nil))),
    inference(resolve,[$cnf( $equal(unique(cons(s(X_276),cons(s(Y),cons(z,nil)))),aux(s(X_276),cons(s(Y),cons(z,nil)),elemNat(s(X_276),cons(s(Y),nil)))) )],[refute_0_85,refute_0_88]) ).

cnf(refute_0_90,plain,
    unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),cons(z,nil))),
    inference(subst,[],[refute_0_89:[bind(Y,$fot(z)),bind(X_276,$fot(s(X)))]]) ).

cnf(refute_0_91,plain,
    elemNat(s(X),cons(z,nil)) = elemNat(s(X),nil),
    inference(subst,[],[refute_0_42:[bind(X_44,$fot(nil))]]) ).

cnf(refute_0_92,plain,
    ( elemNat(s(X),cons(z,nil)) != elemNat(s(X),nil)
    | unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) != aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),cons(z,nil)))
    | unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(X)),cons(s(z),cons(z,nil)))),aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),cons(z,nil)))) ),[1,2],$fot(elemNat(s(X),nil))]]) ).

cnf(refute_0_93,plain,
    ( unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) != aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),cons(z,nil)))
    | unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) ),
    inference(resolve,[$cnf( $equal(elemNat(s(X),cons(z,nil)),elemNat(s(X),nil)) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)),
    inference(resolve,[$cnf( $equal(unique(cons(s(s(X)),cons(s(z),cons(z,nil)))),aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),cons(z,nil)))) )],[refute_0_90,refute_0_93]) ).

cnf(refute_0_95,plain,
    unique(cons(s(X_56),cons(z,X_57))) = aux(s(X_56),cons(z,X_57),elemNat(s(X_56),cons(z,X_57))),
    inference(subst,[],[axiom_014:[bind(Xs,$fot(cons(z,X_57))),bind(Y,$fot(s(X_56)))]]) ).

cnf(refute_0_96,plain,
    ( elemNat(s(X_56),cons(z,X_57)) != elemNat(s(X_56),X_57)
    | unique(cons(s(X_56),cons(z,X_57))) != aux(s(X_56),cons(z,X_57),elemNat(s(X_56),cons(z,X_57)))
    | unique(cons(s(X_56),cons(z,X_57))) = aux(s(X_56),cons(z,X_57),elemNat(s(X_56),X_57)) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(X_56),cons(z,X_57))),aux(s(X_56),cons(z,X_57),elemNat(s(X_56),cons(z,X_57)))) ),[1,2],$fot(elemNat(s(X_56),X_57))]]) ).

cnf(refute_0_97,plain,
    ( unique(cons(s(X_56),cons(z,X_57))) != aux(s(X_56),cons(z,X_57),elemNat(s(X_56),cons(z,X_57)))
    | unique(cons(s(X_56),cons(z,X_57))) = aux(s(X_56),cons(z,X_57),elemNat(s(X_56),X_57)) ),
    inference(resolve,[$cnf( $equal(elemNat(s(X_56),cons(z,X_57)),elemNat(s(X_56),X_57)) )],[refute_0_43,refute_0_96]) ).

cnf(refute_0_98,plain,
    unique(cons(s(X_56),cons(z,X_57))) = aux(s(X_56),cons(z,X_57),elemNat(s(X_56),X_57)),
    inference(resolve,[$cnf( $equal(unique(cons(s(X_56),cons(z,X_57))),aux(s(X_56),cons(z,X_57),elemNat(s(X_56),cons(z,X_57)))) )],[refute_0_95,refute_0_97]) ).

cnf(refute_0_99,plain,
    unique(cons(s(X_67),cons(z,nil))) = aux(s(X_67),cons(z,nil),elemNat(s(X_67),nil)),
    inference(subst,[],[refute_0_98:[bind(X_56,$fot(X_67)),bind(X_57,$fot(nil))]]) ).

cnf(refute_0_100,plain,
    elemNat(s(X_67),nil) = bfalse,
    inference(subst,[],[axiom_011:[bind(X,$fot(s(X_67)))]]) ).

cnf(refute_0_101,plain,
    ( elemNat(s(X_67),nil) != bfalse
    | unique(cons(s(X_67),cons(z,nil))) != aux(s(X_67),cons(z,nil),elemNat(s(X_67),nil))
    | unique(cons(s(X_67),cons(z,nil))) = aux(s(X_67),cons(z,nil),bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(X_67),cons(z,nil))),aux(s(X_67),cons(z,nil),elemNat(s(X_67),nil))) ),[1,2],$fot(bfalse)]]) ).

cnf(refute_0_102,plain,
    ( unique(cons(s(X_67),cons(z,nil))) != aux(s(X_67),cons(z,nil),elemNat(s(X_67),nil))
    | unique(cons(s(X_67),cons(z,nil))) = aux(s(X_67),cons(z,nil),bfalse) ),
    inference(resolve,[$cnf( $equal(elemNat(s(X_67),nil),bfalse) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    unique(cons(s(X_67),cons(z,nil))) = aux(s(X_67),cons(z,nil),bfalse),
    inference(resolve,[$cnf( $equal(unique(cons(s(X_67),cons(z,nil))),aux(s(X_67),cons(z,nil),elemNat(s(X_67),nil))) )],[refute_0_99,refute_0_102]) ).

cnf(refute_0_104,plain,
    unique(cons(X_37,nil)) = aux(X_37,nil,elemNat(X_37,nil)),
    inference(subst,[],[axiom_014:[bind(Xs,$fot(nil)),bind(Y,$fot(X_37))]]) ).

cnf(refute_0_105,plain,
    elemNat(X_37,nil) = bfalse,
    inference(subst,[],[axiom_011:[bind(X,$fot(X_37))]]) ).

cnf(refute_0_106,plain,
    ( elemNat(X_37,nil) != bfalse
    | unique(cons(X_37,nil)) != aux(X_37,nil,elemNat(X_37,nil))
    | unique(cons(X_37,nil)) = aux(X_37,nil,bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(X_37,nil)),aux(X_37,nil,elemNat(X_37,nil))) ),[1,2],$fot(bfalse)]]) ).

cnf(refute_0_107,plain,
    ( unique(cons(X_37,nil)) != aux(X_37,nil,elemNat(X_37,nil))
    | unique(cons(X_37,nil)) = aux(X_37,nil,bfalse) ),
    inference(resolve,[$cnf( $equal(elemNat(X_37,nil),bfalse) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    unique(cons(X_37,nil)) = aux(X_37,nil,bfalse),
    inference(resolve,[$cnf( $equal(unique(cons(X_37,nil)),aux(X_37,nil,elemNat(X_37,nil))) )],[refute_0_104,refute_0_107]) ).

cnf(refute_0_109,plain,
    aux(X_37,nil,bfalse) = unique(nil),
    inference(subst,[],[axiom_001:[bind(Xs,$fot(nil)),bind(Y,$fot(X_37))]]) ).

cnf(refute_0_110,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_111,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_22,refute_0_110]) ).

cnf(refute_0_112,plain,
    ( aux(X_37,nil,bfalse) != unique(nil)
    | unique(nil) != btrue
    | aux(X_37,nil,bfalse) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(aux(X_37,nil,bfalse))),bind(Y0,$fot(unique(nil))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_113,plain,
    ( unique(nil) != btrue
    | aux(X_37,nil,bfalse) = btrue ),
    inference(resolve,[$cnf( $equal(aux(X_37,nil,bfalse),unique(nil)) )],[refute_0_109,refute_0_112]) ).

cnf(refute_0_114,plain,
    aux(X_37,nil,bfalse) = btrue,
    inference(resolve,[$cnf( $equal(unique(nil),btrue) )],[axiom_013,refute_0_113]) ).

cnf(refute_0_115,plain,
    ( aux(X_37,nil,bfalse) != btrue
    | unique(cons(X_37,nil)) != aux(X_37,nil,bfalse)
    | unique(cons(X_37,nil)) = btrue ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(X_37,nil)),aux(X_37,nil,bfalse)) ),[1],$fot(btrue)]]) ).

cnf(refute_0_116,plain,
    ( unique(cons(X_37,nil)) != aux(X_37,nil,bfalse)
    | unique(cons(X_37,nil)) = btrue ),
    inference(resolve,[$cnf( $equal(aux(X_37,nil,bfalse),btrue) )],[refute_0_114,refute_0_115]) ).

cnf(refute_0_117,plain,
    unique(cons(X_37,nil)) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(X_37,nil)),aux(X_37,nil,bfalse)) )],[refute_0_108,refute_0_116]) ).

cnf(refute_0_118,plain,
    unique(cons(z,nil)) = btrue,
    inference(subst,[],[refute_0_117:[bind(X_37,$fot(z))]]) ).

cnf(refute_0_119,plain,
    aux(s(X_67),cons(z,nil),bfalse) = unique(cons(z,nil)),
    inference(subst,[],[axiom_001:[bind(Xs,$fot(cons(z,nil))),bind(Y,$fot(s(X_67)))]]) ).

cnf(refute_0_120,plain,
    ( aux(s(X_67),cons(z,nil),bfalse) != unique(cons(z,nil))
    | unique(cons(z,nil)) != btrue
    | aux(s(X_67),cons(z,nil),bfalse) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(aux(s(X_67),cons(z,nil),bfalse))),bind(Y0,$fot(unique(cons(z,nil)))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_121,plain,
    ( unique(cons(z,nil)) != btrue
    | aux(s(X_67),cons(z,nil),bfalse) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(X_67),cons(z,nil),bfalse),unique(cons(z,nil))) )],[refute_0_119,refute_0_120]) ).

cnf(refute_0_122,plain,
    aux(s(X_67),cons(z,nil),bfalse) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(z,nil)),btrue) )],[refute_0_118,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( aux(s(X_67),cons(z,nil),bfalse) != btrue
    | unique(cons(s(X_67),cons(z,nil))) != aux(s(X_67),cons(z,nil),bfalse)
    | unique(cons(s(X_67),cons(z,nil))) = btrue ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(X_67),cons(z,nil))),aux(s(X_67),cons(z,nil),bfalse)) ),[1],$fot(btrue)]]) ).

cnf(refute_0_124,plain,
    ( unique(cons(s(X_67),cons(z,nil))) != aux(s(X_67),cons(z,nil),bfalse)
    | unique(cons(s(X_67),cons(z,nil))) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(X_67),cons(z,nil),bfalse),btrue) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    unique(cons(s(X_67),cons(z,nil))) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(s(X_67),cons(z,nil))),aux(s(X_67),cons(z,nil),bfalse)) )],[refute_0_103,refute_0_124]) ).

cnf(refute_0_126,plain,
    unique(cons(s(z),cons(z,nil))) = btrue,
    inference(subst,[],[refute_0_125:[bind(X_67,$fot(z))]]) ).

cnf(refute_0_127,plain,
    aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) = unique(cons(s(z),cons(z,nil))),
    inference(subst,[],[axiom_001:[bind(Xs,$fot(cons(s(z),cons(z,nil)))),bind(Y,$fot(s(s(X))))]]) ).

cnf(refute_0_128,plain,
    ( aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) != unique(cons(s(z),cons(z,nil)))
    | unique(cons(s(z),cons(z,nil))) != btrue
    | aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse))),bind(Y0,$fot(unique(cons(s(z),cons(z,nil))))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_129,plain,
    ( unique(cons(s(z),cons(z,nil))) != btrue
    | aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse),unique(cons(s(z),cons(z,nil)))) )],[refute_0_127,refute_0_128]) ).

cnf(refute_0_130,plain,
    aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(s(z),cons(z,nil))),btrue) )],[refute_0_126,refute_0_129]) ).

cnf(refute_0_131,plain,
    elemNat(s(X),nil) = bfalse,
    inference(subst,[],[axiom_011:[bind(X,$fot(s(X)))]]) ).

cnf(refute_0_132,plain,
    aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)),
    introduced(tautology,[refl,[$fot(aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)))]]) ).

cnf(refute_0_133,plain,
    ( aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) != aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))
    | elemNat(s(X),nil) != bfalse
    | aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)),aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))) ),[1,2],$fot(bfalse)]]) ).

cnf(refute_0_134,plain,
    ( elemNat(s(X),nil) != bfalse
    | aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) ),
    inference(resolve,[$cnf( $equal(aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)),aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))) )],[refute_0_132,refute_0_133]) ).

cnf(refute_0_135,plain,
    aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse),
    inference(resolve,[$cnf( $equal(elemNat(s(X),nil),bfalse) )],[refute_0_131,refute_0_134]) ).

cnf(refute_0_136,plain,
    ( aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) != btrue
    | aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) != aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse)
    | aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)))),bind(Y0,$fot(aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_137,plain,
    ( aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse) != btrue
    | aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)),aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse)) )],[refute_0_135,refute_0_136]) ).

cnf(refute_0_138,plain,
    aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) = btrue,
    inference(resolve,[$cnf( $equal(aux(s(s(X)),cons(s(z),cons(z,nil)),bfalse),btrue) )],[refute_0_130,refute_0_137]) ).

cnf(refute_0_139,plain,
    ( aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)) != btrue
    | unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) != aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))
    | unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = btrue ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(X)),cons(s(z),cons(z,nil)))),aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))) ),[1],$fot(btrue)]]) ).

cnf(refute_0_140,plain,
    ( unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) != aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))
    | unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil)),btrue) )],[refute_0_138,refute_0_139]) ).

cnf(refute_0_141,plain,
    unique(cons(s(s(X)),cons(s(z),cons(z,nil)))) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(s(s(X)),cons(s(z),cons(z,nil)))),aux(s(s(X)),cons(s(z),cons(z,nil)),elemNat(s(X),nil))) )],[refute_0_94,refute_0_140]) ).

cnf(refute_0_142,plain,
    unique(cons(s(s(z)),cons(s(z),cons(z,nil)))) = btrue,
    inference(subst,[],[refute_0_141:[bind(X,$fot(z))]]) ).

cnf(refute_0_143,plain,
    aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) = unique(cons(s(s(z)),cons(s(z),cons(z,nil)))),
    inference(subst,[],[axiom_001:[bind(Xs,$fot(cons(s(s(z)),cons(s(z),cons(z,nil))))),bind(Y,$fot(s(s(s(X)))))]]) ).

cnf(refute_0_144,plain,
    ( aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) != unique(cons(s(s(z)),cons(s(z),cons(z,nil))))
    | unique(cons(s(s(z)),cons(s(z),cons(z,nil)))) != btrue
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse))),bind(Y0,$fot(unique(cons(s(s(z)),cons(s(z),cons(z,nil)))))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_145,plain,
    ( unique(cons(s(s(z)),cons(s(z),cons(z,nil)))) != btrue
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse),unique(cons(s(s(z)),cons(s(z),cons(z,nil))))) )],[refute_0_143,refute_0_144]) ).

cnf(refute_0_146,plain,
    aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(s(s(z)),cons(s(z),cons(z,nil)))),btrue) )],[refute_0_142,refute_0_145]) ).

cnf(refute_0_147,plain,
    elemNat(s(s(X)),nil) = bfalse,
    inference(subst,[],[axiom_011:[bind(X,$fot(s(s(X))))]]) ).

cnf(refute_0_148,plain,
    aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)),
    introduced(tautology,[refl,[$fot(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)))]]) ).

cnf(refute_0_149,plain,
    ( aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) != aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))
    | elemNat(s(s(X)),nil) != bfalse
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))) ),[1,2],$fot(bfalse)]]) ).

cnf(refute_0_150,plain,
    ( elemNat(s(s(X)),nil) != bfalse
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) ),
    inference(resolve,[$cnf( $equal(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse),
    inference(resolve,[$cnf( $equal(elemNat(s(s(X)),nil),bfalse) )],[refute_0_147,refute_0_150]) ).

cnf(refute_0_152,plain,
    ( aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) != btrue
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) != aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse)
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)))),bind(Y0,$fot(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_153,plain,
    ( aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) != btrue
    | aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse)) )],[refute_0_151,refute_0_152]) ).

cnf(refute_0_154,plain,
    aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) = btrue,
    inference(resolve,[$cnf( $equal(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse),btrue) )],[refute_0_146,refute_0_153]) ).

cnf(refute_0_155,plain,
    ( aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)) != btrue
    | unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))
    | unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = btrue ),
    introduced(tautology,[equality,[$cnf( $equal(unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))) ),[1],$fot(btrue)]]) ).

cnf(refute_0_156,plain,
    ( unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))
    | unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = btrue ),
    inference(resolve,[$cnf( $equal(aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil)),btrue) )],[refute_0_154,refute_0_155]) ).

cnf(refute_0_157,plain,
    unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = btrue,
    inference(resolve,[$cnf( $equal(unique(cons(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))))),aux(s(s(s(X))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(X)),nil))) )],[refute_0_79,refute_0_156]) ).

cnf(refute_0_158,plain,
    unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = btrue,
    inference(subst,[],[refute_0_157:[bind(X,$fot(X_3137))]]) ).

cnf(refute_0_159,plain,
    ( psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != btrue
    | psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) ),
    introduced(tautology,[equality,[$cnf( $equal(psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) ),[1,1,0,0],$fot(btrue)]]) ).

cnf(refute_0_160,plain,
    ( psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) ),
    inference(resolve,[$cnf( $equal(unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
    inference(resolve,[$cnf( $equal(psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) )],[refute_0_1,refute_0_160]) ).

cnf(refute_0_162,plain,
    impl(btrue,bfalse) = bfalse,
    inference(subst,[],[axiom_009:[bind(Q,$fot(bfalse))]]) ).

cnf(refute_0_163,plain,
    leqNat(s(z),z) = bfalse,
    inference(subst,[],[axiom_005:[bind(Z,$fot(z))]]) ).

cnf(refute_0_164,plain,
    leqNat(s(s(z)),s(z)) = leqNat(s(z),z),
    inference(subst,[],[axiom_006:[bind(M,$fot(z)),bind(Z,$fot(s(z)))]]) ).

cnf(refute_0_165,plain,
    ( leqNat(s(s(z)),s(z)) != leqNat(s(z),z)
    | leqNat(s(z),z) != bfalse
    | leqNat(s(s(z)),s(z)) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(leqNat(s(s(z)),s(z)))),bind(Y0,$fot(leqNat(s(z),z))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_166,plain,
    ( leqNat(s(z),z) != bfalse
    | leqNat(s(s(z)),s(z)) = bfalse ),
    inference(resolve,[$cnf( $equal(leqNat(s(s(z)),s(z)),leqNat(s(z),z)) )],[refute_0_164,refute_0_165]) ).

cnf(refute_0_167,plain,
    leqNat(s(s(z)),s(z)) = bfalse,
    inference(resolve,[$cnf( $equal(leqNat(s(z),z),bfalse) )],[refute_0_163,refute_0_166]) ).

cnf(refute_0_168,plain,
    leqNat(s(s(s(z))),s(s(z))) = leqNat(s(s(z)),s(z)),
    inference(subst,[],[axiom_006:[bind(M,$fot(s(z))),bind(Z,$fot(s(s(z))))]]) ).

cnf(refute_0_169,plain,
    ( leqNat(s(s(s(z))),s(s(z))) != leqNat(s(s(z)),s(z))
    | leqNat(s(s(z)),s(z)) != bfalse
    | leqNat(s(s(s(z))),s(s(z))) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(leqNat(s(s(s(z))),s(s(z))))),bind(Y0,$fot(leqNat(s(s(z)),s(z)))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_170,plain,
    ( leqNat(s(s(z)),s(z)) != bfalse
    | leqNat(s(s(s(z))),s(s(z))) = bfalse ),
    inference(resolve,[$cnf( $equal(leqNat(s(s(s(z))),s(s(z))),leqNat(s(s(z)),s(z))) )],[refute_0_168,refute_0_169]) ).

cnf(refute_0_171,plain,
    leqNat(s(s(s(z))),s(s(z))) = bfalse,
    inference(resolve,[$cnf( $equal(leqNat(s(s(z)),s(z)),bfalse) )],[refute_0_167,refute_0_170]) ).

cnf(refute_0_172,plain,
    leqNat(s(s(s(s(z)))),s(s(s(z)))) = leqNat(s(s(s(z))),s(s(z))),
    inference(subst,[],[axiom_006:[bind(M,$fot(s(s(z)))),bind(Z,$fot(s(s(s(z)))))]]) ).

cnf(refute_0_173,plain,
    ( leqNat(s(s(s(s(z)))),s(s(s(z)))) != leqNat(s(s(s(z))),s(s(z)))
    | leqNat(s(s(s(z))),s(s(z))) != bfalse
    | leqNat(s(s(s(s(z)))),s(s(s(z)))) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(leqNat(s(s(s(s(z)))),s(s(s(z)))))),bind(Y0,$fot(leqNat(s(s(s(z))),s(s(z))))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_174,plain,
    ( leqNat(s(s(s(z))),s(s(z))) != bfalse
    | leqNat(s(s(s(s(z)))),s(s(s(z)))) = bfalse ),
    inference(resolve,[$cnf( $equal(leqNat(s(s(s(s(z)))),s(s(s(z)))),leqNat(s(s(s(z))),s(s(z)))) )],[refute_0_172,refute_0_173]) ).

cnf(refute_0_175,plain,
    leqNat(s(s(s(s(z)))),s(s(s(z)))) = bfalse,
    inference(resolve,[$cnf( $equal(leqNat(s(s(s(z))),s(s(z))),bfalse) )],[refute_0_171,refute_0_174]) ).

cnf(refute_0_176,plain,
    s(lengthNat(nil)) = s(lengthNat(nil)),
    introduced(tautology,[refl,[$fot(s(lengthNat(nil)))]]) ).

cnf(refute_0_177,plain,
    ( lengthNat(nil) != z
    | s(lengthNat(nil)) != s(lengthNat(nil))
    | s(lengthNat(nil)) = s(z) ),
    introduced(tautology,[equality,[$cnf( $equal(s(lengthNat(nil)),s(lengthNat(nil))) ),[1,0],$fot(z)]]) ).

cnf(refute_0_178,plain,
    ( lengthNat(nil) != z
    | s(lengthNat(nil)) = s(z) ),
    inference(resolve,[$cnf( $equal(s(lengthNat(nil)),s(lengthNat(nil))) )],[refute_0_176,refute_0_177]) ).

cnf(refute_0_179,plain,
    s(lengthNat(nil)) = s(z),
    inference(resolve,[$cnf( $equal(lengthNat(nil),z) )],[axiom_007,refute_0_178]) ).

cnf(refute_0_180,plain,
    lengthNat(cons(z,nil)) = s(lengthNat(nil)),
    inference(subst,[],[axiom_008:[bind(Xs,$fot(nil)),bind(Y,$fot(z))]]) ).

cnf(refute_0_181,plain,
    ( lengthNat(cons(z,nil)) != s(lengthNat(nil))
    | s(lengthNat(nil)) != s(z)
    | lengthNat(cons(z,nil)) = s(z) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(lengthNat(cons(z,nil)))),bind(Y0,$fot(s(lengthNat(nil)))),bind(Z0,$fot(s(z)))]]) ).

cnf(refute_0_182,plain,
    ( s(lengthNat(nil)) != s(z)
    | lengthNat(cons(z,nil)) = s(z) ),
    inference(resolve,[$cnf( $equal(lengthNat(cons(z,nil)),s(lengthNat(nil))) )],[refute_0_180,refute_0_181]) ).

cnf(refute_0_183,plain,
    lengthNat(cons(z,nil)) = s(z),
    inference(resolve,[$cnf( $equal(s(lengthNat(nil)),s(z)) )],[refute_0_179,refute_0_182]) ).

cnf(refute_0_184,plain,
    s(lengthNat(cons(z,nil))) = s(lengthNat(cons(z,nil))),
    introduced(tautology,[refl,[$fot(s(lengthNat(cons(z,nil))))]]) ).

cnf(refute_0_185,plain,
    ( lengthNat(cons(z,nil)) != s(z)
    | s(lengthNat(cons(z,nil))) != s(lengthNat(cons(z,nil)))
    | s(lengthNat(cons(z,nil))) = s(s(z)) ),
    introduced(tautology,[equality,[$cnf( $equal(s(lengthNat(cons(z,nil))),s(lengthNat(cons(z,nil)))) ),[1,0],$fot(s(z))]]) ).

cnf(refute_0_186,plain,
    ( lengthNat(cons(z,nil)) != s(z)
    | s(lengthNat(cons(z,nil))) = s(s(z)) ),
    inference(resolve,[$cnf( $equal(s(lengthNat(cons(z,nil))),s(lengthNat(cons(z,nil)))) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    s(lengthNat(cons(z,nil))) = s(s(z)),
    inference(resolve,[$cnf( $equal(lengthNat(cons(z,nil)),s(z)) )],[refute_0_183,refute_0_186]) ).

cnf(refute_0_188,plain,
    lengthNat(cons(s(z),cons(z,nil))) = s(lengthNat(cons(z,nil))),
    inference(subst,[],[axiom_008:[bind(Xs,$fot(cons(z,nil))),bind(Y,$fot(s(z)))]]) ).

cnf(refute_0_189,plain,
    ( lengthNat(cons(s(z),cons(z,nil))) != s(lengthNat(cons(z,nil)))
    | s(lengthNat(cons(z,nil))) != s(s(z))
    | lengthNat(cons(s(z),cons(z,nil))) = s(s(z)) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(lengthNat(cons(s(z),cons(z,nil))))),bind(Y0,$fot(s(lengthNat(cons(z,nil))))),bind(Z0,$fot(s(s(z))))]]) ).

cnf(refute_0_190,plain,
    ( s(lengthNat(cons(z,nil))) != s(s(z))
    | lengthNat(cons(s(z),cons(z,nil))) = s(s(z)) ),
    inference(resolve,[$cnf( $equal(lengthNat(cons(s(z),cons(z,nil))),s(lengthNat(cons(z,nil)))) )],[refute_0_188,refute_0_189]) ).

cnf(refute_0_191,plain,
    lengthNat(cons(s(z),cons(z,nil))) = s(s(z)),
    inference(resolve,[$cnf( $equal(s(lengthNat(cons(z,nil))),s(s(z))) )],[refute_0_187,refute_0_190]) ).

cnf(refute_0_192,plain,
    s(lengthNat(cons(s(z),cons(z,nil)))) = s(lengthNat(cons(s(z),cons(z,nil)))),
    introduced(tautology,[refl,[$fot(s(lengthNat(cons(s(z),cons(z,nil)))))]]) ).

cnf(refute_0_193,plain,
    ( lengthNat(cons(s(z),cons(z,nil))) != s(s(z))
    | s(lengthNat(cons(s(z),cons(z,nil)))) != s(lengthNat(cons(s(z),cons(z,nil))))
    | s(lengthNat(cons(s(z),cons(z,nil)))) = s(s(s(z))) ),
    introduced(tautology,[equality,[$cnf( $equal(s(lengthNat(cons(s(z),cons(z,nil)))),s(lengthNat(cons(s(z),cons(z,nil))))) ),[1,0],$fot(s(s(z)))]]) ).

cnf(refute_0_194,plain,
    ( lengthNat(cons(s(z),cons(z,nil))) != s(s(z))
    | s(lengthNat(cons(s(z),cons(z,nil)))) = s(s(s(z))) ),
    inference(resolve,[$cnf( $equal(s(lengthNat(cons(s(z),cons(z,nil)))),s(lengthNat(cons(s(z),cons(z,nil))))) )],[refute_0_192,refute_0_193]) ).

cnf(refute_0_195,plain,
    s(lengthNat(cons(s(z),cons(z,nil)))) = s(s(s(z))),
    inference(resolve,[$cnf( $equal(lengthNat(cons(s(z),cons(z,nil))),s(s(z))) )],[refute_0_191,refute_0_194]) ).

cnf(refute_0_196,plain,
    lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) = s(lengthNat(cons(s(z),cons(z,nil)))),
    inference(subst,[],[axiom_008:[bind(Xs,$fot(cons(s(z),cons(z,nil)))),bind(Y,$fot(s(s(z))))]]) ).

cnf(refute_0_197,plain,
    ( lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) != s(lengthNat(cons(s(z),cons(z,nil))))
    | s(lengthNat(cons(s(z),cons(z,nil)))) != s(s(s(z)))
    | lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) = s(s(s(z))) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))))),bind(Y0,$fot(s(lengthNat(cons(s(z),cons(z,nil)))))),bind(Z0,$fot(s(s(s(z)))))]]) ).

cnf(refute_0_198,plain,
    ( s(lengthNat(cons(s(z),cons(z,nil)))) != s(s(s(z)))
    | lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) = s(s(s(z))) ),
    inference(resolve,[$cnf( $equal(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(lengthNat(cons(s(z),cons(z,nil))))) )],[refute_0_196,refute_0_197]) ).

cnf(refute_0_199,plain,
    lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) = s(s(s(z))),
    inference(resolve,[$cnf( $equal(s(lengthNat(cons(s(z),cons(z,nil)))),s(s(s(z)))) )],[refute_0_195,refute_0_198]) ).

cnf(refute_0_200,plain,
    s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),
    introduced(tautology,[refl,[$fot(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))))]]) ).

cnf(refute_0_201,plain,
    ( lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) != s(s(s(z)))
    | s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) != s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))))
    | s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(s(s(s(z)))) ),
    introduced(tautology,[equality,[$cnf( $equal(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))))) ),[1,0],$fot(s(s(s(z))))]]) ).

cnf(refute_0_202,plain,
    ( lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) != s(s(s(z)))
    | s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(s(s(s(z)))) ),
    inference(resolve,[$cnf( $equal(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))))) )],[refute_0_200,refute_0_201]) ).

cnf(refute_0_203,plain,
    s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(s(s(s(z)))),
    inference(resolve,[$cnf( $equal(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(s(s(z)))) )],[refute_0_199,refute_0_202]) ).

cnf(refute_0_204,plain,
    lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),
    inference(subst,[],[axiom_008:[bind(Xs,$fot(cons(s(s(z)),cons(s(z),cons(z,nil))))),bind(Y,$fot(s(s(s(X_3137)))))]]) ).

cnf(refute_0_205,plain,
    ( lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))))
    | s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) != s(s(s(s(z))))
    | lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(s(s(s(z)))) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))))),bind(Y0,$fot(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))))),bind(Z0,$fot(s(s(s(s(z))))))]]) ).

cnf(refute_0_206,plain,
    ( s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))) != s(s(s(s(z))))
    | lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(s(s(s(z)))) ),
    inference(resolve,[$cnf( $equal(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))))) )],[refute_0_204,refute_0_205]) ).

cnf(refute_0_207,plain,
    lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(s(s(s(z)))),
    inference(resolve,[$cnf( $equal(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(s(z))))) )],[refute_0_203,refute_0_206]) ).

cnf(refute_0_208,plain,
    leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),
    introduced(tautology,[refl,[$fot(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))))]]) ).

cnf(refute_0_209,plain,
    ( lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != s(s(s(s(z))))
    | leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) != leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z))))
    | leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = leqNat(s(s(s(s(z)))),s(s(s(z)))) ),
    introduced(tautology,[equality,[$cnf( $equal(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z))))) ),[1,0],$fot(s(s(s(s(z)))))]]) ).

cnf(refute_0_210,plain,
    ( lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != s(s(s(s(z))))
    | leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = leqNat(s(s(s(s(z)))),s(s(s(z)))) ),
    inference(resolve,[$cnf( $equal(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z))))) )],[refute_0_208,refute_0_209]) ).

cnf(refute_0_211,plain,
    leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = leqNat(s(s(s(s(z)))),s(s(s(z)))),
    inference(resolve,[$cnf( $equal(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(s(z))))) )],[refute_0_207,refute_0_210]) ).

cnf(refute_0_212,plain,
    ( leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) != leqNat(s(s(s(s(z)))),s(s(s(z))))
    | leqNat(s(s(s(s(z)))),s(s(s(z)))) != bfalse
    | leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))))),bind(Y0,$fot(leqNat(s(s(s(s(z)))),s(s(s(z)))))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_213,plain,
    ( leqNat(s(s(s(s(z)))),s(s(s(z)))) != bfalse
    | leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = bfalse ),
    inference(resolve,[$cnf( $equal(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),leqNat(s(s(s(s(z)))),s(s(s(z))))) )],[refute_0_211,refute_0_212]) ).

cnf(refute_0_214,plain,
    leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = bfalse,
    inference(resolve,[$cnf( $equal(leqNat(s(s(s(s(z)))),s(s(s(z)))),bfalse) )],[refute_0_175,refute_0_213]) ).

cnf(refute_0_215,plain,
    eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),
    introduced(tautology,[refl,[$fot(eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))]]) ).

cnf(refute_0_216,plain,
    ( eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) != eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)
    | leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) != bfalse
    | eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = eq2(bfalse,btrue) ),
    introduced(tautology,[equality,[$cnf( $equal(eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) ),[1,0],$fot(bfalse)]]) ).

cnf(refute_0_217,plain,
    ( leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) != bfalse
    | eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = eq2(bfalse,btrue) ),
    inference(resolve,[$cnf( $equal(eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) )],[refute_0_215,refute_0_216]) ).

cnf(refute_0_218,plain,
    eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = eq2(bfalse,btrue),
    inference(resolve,[$cnf( $equal(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),bfalse) )],[refute_0_214,refute_0_217]) ).

cnf(refute_0_219,plain,
    ( eq2(bfalse,btrue) != bfalse
    | eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) != eq2(bfalse,btrue)
    | eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),bind(Y0,$fot(eq2(bfalse,btrue))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_220,plain,
    ( eq2(bfalse,btrue) != bfalse
    | eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = bfalse ),
    inference(resolve,[$cnf( $equal(eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),eq2(bfalse,btrue)) )],[refute_0_218,refute_0_219]) ).

cnf(refute_0_221,plain,
    eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = bfalse,
    inference(resolve,[$cnf( $equal(eq2(bfalse,btrue),bfalse) )],[axiom_025,refute_0_220]) ).

cnf(refute_0_222,plain,
    impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),
    introduced(tautology,[refl,[$fot(impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))]]) ).

cnf(refute_0_223,plain,
    ( eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) != bfalse
    | impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))
    | impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) ),[1,1],$fot(bfalse)]]) ).

cnf(refute_0_224,plain,
    ( eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) != bfalse
    | impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,bfalse) ),
    inference(resolve,[$cnf( $equal(impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,bfalse),
    inference(resolve,[$cnf( $equal(eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),bfalse) )],[refute_0_221,refute_0_224]) ).

cnf(refute_0_226,plain,
    eq2(btrue,btrue) = btrue,
    inference(subst,[],[axiom_031:[bind(X,$fot(btrue))]]) ).

cnf(refute_0_227,plain,
    impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),
    introduced(tautology,[refl,[$fot(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))]]) ).

cnf(refute_0_228,plain,
    ( eq2(btrue,btrue) != btrue
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) ),
    introduced(tautology,[equality,[$cnf( $equal(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) ),[1,0],$fot(btrue)]]) ).

cnf(refute_0_229,plain,
    ( eq2(btrue,btrue) != btrue
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) ),
    inference(resolve,[$cnf( $equal(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) )],[refute_0_227,refute_0_228]) ).

cnf(refute_0_230,plain,
    impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),
    inference(resolve,[$cnf( $equal(eq2(btrue,btrue),btrue) )],[refute_0_226,refute_0_229]) ).

cnf(refute_0_231,plain,
    ( impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != impl(btrue,bfalse)
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,bfalse) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))),bind(Y0,$fot(impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))),bind(Z0,$fot(impl(btrue,bfalse)))]]) ).

cnf(refute_0_232,plain,
    ( impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != impl(btrue,bfalse)
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,bfalse) ),
    inference(resolve,[$cnf( $equal(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) )],[refute_0_230,refute_0_231]) ).

cnf(refute_0_233,plain,
    impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,bfalse),
    inference(resolve,[$cnf( $equal(impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(btrue,bfalse)) )],[refute_0_225,refute_0_232]) ).

cnf(refute_0_234,plain,
    ( impl(btrue,bfalse) != bfalse
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != impl(btrue,bfalse)
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))),bind(Y0,$fot(impl(btrue,bfalse))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_235,plain,
    ( impl(btrue,bfalse) != bfalse
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = bfalse ),
    inference(resolve,[$cnf( $equal(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),impl(btrue,bfalse)) )],[refute_0_233,refute_0_234]) ).

cnf(refute_0_236,plain,
    impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = bfalse,
    inference(resolve,[$cnf( $equal(impl(btrue,bfalse),bfalse) )],[refute_0_162,refute_0_235]) ).

cnf(refute_0_237,plain,
    impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
    introduced(tautology,[refl,[$fot(impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))))]]) ).

cnf(refute_0_238,plain,
    ( impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != bfalse
    | impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,bfalse) ),
    introduced(tautology,[equality,[$cnf( $equal(impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) ),[1,1],$fot(bfalse)]]) ).

cnf(refute_0_239,plain,
    ( impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) != bfalse
    | impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,bfalse) ),
    inference(resolve,[$cnf( $equal(impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) )],[refute_0_237,refute_0_238]) ).

cnf(refute_0_240,plain,
    impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,bfalse),
    inference(resolve,[$cnf( $equal(impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),bfalse) )],[refute_0_236,refute_0_239]) ).

cnf(refute_0_241,plain,
    sorted(cons(s(s(z)),nil)) = btrue,
    inference(subst,[],[axiom_022:[bind(Y,$fot(s(s(z))))]]) ).

cnf(refute_0_242,plain,
    sorted(cons(s(Z),cons(s(M),X_79))) = andb(leqNat(s(Z),s(M)),sorted(cons(s(M),X_79))),
    inference(subst,[],[axiom_023:[bind(Xs,$fot(X_79)),bind(Y,$fot(s(Z))),bind(Y2,$fot(s(M)))]]) ).

cnf(refute_0_243,plain,
    ( leqNat(s(Z),s(M)) != leqNat(Z,M)
    | sorted(cons(s(Z),cons(s(M),X_79))) != andb(leqNat(s(Z),s(M)),sorted(cons(s(M),X_79)))
    | sorted(cons(s(Z),cons(s(M),X_79))) = andb(leqNat(Z,M),sorted(cons(s(M),X_79))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(s(Z),cons(s(M),X_79))),andb(leqNat(s(Z),s(M)),sorted(cons(s(M),X_79)))) ),[1,0],$fot(leqNat(Z,M))]]) ).

cnf(refute_0_244,plain,
    ( sorted(cons(s(Z),cons(s(M),X_79))) != andb(leqNat(s(Z),s(M)),sorted(cons(s(M),X_79)))
    | sorted(cons(s(Z),cons(s(M),X_79))) = andb(leqNat(Z,M),sorted(cons(s(M),X_79))) ),
    inference(resolve,[$cnf( $equal(leqNat(s(Z),s(M)),leqNat(Z,M)) )],[axiom_006,refute_0_243]) ).

cnf(refute_0_245,plain,
    sorted(cons(s(Z),cons(s(M),X_79))) = andb(leqNat(Z,M),sorted(cons(s(M),X_79))),
    inference(resolve,[$cnf( $equal(sorted(cons(s(Z),cons(s(M),X_79))),andb(leqNat(s(Z),s(M)),sorted(cons(s(M),X_79)))) )],[refute_0_242,refute_0_244]) ).

cnf(refute_0_246,plain,
    sorted(cons(s(z),cons(s(X_155),X_157))) = andb(leqNat(z,X_155),sorted(cons(s(X_155),X_157))),
    inference(subst,[],[refute_0_245:[bind(M,$fot(X_155)),bind(Z,$fot(z)),bind(X_79,$fot(X_157))]]) ).

cnf(refute_0_247,plain,
    leqNat(z,X_155) = btrue,
    inference(subst,[],[axiom_004:[bind(Y,$fot(X_155))]]) ).

cnf(refute_0_248,plain,
    ( leqNat(z,X_155) != btrue
    | sorted(cons(s(z),cons(s(X_155),X_157))) != andb(leqNat(z,X_155),sorted(cons(s(X_155),X_157)))
    | sorted(cons(s(z),cons(s(X_155),X_157))) = andb(btrue,sorted(cons(s(X_155),X_157))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(s(z),cons(s(X_155),X_157))),andb(leqNat(z,X_155),sorted(cons(s(X_155),X_157)))) ),[1,0],$fot(btrue)]]) ).

cnf(refute_0_249,plain,
    ( sorted(cons(s(z),cons(s(X_155),X_157))) != andb(leqNat(z,X_155),sorted(cons(s(X_155),X_157)))
    | sorted(cons(s(z),cons(s(X_155),X_157))) = andb(btrue,sorted(cons(s(X_155),X_157))) ),
    inference(resolve,[$cnf( $equal(leqNat(z,X_155),btrue) )],[refute_0_247,refute_0_248]) ).

cnf(refute_0_250,plain,
    sorted(cons(s(z),cons(s(X_155),X_157))) = andb(btrue,sorted(cons(s(X_155),X_157))),
    inference(resolve,[$cnf( $equal(sorted(cons(s(z),cons(s(X_155),X_157))),andb(leqNat(z,X_155),sorted(cons(s(X_155),X_157)))) )],[refute_0_246,refute_0_249]) ).

cnf(refute_0_251,plain,
    andb(btrue,sorted(cons(s(X_155),X_157))) = sorted(cons(s(X_155),X_157)),
    inference(subst,[],[axiom_019:[bind(Q,$fot(sorted(cons(s(X_155),X_157))))]]) ).

cnf(refute_0_252,plain,
    ( andb(btrue,sorted(cons(s(X_155),X_157))) != sorted(cons(s(X_155),X_157))
    | sorted(cons(s(z),cons(s(X_155),X_157))) != andb(btrue,sorted(cons(s(X_155),X_157)))
    | sorted(cons(s(z),cons(s(X_155),X_157))) = sorted(cons(s(X_155),X_157)) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(s(z),cons(s(X_155),X_157))),andb(btrue,sorted(cons(s(X_155),X_157)))) ),[1],$fot(sorted(cons(s(X_155),X_157)))]]) ).

cnf(refute_0_253,plain,
    ( sorted(cons(s(z),cons(s(X_155),X_157))) != andb(btrue,sorted(cons(s(X_155),X_157)))
    | sorted(cons(s(z),cons(s(X_155),X_157))) = sorted(cons(s(X_155),X_157)) ),
    inference(resolve,[$cnf( $equal(andb(btrue,sorted(cons(s(X_155),X_157))),sorted(cons(s(X_155),X_157))) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    sorted(cons(s(z),cons(s(X_155),X_157))) = sorted(cons(s(X_155),X_157)),
    inference(resolve,[$cnf( $equal(sorted(cons(s(z),cons(s(X_155),X_157))),andb(btrue,sorted(cons(s(X_155),X_157)))) )],[refute_0_250,refute_0_253]) ).

cnf(refute_0_255,plain,
    sorted(cons(s(z),cons(s(s(z)),nil))) = sorted(cons(s(s(z)),nil)),
    inference(subst,[],[refute_0_254:[bind(X_155,$fot(s(z))),bind(X_157,$fot(nil))]]) ).

cnf(refute_0_256,plain,
    ( sorted(cons(s(s(z)),nil)) != btrue
    | sorted(cons(s(z),cons(s(s(z)),nil))) != sorted(cons(s(s(z)),nil))
    | sorted(cons(s(z),cons(s(s(z)),nil))) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(sorted(cons(s(z),cons(s(s(z)),nil))))),bind(Y0,$fot(sorted(cons(s(s(z)),nil)))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_257,plain,
    ( sorted(cons(s(s(z)),nil)) != btrue
    | sorted(cons(s(z),cons(s(s(z)),nil))) = btrue ),
    inference(resolve,[$cnf( $equal(sorted(cons(s(z),cons(s(s(z)),nil))),sorted(cons(s(s(z)),nil))) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    sorted(cons(s(z),cons(s(s(z)),nil))) = btrue,
    inference(resolve,[$cnf( $equal(sorted(cons(s(s(z)),nil)),btrue) )],[refute_0_241,refute_0_257]) ).

cnf(refute_0_259,plain,
    sorted(cons(s(Z),cons(s(s(z)),X_79))) = andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79))),
    inference(subst,[],[refute_0_245:[bind(M,$fot(s(z)))]]) ).

cnf(refute_0_260,plain,
    sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))) = andb(leqNat(Y,s(z)),sorted(cons(s(z),cons(s(X_232),X_233)))),
    inference(subst,[],[axiom_023:[bind(Xs,$fot(cons(s(X_232),X_233))),bind(Y2,$fot(s(z)))]]) ).

cnf(refute_0_261,plain,
    sorted(cons(s(z),cons(s(X_232),X_233))) = sorted(cons(s(X_232),X_233)),
    inference(subst,[],[refute_0_254:[bind(X_155,$fot(X_232)),bind(X_157,$fot(X_233))]]) ).

cnf(refute_0_262,plain,
    ( sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))) != andb(leqNat(Y,s(z)),sorted(cons(s(z),cons(s(X_232),X_233))))
    | sorted(cons(s(z),cons(s(X_232),X_233))) != sorted(cons(s(X_232),X_233))
    | sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))) = andb(leqNat(Y,s(z)),sorted(cons(s(X_232),X_233))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))),andb(leqNat(Y,s(z)),sorted(cons(s(z),cons(s(X_232),X_233))))) ),[1,1],$fot(sorted(cons(s(X_232),X_233)))]]) ).

cnf(refute_0_263,plain,
    ( sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))) != andb(leqNat(Y,s(z)),sorted(cons(s(z),cons(s(X_232),X_233))))
    | sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))) = andb(leqNat(Y,s(z)),sorted(cons(s(X_232),X_233))) ),
    inference(resolve,[$cnf( $equal(sorted(cons(s(z),cons(s(X_232),X_233))),sorted(cons(s(X_232),X_233))) )],[refute_0_261,refute_0_262]) ).

cnf(refute_0_264,plain,
    sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))) = andb(leqNat(Y,s(z)),sorted(cons(s(X_232),X_233))),
    inference(resolve,[$cnf( $equal(sorted(cons(Y,cons(s(z),cons(s(X_232),X_233)))),andb(leqNat(Y,s(z)),sorted(cons(s(z),cons(s(X_232),X_233))))) )],[refute_0_260,refute_0_263]) ).

cnf(refute_0_265,plain,
    sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) = andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79))),
    inference(subst,[],[refute_0_264:[bind(Y,$fot(Z)),bind(X_232,$fot(s(z))),bind(X_233,$fot(X_79))]]) ).

cnf(refute_0_266,plain,
    ( sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) != andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))
    | andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79))) = sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) ),
    inference(subst,[],[refute_0_22:[bind(X0,$fot(sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))))),bind(Y0,$fot(andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))))]]) ).

cnf(refute_0_267,plain,
    andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79))) = sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))),
    inference(resolve,[$cnf( $equal(sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))),andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))) )],[refute_0_265,refute_0_266]) ).

cnf(refute_0_268,plain,
    ( andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79))) != sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79))))
    | sorted(cons(s(Z),cons(s(s(z)),X_79))) != andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))
    | sorted(cons(s(Z),cons(s(s(z)),X_79))) = sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(s(Z),cons(s(s(z)),X_79))),andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))) ),[1],$fot(sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))))]]) ).

cnf(refute_0_269,plain,
    ( sorted(cons(s(Z),cons(s(s(z)),X_79))) != andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))
    | sorted(cons(s(Z),cons(s(s(z)),X_79))) = sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) ),
    inference(resolve,[$cnf( $equal(andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79))),sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79))))) )],[refute_0_267,refute_0_268]) ).

cnf(refute_0_270,plain,
    sorted(cons(s(Z),cons(s(s(z)),X_79))) = sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))),
    inference(resolve,[$cnf( $equal(sorted(cons(s(Z),cons(s(s(z)),X_79))),andb(leqNat(Z,s(z)),sorted(cons(s(s(z)),X_79)))) )],[refute_0_259,refute_0_269]) ).

cnf(refute_0_271,plain,
    ( sorted(cons(s(Z),cons(s(s(z)),X_79))) != sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79))))
    | sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) = sorted(cons(s(Z),cons(s(s(z)),X_79))) ),
    inference(subst,[],[refute_0_22:[bind(X0,$fot(sorted(cons(s(Z),cons(s(s(z)),X_79))))),bind(Y0,$fot(sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79))))))]]) ).

cnf(refute_0_272,plain,
    sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79)))) = sorted(cons(s(Z),cons(s(s(z)),X_79))),
    inference(resolve,[$cnf( $equal(sorted(cons(s(Z),cons(s(s(z)),X_79))),sorted(cons(Z,cons(s(z),cons(s(s(z)),X_79))))) )],[refute_0_270,refute_0_271]) ).

cnf(refute_0_273,plain,
    sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) = sorted(cons(s(z),cons(s(s(z)),nil))),
    inference(subst,[],[refute_0_272:[bind(Z,$fot(z)),bind(X_79,$fot(nil))]]) ).

cnf(refute_0_274,plain,
    ( sorted(cons(s(z),cons(s(s(z)),nil))) != btrue
    | sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) != sorted(cons(s(z),cons(s(s(z)),nil)))
    | sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))))),bind(Y0,$fot(sorted(cons(s(z),cons(s(s(z)),nil))))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_275,plain,
    ( sorted(cons(s(z),cons(s(s(z)),nil))) != btrue
    | sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) = btrue ),
    inference(resolve,[$cnf( $equal(sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))),sorted(cons(s(z),cons(s(s(z)),nil)))) )],[refute_0_273,refute_0_274]) ).

cnf(refute_0_276,plain,
    sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) = btrue,
    inference(resolve,[$cnf( $equal(sorted(cons(s(z),cons(s(s(z)),nil))),btrue) )],[refute_0_258,refute_0_275]) ).

cnf(refute_0_277,plain,
    sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))) = andb(leqNat(Y,Y2),sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))),
    inference(subst,[],[axiom_023:[bind(Xs,$fot(cons(s(s(X_323)),cons(s(s(X_322)),nil))))]]) ).

cnf(refute_0_278,plain,
    sorted(cons(Y,cons(Y2,cons(X_90,nil)))) = andb(leqNat(Y,Y2),sorted(cons(Y2,cons(X_90,nil)))),
    inference(subst,[],[axiom_023:[bind(Xs,$fot(cons(X_90,nil)))]]) ).

cnf(refute_0_279,plain,
    sorted(cons(X_80,cons(X_81,nil))) = andb(leqNat(X_80,X_81),sorted(cons(X_81,nil))),
    inference(subst,[],[axiom_023:[bind(Xs,$fot(nil)),bind(Y,$fot(X_80)),bind(Y2,$fot(X_81))]]) ).

cnf(refute_0_280,plain,
    sorted(cons(X_81,nil)) = btrue,
    inference(subst,[],[axiom_022:[bind(Y,$fot(X_81))]]) ).

cnf(refute_0_281,plain,
    ( sorted(cons(X_80,cons(X_81,nil))) != andb(leqNat(X_80,X_81),sorted(cons(X_81,nil)))
    | sorted(cons(X_81,nil)) != btrue
    | sorted(cons(X_80,cons(X_81,nil))) = andb(leqNat(X_80,X_81),btrue) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(X_80,cons(X_81,nil))),andb(leqNat(X_80,X_81),sorted(cons(X_81,nil)))) ),[1,1],$fot(btrue)]]) ).

cnf(refute_0_282,plain,
    ( sorted(cons(X_80,cons(X_81,nil))) != andb(leqNat(X_80,X_81),sorted(cons(X_81,nil)))
    | sorted(cons(X_80,cons(X_81,nil))) = andb(leqNat(X_80,X_81),btrue) ),
    inference(resolve,[$cnf( $equal(sorted(cons(X_81,nil)),btrue) )],[refute_0_280,refute_0_281]) ).

cnf(refute_0_283,plain,
    sorted(cons(X_80,cons(X_81,nil))) = andb(leqNat(X_80,X_81),btrue),
    inference(resolve,[$cnf( $equal(sorted(cons(X_80,cons(X_81,nil))),andb(leqNat(X_80,X_81),sorted(cons(X_81,nil)))) )],[refute_0_279,refute_0_282]) ).

cnf(refute_0_284,plain,
    sorted(cons(Y2,cons(X_90,nil))) = andb(leqNat(Y2,X_90),btrue),
    inference(subst,[],[refute_0_283:[bind(X_80,$fot(Y2)),bind(X_81,$fot(X_90))]]) ).

cnf(refute_0_285,plain,
    ( sorted(cons(Y,cons(Y2,cons(X_90,nil)))) != andb(leqNat(Y,Y2),sorted(cons(Y2,cons(X_90,nil))))
    | sorted(cons(Y2,cons(X_90,nil))) != andb(leqNat(Y2,X_90),btrue)
    | sorted(cons(Y,cons(Y2,cons(X_90,nil)))) = andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue)) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(Y,cons(Y2,cons(X_90,nil)))),andb(leqNat(Y,Y2),sorted(cons(Y2,cons(X_90,nil))))) ),[1,1],$fot(andb(leqNat(Y2,X_90),btrue))]]) ).

cnf(refute_0_286,plain,
    ( sorted(cons(Y,cons(Y2,cons(X_90,nil)))) != andb(leqNat(Y,Y2),sorted(cons(Y2,cons(X_90,nil))))
    | sorted(cons(Y,cons(Y2,cons(X_90,nil)))) = andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue)) ),
    inference(resolve,[$cnf( $equal(sorted(cons(Y2,cons(X_90,nil))),andb(leqNat(Y2,X_90),btrue)) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    sorted(cons(Y,cons(Y2,cons(X_90,nil)))) = andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue)),
    inference(resolve,[$cnf( $equal(sorted(cons(Y,cons(Y2,cons(X_90,nil)))),andb(leqNat(Y,Y2),sorted(cons(Y2,cons(X_90,nil))))) )],[refute_0_278,refute_0_286]) ).

cnf(refute_0_288,plain,
    sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))) = andb(leqNat(X_118,s(Z)),andb(leqNat(s(Z),s(M)),btrue)),
    inference(subst,[],[refute_0_287:[bind(Y,$fot(X_118)),bind(Y2,$fot(s(Z))),bind(X_90,$fot(s(M)))]]) ).

cnf(refute_0_289,plain,
    ( leqNat(s(Z),s(M)) != leqNat(Z,M)
    | sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))) != andb(leqNat(X_118,s(Z)),andb(leqNat(s(Z),s(M)),btrue))
    | sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))) = andb(leqNat(X_118,s(Z)),andb(leqNat(Z,M),btrue)) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))),andb(leqNat(X_118,s(Z)),andb(leqNat(s(Z),s(M)),btrue))) ),[1,1,0],$fot(leqNat(Z,M))]]) ).

cnf(refute_0_290,plain,
    ( sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))) != andb(leqNat(X_118,s(Z)),andb(leqNat(s(Z),s(M)),btrue))
    | sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))) = andb(leqNat(X_118,s(Z)),andb(leqNat(Z,M),btrue)) ),
    inference(resolve,[$cnf( $equal(leqNat(s(Z),s(M)),leqNat(Z,M)) )],[axiom_006,refute_0_289]) ).

cnf(refute_0_291,plain,
    sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))) = andb(leqNat(X_118,s(Z)),andb(leqNat(Z,M),btrue)),
    inference(resolve,[$cnf( $equal(sorted(cons(X_118,cons(s(Z),cons(s(M),nil)))),andb(leqNat(X_118,s(Z)),andb(leqNat(s(Z),s(M)),btrue))) )],[refute_0_288,refute_0_290]) ).

cnf(refute_0_292,plain,
    sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))) = andb(leqNat(X_217,s(s(Z))),andb(leqNat(s(Z),s(M)),btrue)),
    inference(subst,[],[refute_0_291:[bind(M,$fot(s(M))),bind(Z,$fot(s(Z))),bind(X_118,$fot(X_217))]]) ).

cnf(refute_0_293,plain,
    ( leqNat(s(Z),s(M)) != leqNat(Z,M)
    | sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))) != andb(leqNat(X_217,s(s(Z))),andb(leqNat(s(Z),s(M)),btrue))
    | sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))) = andb(leqNat(X_217,s(s(Z))),andb(leqNat(Z,M),btrue)) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))),andb(leqNat(X_217,s(s(Z))),andb(leqNat(s(Z),s(M)),btrue))) ),[1,1,0],$fot(leqNat(Z,M))]]) ).

cnf(refute_0_294,plain,
    ( sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))) != andb(leqNat(X_217,s(s(Z))),andb(leqNat(s(Z),s(M)),btrue))
    | sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))) = andb(leqNat(X_217,s(s(Z))),andb(leqNat(Z,M),btrue)) ),
    inference(resolve,[$cnf( $equal(leqNat(s(Z),s(M)),leqNat(Z,M)) )],[axiom_006,refute_0_293]) ).

cnf(refute_0_295,plain,
    sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))) = andb(leqNat(X_217,s(s(Z))),andb(leqNat(Z,M),btrue)),
    inference(resolve,[$cnf( $equal(sorted(cons(X_217,cons(s(s(Z)),cons(s(s(M)),nil)))),andb(leqNat(X_217,s(s(Z))),andb(leqNat(s(Z),s(M)),btrue))) )],[refute_0_292,refute_0_294]) ).

cnf(refute_0_296,plain,
    sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))) = andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue)),
    inference(subst,[],[refute_0_295:[bind(M,$fot(X_322)),bind(Z,$fot(X_323)),bind(X_217,$fot(Y2))]]) ).

cnf(refute_0_297,plain,
    ( sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))) != andb(leqNat(Y,Y2),sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))))
    | sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))) != andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue))
    | sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))) = andb(leqNat(Y,Y2),andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))),andb(leqNat(Y,Y2),sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))))) ),[1,1],$fot(andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue)))]]) ).

cnf(refute_0_298,plain,
    ( sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))) != andb(leqNat(Y,Y2),sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))))
    | sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))) = andb(leqNat(Y,Y2),andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue))) ),
    inference(resolve,[$cnf( $equal(sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))),andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue))) )],[refute_0_296,refute_0_297]) ).

cnf(refute_0_299,plain,
    sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))) = andb(leqNat(Y,Y2),andb(leqNat(Y2,s(s(X_323))),andb(leqNat(X_323,X_322),btrue))),
    inference(resolve,[$cnf( $equal(sorted(cons(Y,cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil))))),andb(leqNat(Y,Y2),sorted(cons(Y2,cons(s(s(X_323)),cons(s(s(X_322)),nil)))))) )],[refute_0_277,refute_0_298]) ).

cnf(refute_0_300,plain,
    sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(leqNat(z,X_2063),btrue))),
    inference(subst,[],[refute_0_299:[bind(Y,$fot(X_2061)),bind(Y2,$fot(X_2062)),bind(X_322,$fot(X_2063)),bind(X_323,$fot(z))]]) ).

cnf(refute_0_301,plain,
    leqNat(z,X_2063) = btrue,
    inference(subst,[],[axiom_004:[bind(Y,$fot(X_2063))]]) ).

cnf(refute_0_302,plain,
    ( leqNat(z,X_2063) != btrue
    | sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) != andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(leqNat(z,X_2063),btrue)))
    | sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(leqNat(z,X_2063),btrue)))) ),[1,1,1,0],$fot(btrue)]]) ).

cnf(refute_0_303,plain,
    ( sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) != andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(leqNat(z,X_2063),btrue)))
    | sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) ),
    inference(resolve,[$cnf( $equal(leqNat(z,X_2063),btrue) )],[refute_0_301,refute_0_302]) ).

cnf(refute_0_304,plain,
    sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))),
    inference(resolve,[$cnf( $equal(sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(leqNat(z,X_2063),btrue)))) )],[refute_0_300,refute_0_303]) ).

cnf(refute_0_305,plain,
    ( sorted(cons(Y,cons(Y2,cons(X_90,nil)))) != andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue))
    | andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue)) = sorted(cons(Y,cons(Y2,cons(X_90,nil)))) ),
    inference(subst,[],[refute_0_22:[bind(X0,$fot(sorted(cons(Y,cons(Y2,cons(X_90,nil)))))),bind(Y0,$fot(andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue))))]]) ).

cnf(refute_0_306,plain,
    andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue)) = sorted(cons(Y,cons(Y2,cons(X_90,nil)))),
    inference(resolve,[$cnf( $equal(sorted(cons(Y,cons(Y2,cons(X_90,nil)))),andb(leqNat(Y,Y2),andb(leqNat(Y2,X_90),btrue))) )],[refute_0_287,refute_0_305]) ).

cnf(refute_0_307,plain,
    andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))),
    inference(subst,[],[refute_0_306:[bind(Y,$fot(X_2061)),bind(Y2,$fot(X_2062)),bind(X_90,$fot(s(s(z))))]]) ).

cnf(refute_0_308,plain,
    andb(btrue,btrue) = btrue,
    inference(subst,[],[axiom_019:[bind(Q,$fot(btrue))]]) ).

cnf(refute_0_309,plain,
    andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) = andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)),
    introduced(tautology,[refl,[$fot(andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))]]) ).

cnf(refute_0_310,plain,
    ( andb(btrue,btrue) != btrue
    | andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) != andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))
    | andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) = andb(leqNat(X_2062,s(s(z))),btrue) ),
    introduced(tautology,[equality,[$cnf( $equal(andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) ),[1,1],$fot(btrue)]]) ).

cnf(refute_0_311,plain,
    ( andb(btrue,btrue) != btrue
    | andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) = andb(leqNat(X_2062,s(s(z))),btrue) ),
    inference(resolve,[$cnf( $equal(andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) )],[refute_0_309,refute_0_310]) ).

cnf(refute_0_312,plain,
    andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) = andb(leqNat(X_2062,s(s(z))),btrue),
    inference(resolve,[$cnf( $equal(andb(btrue,btrue),btrue) )],[refute_0_308,refute_0_311]) ).

cnf(refute_0_313,plain,
    andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))),
    introduced(tautology,[refl,[$fot(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))))]]) ).

cnf(refute_0_314,plain,
    ( andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) != andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))
    | andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) != andb(leqNat(X_2062,s(s(z))),btrue)
    | andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)) ),
    introduced(tautology,[equality,[$cnf( $equal(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))) ),[1,1],$fot(andb(leqNat(X_2062,s(s(z))),btrue))]]) ).

cnf(refute_0_315,plain,
    ( andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)) != andb(leqNat(X_2062,s(s(z))),btrue)
    | andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)) ),
    inference(resolve,[$cnf( $equal(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))) )],[refute_0_313,refute_0_314]) ).

cnf(refute_0_316,plain,
    andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)),
    inference(resolve,[$cnf( $equal(andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)),andb(leqNat(X_2062,s(s(z))),btrue)) )],[refute_0_312,refute_0_315]) ).

cnf(refute_0_317,plain,
    ( andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) != andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue))
    | andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)) != sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil))))
    | andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))))),bind(Y0,$fot(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)))),bind(Z0,$fot(sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil))))))]]) ).

cnf(refute_0_318,plain,
    ( andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)) != sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil))))
    | andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))) ),
    inference(resolve,[$cnf( $equal(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue))) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))),
    inference(resolve,[$cnf( $equal(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),btrue)),sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil))))) )],[refute_0_307,refute_0_318]) ).

cnf(refute_0_320,plain,
    ( andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))) != sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil))))
    | sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) != andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))
    | sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))) ),[1],$fot(sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))))]]) ).

cnf(refute_0_321,plain,
    ( sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) != andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))
    | sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))) ),
    inference(resolve,[$cnf( $equal(andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue))),sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil))))) )],[refute_0_319,refute_0_320]) ).

cnf(refute_0_322,plain,
    sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))) = sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),nil)))),
    inference(resolve,[$cnf( $equal(sorted(cons(X_2061,cons(X_2062,cons(s(s(z)),cons(s(s(X_2063)),nil))))),andb(leqNat(X_2061,X_2062),andb(leqNat(X_2062,s(s(z))),andb(btrue,btrue)))) )],[refute_0_304,refute_0_321]) ).

cnf(refute_0_323,plain,
    sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) = sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))),
    inference(subst,[],[refute_0_322:[bind(X_2061,$fot(z)),bind(X_2062,$fot(s(z))),bind(X_2063,$fot(s(X_3137)))]]) ).

cnf(refute_0_324,plain,
    ( sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) != sorted(cons(z,cons(s(z),cons(s(s(z)),nil))))
    | sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) != btrue
    | sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))))),bind(Y0,$fot(sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_325,plain,
    ( sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))) != btrue
    | sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) = btrue ),
    inference(resolve,[$cnf( $equal(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))),sorted(cons(z,cons(s(z),cons(s(s(z)),nil))))) )],[refute_0_323,refute_0_324]) ).

cnf(refute_0_326,plain,
    sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) = btrue,
    inference(resolve,[$cnf( $equal(sorted(cons(z,cons(s(z),cons(s(s(z)),nil)))),btrue) )],[refute_0_276,refute_0_325]) ).

cnf(refute_0_327,plain,
    rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = append(rev(cons(X_33,cons(X_34,cons(X_35,nil)))),cons(Y,nil)),
    inference(subst,[],[axiom_018:[bind(Xs,$fot(cons(X_33,cons(X_34,cons(X_35,nil)))))]]) ).

cnf(refute_0_328,plain,
    rev(cons(Y,cons(X_29,cons(X_30,nil)))) = append(rev(cons(X_29,cons(X_30,nil))),cons(Y,nil)),
    inference(subst,[],[axiom_018:[bind(Xs,$fot(cons(X_29,cons(X_30,nil))))]]) ).

cnf(refute_0_329,plain,
    rev(cons(Y,cons(X_28,nil))) = append(rev(cons(X_28,nil)),cons(Y,nil)),
    inference(subst,[],[axiom_018:[bind(Xs,$fot(cons(X_28,nil)))]]) ).

cnf(refute_0_330,plain,
    rev(cons(X_27,nil)) = append(rev(nil),cons(X_27,nil)),
    inference(subst,[],[axiom_018:[bind(Xs,$fot(nil)),bind(Y,$fot(X_27))]]) ).

cnf(refute_0_331,plain,
    ( rev(cons(X_27,nil)) != append(rev(nil),cons(X_27,nil))
    | rev(nil) != nil
    | rev(cons(X_27,nil)) = append(nil,cons(X_27,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(X_27,nil)),append(rev(nil),cons(X_27,nil))) ),[1,0],$fot(nil)]]) ).

cnf(refute_0_332,plain,
    ( rev(cons(X_27,nil)) != append(rev(nil),cons(X_27,nil))
    | rev(cons(X_27,nil)) = append(nil,cons(X_27,nil)) ),
    inference(resolve,[$cnf( $equal(rev(nil),nil) )],[axiom_017,refute_0_331]) ).

cnf(refute_0_333,plain,
    rev(cons(X_27,nil)) = append(nil,cons(X_27,nil)),
    inference(resolve,[$cnf( $equal(rev(cons(X_27,nil)),append(rev(nil),cons(X_27,nil))) )],[refute_0_330,refute_0_332]) ).

cnf(refute_0_334,plain,
    append(nil,cons(X_27,nil)) = cons(X_27,nil),
    inference(subst,[],[axiom_015:[bind(Y,$fot(cons(X_27,nil)))]]) ).

cnf(refute_0_335,plain,
    ( append(nil,cons(X_27,nil)) != cons(X_27,nil)
    | rev(cons(X_27,nil)) != append(nil,cons(X_27,nil))
    | rev(cons(X_27,nil)) = cons(X_27,nil) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(X_27,nil)),append(nil,cons(X_27,nil))) ),[1],$fot(cons(X_27,nil))]]) ).

cnf(refute_0_336,plain,
    ( rev(cons(X_27,nil)) != append(nil,cons(X_27,nil))
    | rev(cons(X_27,nil)) = cons(X_27,nil) ),
    inference(resolve,[$cnf( $equal(append(nil,cons(X_27,nil)),cons(X_27,nil)) )],[refute_0_334,refute_0_335]) ).

cnf(refute_0_337,plain,
    rev(cons(X_27,nil)) = cons(X_27,nil),
    inference(resolve,[$cnf( $equal(rev(cons(X_27,nil)),append(nil,cons(X_27,nil))) )],[refute_0_333,refute_0_336]) ).

cnf(refute_0_338,plain,
    rev(cons(X_28,nil)) = cons(X_28,nil),
    inference(subst,[],[refute_0_337:[bind(X_27,$fot(X_28))]]) ).

cnf(refute_0_339,plain,
    ( rev(cons(Y,cons(X_28,nil))) != append(rev(cons(X_28,nil)),cons(Y,nil))
    | rev(cons(X_28,nil)) != cons(X_28,nil)
    | rev(cons(Y,cons(X_28,nil))) = append(cons(X_28,nil),cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(Y,cons(X_28,nil))),append(rev(cons(X_28,nil)),cons(Y,nil))) ),[1,0],$fot(cons(X_28,nil))]]) ).

cnf(refute_0_340,plain,
    ( rev(cons(Y,cons(X_28,nil))) != append(rev(cons(X_28,nil)),cons(Y,nil))
    | rev(cons(Y,cons(X_28,nil))) = append(cons(X_28,nil),cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(rev(cons(X_28,nil)),cons(X_28,nil)) )],[refute_0_338,refute_0_339]) ).

cnf(refute_0_341,plain,
    rev(cons(Y,cons(X_28,nil))) = append(cons(X_28,nil),cons(Y,nil)),
    inference(resolve,[$cnf( $equal(rev(cons(Y,cons(X_28,nil))),append(rev(cons(X_28,nil)),cons(Y,nil))) )],[refute_0_329,refute_0_340]) ).

cnf(refute_0_342,plain,
    append(nil,cons(Y,nil)) = cons(Y,nil),
    inference(subst,[],[axiom_015:[bind(Y,$fot(cons(Y,nil)))]]) ).

cnf(refute_0_343,plain,
    cons(X_28,append(nil,cons(Y,nil))) = cons(X_28,append(nil,cons(Y,nil))),
    introduced(tautology,[refl,[$fot(cons(X_28,append(nil,cons(Y,nil))))]]) ).

cnf(refute_0_344,plain,
    ( cons(X_28,append(nil,cons(Y,nil))) != cons(X_28,append(nil,cons(Y,nil)))
    | append(nil,cons(Y,nil)) != cons(Y,nil)
    | cons(X_28,append(nil,cons(Y,nil))) = cons(X_28,cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(cons(X_28,append(nil,cons(Y,nil))),cons(X_28,append(nil,cons(Y,nil)))) ),[1,1],$fot(cons(Y,nil))]]) ).

cnf(refute_0_345,plain,
    ( append(nil,cons(Y,nil)) != cons(Y,nil)
    | cons(X_28,append(nil,cons(Y,nil))) = cons(X_28,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(cons(X_28,append(nil,cons(Y,nil))),cons(X_28,append(nil,cons(Y,nil)))) )],[refute_0_343,refute_0_344]) ).

cnf(refute_0_346,plain,
    cons(X_28,append(nil,cons(Y,nil))) = cons(X_28,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(append(nil,cons(Y,nil)),cons(Y,nil)) )],[refute_0_342,refute_0_345]) ).

cnf(refute_0_347,plain,
    append(cons(X_28,nil),cons(Y,nil)) = cons(X_28,append(nil,cons(Y,nil))),
    inference(subst,[],[axiom_016:[bind(Xs,$fot(nil)),bind(Y,$fot(cons(Y,nil))),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_348,plain,
    ( cons(X_28,append(nil,cons(Y,nil))) != cons(X_28,cons(Y,nil))
    | append(cons(X_28,nil),cons(Y,nil)) != cons(X_28,append(nil,cons(Y,nil)))
    | append(cons(X_28,nil),cons(Y,nil)) = cons(X_28,cons(Y,nil)) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(append(cons(X_28,nil),cons(Y,nil)))),bind(Y0,$fot(cons(X_28,append(nil,cons(Y,nil))))),bind(Z0,$fot(cons(X_28,cons(Y,nil))))]]) ).

cnf(refute_0_349,plain,
    ( cons(X_28,append(nil,cons(Y,nil))) != cons(X_28,cons(Y,nil))
    | append(cons(X_28,nil),cons(Y,nil)) = cons(X_28,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(append(cons(X_28,nil),cons(Y,nil)),cons(X_28,append(nil,cons(Y,nil)))) )],[refute_0_347,refute_0_348]) ).

cnf(refute_0_350,plain,
    append(cons(X_28,nil),cons(Y,nil)) = cons(X_28,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(cons(X_28,append(nil,cons(Y,nil))),cons(X_28,cons(Y,nil))) )],[refute_0_346,refute_0_349]) ).

cnf(refute_0_351,plain,
    ( append(cons(X_28,nil),cons(Y,nil)) != cons(X_28,cons(Y,nil))
    | rev(cons(Y,cons(X_28,nil))) != append(cons(X_28,nil),cons(Y,nil))
    | rev(cons(Y,cons(X_28,nil))) = cons(X_28,cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(Y,cons(X_28,nil))),append(cons(X_28,nil),cons(Y,nil))) ),[1],$fot(cons(X_28,cons(Y,nil)))]]) ).

cnf(refute_0_352,plain,
    ( rev(cons(Y,cons(X_28,nil))) != append(cons(X_28,nil),cons(Y,nil))
    | rev(cons(Y,cons(X_28,nil))) = cons(X_28,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(append(cons(X_28,nil),cons(Y,nil)),cons(X_28,cons(Y,nil))) )],[refute_0_350,refute_0_351]) ).

cnf(refute_0_353,plain,
    rev(cons(Y,cons(X_28,nil))) = cons(X_28,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(rev(cons(Y,cons(X_28,nil))),append(cons(X_28,nil),cons(Y,nil))) )],[refute_0_341,refute_0_352]) ).

cnf(refute_0_354,plain,
    rev(cons(X_29,cons(X_30,nil))) = cons(X_30,cons(X_29,nil)),
    inference(subst,[],[refute_0_353:[bind(Y,$fot(X_29)),bind(X_28,$fot(X_30))]]) ).

cnf(refute_0_355,plain,
    ( rev(cons(Y,cons(X_29,cons(X_30,nil)))) != append(rev(cons(X_29,cons(X_30,nil))),cons(Y,nil))
    | rev(cons(X_29,cons(X_30,nil))) != cons(X_30,cons(X_29,nil))
    | rev(cons(Y,cons(X_29,cons(X_30,nil)))) = append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(Y,cons(X_29,cons(X_30,nil)))),append(rev(cons(X_29,cons(X_30,nil))),cons(Y,nil))) ),[1,0],$fot(cons(X_30,cons(X_29,nil)))]]) ).

cnf(refute_0_356,plain,
    ( rev(cons(Y,cons(X_29,cons(X_30,nil)))) != append(rev(cons(X_29,cons(X_30,nil))),cons(Y,nil))
    | rev(cons(Y,cons(X_29,cons(X_30,nil)))) = append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(rev(cons(X_29,cons(X_30,nil))),cons(X_30,cons(X_29,nil))) )],[refute_0_354,refute_0_355]) ).

cnf(refute_0_357,plain,
    rev(cons(Y,cons(X_29,cons(X_30,nil)))) = append(cons(X_30,cons(X_29,nil)),cons(Y,nil)),
    inference(resolve,[$cnf( $equal(rev(cons(Y,cons(X_29,cons(X_30,nil)))),append(rev(cons(X_29,cons(X_30,nil))),cons(Y,nil))) )],[refute_0_328,refute_0_356]) ).

cnf(refute_0_358,plain,
    cons(X_29,append(nil,cons(Y,nil))) = cons(X_29,append(nil,cons(Y,nil))),
    introduced(tautology,[refl,[$fot(cons(X_29,append(nil,cons(Y,nil))))]]) ).

cnf(refute_0_359,plain,
    ( cons(X_29,append(nil,cons(Y,nil))) != cons(X_29,append(nil,cons(Y,nil)))
    | append(nil,cons(Y,nil)) != cons(Y,nil)
    | cons(X_29,append(nil,cons(Y,nil))) = cons(X_29,cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(cons(X_29,append(nil,cons(Y,nil))),cons(X_29,append(nil,cons(Y,nil)))) ),[1,1],$fot(cons(Y,nil))]]) ).

cnf(refute_0_360,plain,
    ( append(nil,cons(Y,nil)) != cons(Y,nil)
    | cons(X_29,append(nil,cons(Y,nil))) = cons(X_29,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(cons(X_29,append(nil,cons(Y,nil))),cons(X_29,append(nil,cons(Y,nil)))) )],[refute_0_358,refute_0_359]) ).

cnf(refute_0_361,plain,
    cons(X_29,append(nil,cons(Y,nil))) = cons(X_29,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(append(nil,cons(Y,nil)),cons(Y,nil)) )],[refute_0_342,refute_0_360]) ).

cnf(refute_0_362,plain,
    append(cons(X_29,nil),cons(Y,nil)) = cons(X_29,append(nil,cons(Y,nil))),
    inference(subst,[],[axiom_016:[bind(Xs,$fot(nil)),bind(Y,$fot(cons(Y,nil))),bind(Z,$fot(X_29))]]) ).

cnf(refute_0_363,plain,
    ( cons(X_29,append(nil,cons(Y,nil))) != cons(X_29,cons(Y,nil))
    | append(cons(X_29,nil),cons(Y,nil)) != cons(X_29,append(nil,cons(Y,nil)))
    | append(cons(X_29,nil),cons(Y,nil)) = cons(X_29,cons(Y,nil)) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(append(cons(X_29,nil),cons(Y,nil)))),bind(Y0,$fot(cons(X_29,append(nil,cons(Y,nil))))),bind(Z0,$fot(cons(X_29,cons(Y,nil))))]]) ).

cnf(refute_0_364,plain,
    ( cons(X_29,append(nil,cons(Y,nil))) != cons(X_29,cons(Y,nil))
    | append(cons(X_29,nil),cons(Y,nil)) = cons(X_29,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(append(cons(X_29,nil),cons(Y,nil)),cons(X_29,append(nil,cons(Y,nil)))) )],[refute_0_362,refute_0_363]) ).

cnf(refute_0_365,plain,
    append(cons(X_29,nil),cons(Y,nil)) = cons(X_29,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(cons(X_29,append(nil,cons(Y,nil))),cons(X_29,cons(Y,nil))) )],[refute_0_361,refute_0_364]) ).

cnf(refute_0_366,plain,
    cons(X_30,append(cons(X_29,nil),cons(Y,nil))) = cons(X_30,append(cons(X_29,nil),cons(Y,nil))),
    introduced(tautology,[refl,[$fot(cons(X_30,append(cons(X_29,nil),cons(Y,nil))))]]) ).

cnf(refute_0_367,plain,
    ( cons(X_30,append(cons(X_29,nil),cons(Y,nil))) != cons(X_30,append(cons(X_29,nil),cons(Y,nil)))
    | append(cons(X_29,nil),cons(Y,nil)) != cons(X_29,cons(Y,nil))
    | cons(X_30,append(cons(X_29,nil),cons(Y,nil))) = cons(X_30,cons(X_29,cons(Y,nil))) ),
    introduced(tautology,[equality,[$cnf( $equal(cons(X_30,append(cons(X_29,nil),cons(Y,nil))),cons(X_30,append(cons(X_29,nil),cons(Y,nil)))) ),[1,1],$fot(cons(X_29,cons(Y,nil)))]]) ).

cnf(refute_0_368,plain,
    ( append(cons(X_29,nil),cons(Y,nil)) != cons(X_29,cons(Y,nil))
    | cons(X_30,append(cons(X_29,nil),cons(Y,nil))) = cons(X_30,cons(X_29,cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(cons(X_30,append(cons(X_29,nil),cons(Y,nil))),cons(X_30,append(cons(X_29,nil),cons(Y,nil)))) )],[refute_0_366,refute_0_367]) ).

cnf(refute_0_369,plain,
    cons(X_30,append(cons(X_29,nil),cons(Y,nil))) = cons(X_30,cons(X_29,cons(Y,nil))),
    inference(resolve,[$cnf( $equal(append(cons(X_29,nil),cons(Y,nil)),cons(X_29,cons(Y,nil))) )],[refute_0_365,refute_0_368]) ).

cnf(refute_0_370,plain,
    append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) = cons(X_30,append(cons(X_29,nil),cons(Y,nil))),
    inference(subst,[],[axiom_016:[bind(Xs,$fot(cons(X_29,nil))),bind(Y,$fot(cons(Y,nil))),bind(Z,$fot(X_30))]]) ).

cnf(refute_0_371,plain,
    ( cons(X_30,append(cons(X_29,nil),cons(Y,nil))) != cons(X_30,cons(X_29,cons(Y,nil)))
    | append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) != cons(X_30,append(cons(X_29,nil),cons(Y,nil)))
    | append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) = cons(X_30,cons(X_29,cons(Y,nil))) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(append(cons(X_30,cons(X_29,nil)),cons(Y,nil)))),bind(Y0,$fot(cons(X_30,append(cons(X_29,nil),cons(Y,nil))))),bind(Z0,$fot(cons(X_30,cons(X_29,cons(Y,nil)))))]]) ).

cnf(refute_0_372,plain,
    ( cons(X_30,append(cons(X_29,nil),cons(Y,nil))) != cons(X_30,cons(X_29,cons(Y,nil)))
    | append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) = cons(X_30,cons(X_29,cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(append(cons(X_30,cons(X_29,nil)),cons(Y,nil)),cons(X_30,append(cons(X_29,nil),cons(Y,nil)))) )],[refute_0_370,refute_0_371]) ).

cnf(refute_0_373,plain,
    append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) = cons(X_30,cons(X_29,cons(Y,nil))),
    inference(resolve,[$cnf( $equal(cons(X_30,append(cons(X_29,nil),cons(Y,nil))),cons(X_30,cons(X_29,cons(Y,nil)))) )],[refute_0_369,refute_0_372]) ).

cnf(refute_0_374,plain,
    ( append(cons(X_30,cons(X_29,nil)),cons(Y,nil)) != cons(X_30,cons(X_29,cons(Y,nil)))
    | rev(cons(Y,cons(X_29,cons(X_30,nil)))) != append(cons(X_30,cons(X_29,nil)),cons(Y,nil))
    | rev(cons(Y,cons(X_29,cons(X_30,nil)))) = cons(X_30,cons(X_29,cons(Y,nil))) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(Y,cons(X_29,cons(X_30,nil)))),append(cons(X_30,cons(X_29,nil)),cons(Y,nil))) ),[1],$fot(cons(X_30,cons(X_29,cons(Y,nil))))]]) ).

cnf(refute_0_375,plain,
    ( rev(cons(Y,cons(X_29,cons(X_30,nil)))) != append(cons(X_30,cons(X_29,nil)),cons(Y,nil))
    | rev(cons(Y,cons(X_29,cons(X_30,nil)))) = cons(X_30,cons(X_29,cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(append(cons(X_30,cons(X_29,nil)),cons(Y,nil)),cons(X_30,cons(X_29,cons(Y,nil)))) )],[refute_0_373,refute_0_374]) ).

cnf(refute_0_376,plain,
    rev(cons(Y,cons(X_29,cons(X_30,nil)))) = cons(X_30,cons(X_29,cons(Y,nil))),
    inference(resolve,[$cnf( $equal(rev(cons(Y,cons(X_29,cons(X_30,nil)))),append(cons(X_30,cons(X_29,nil)),cons(Y,nil))) )],[refute_0_357,refute_0_375]) ).

cnf(refute_0_377,plain,
    rev(cons(X_33,cons(X_34,cons(X_35,nil)))) = cons(X_35,cons(X_34,cons(X_33,nil))),
    inference(subst,[],[refute_0_376:[bind(Y,$fot(X_33)),bind(X_29,$fot(X_34)),bind(X_30,$fot(X_35))]]) ).

cnf(refute_0_378,plain,
    ( rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) != append(rev(cons(X_33,cons(X_34,cons(X_35,nil)))),cons(Y,nil))
    | rev(cons(X_33,cons(X_34,cons(X_35,nil)))) != cons(X_35,cons(X_34,cons(X_33,nil)))
    | rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))),append(rev(cons(X_33,cons(X_34,cons(X_35,nil)))),cons(Y,nil))) ),[1,0],$fot(cons(X_35,cons(X_34,cons(X_33,nil))))]]) ).

cnf(refute_0_379,plain,
    ( rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) != append(rev(cons(X_33,cons(X_34,cons(X_35,nil)))),cons(Y,nil))
    | rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(rev(cons(X_33,cons(X_34,cons(X_35,nil)))),cons(X_35,cons(X_34,cons(X_33,nil)))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)),
    inference(resolve,[$cnf( $equal(rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))),append(rev(cons(X_33,cons(X_34,cons(X_35,nil)))),cons(Y,nil))) )],[refute_0_327,refute_0_379]) ).

cnf(refute_0_381,plain,
    cons(X_33,append(nil,cons(Y,nil))) = cons(X_33,append(nil,cons(Y,nil))),
    introduced(tautology,[refl,[$fot(cons(X_33,append(nil,cons(Y,nil))))]]) ).

cnf(refute_0_382,plain,
    ( cons(X_33,append(nil,cons(Y,nil))) != cons(X_33,append(nil,cons(Y,nil)))
    | append(nil,cons(Y,nil)) != cons(Y,nil)
    | cons(X_33,append(nil,cons(Y,nil))) = cons(X_33,cons(Y,nil)) ),
    introduced(tautology,[equality,[$cnf( $equal(cons(X_33,append(nil,cons(Y,nil))),cons(X_33,append(nil,cons(Y,nil)))) ),[1,1],$fot(cons(Y,nil))]]) ).

cnf(refute_0_383,plain,
    ( append(nil,cons(Y,nil)) != cons(Y,nil)
    | cons(X_33,append(nil,cons(Y,nil))) = cons(X_33,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(cons(X_33,append(nil,cons(Y,nil))),cons(X_33,append(nil,cons(Y,nil)))) )],[refute_0_381,refute_0_382]) ).

cnf(refute_0_384,plain,
    cons(X_33,append(nil,cons(Y,nil))) = cons(X_33,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(append(nil,cons(Y,nil)),cons(Y,nil)) )],[refute_0_342,refute_0_383]) ).

cnf(refute_0_385,plain,
    append(cons(X_33,nil),cons(Y,nil)) = cons(X_33,append(nil,cons(Y,nil))),
    inference(subst,[],[axiom_016:[bind(Xs,$fot(nil)),bind(Y,$fot(cons(Y,nil))),bind(Z,$fot(X_33))]]) ).

cnf(refute_0_386,plain,
    ( cons(X_33,append(nil,cons(Y,nil))) != cons(X_33,cons(Y,nil))
    | append(cons(X_33,nil),cons(Y,nil)) != cons(X_33,append(nil,cons(Y,nil)))
    | append(cons(X_33,nil),cons(Y,nil)) = cons(X_33,cons(Y,nil)) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(append(cons(X_33,nil),cons(Y,nil)))),bind(Y0,$fot(cons(X_33,append(nil,cons(Y,nil))))),bind(Z0,$fot(cons(X_33,cons(Y,nil))))]]) ).

cnf(refute_0_387,plain,
    ( cons(X_33,append(nil,cons(Y,nil))) != cons(X_33,cons(Y,nil))
    | append(cons(X_33,nil),cons(Y,nil)) = cons(X_33,cons(Y,nil)) ),
    inference(resolve,[$cnf( $equal(append(cons(X_33,nil),cons(Y,nil)),cons(X_33,append(nil,cons(Y,nil)))) )],[refute_0_385,refute_0_386]) ).

cnf(refute_0_388,plain,
    append(cons(X_33,nil),cons(Y,nil)) = cons(X_33,cons(Y,nil)),
    inference(resolve,[$cnf( $equal(cons(X_33,append(nil,cons(Y,nil))),cons(X_33,cons(Y,nil))) )],[refute_0_384,refute_0_387]) ).

cnf(refute_0_389,plain,
    cons(X_34,append(cons(X_33,nil),cons(Y,nil))) = cons(X_34,append(cons(X_33,nil),cons(Y,nil))),
    introduced(tautology,[refl,[$fot(cons(X_34,append(cons(X_33,nil),cons(Y,nil))))]]) ).

cnf(refute_0_390,plain,
    ( cons(X_34,append(cons(X_33,nil),cons(Y,nil))) != cons(X_34,append(cons(X_33,nil),cons(Y,nil)))
    | append(cons(X_33,nil),cons(Y,nil)) != cons(X_33,cons(Y,nil))
    | cons(X_34,append(cons(X_33,nil),cons(Y,nil))) = cons(X_34,cons(X_33,cons(Y,nil))) ),
    introduced(tautology,[equality,[$cnf( $equal(cons(X_34,append(cons(X_33,nil),cons(Y,nil))),cons(X_34,append(cons(X_33,nil),cons(Y,nil)))) ),[1,1],$fot(cons(X_33,cons(Y,nil)))]]) ).

cnf(refute_0_391,plain,
    ( append(cons(X_33,nil),cons(Y,nil)) != cons(X_33,cons(Y,nil))
    | cons(X_34,append(cons(X_33,nil),cons(Y,nil))) = cons(X_34,cons(X_33,cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(cons(X_34,append(cons(X_33,nil),cons(Y,nil))),cons(X_34,append(cons(X_33,nil),cons(Y,nil)))) )],[refute_0_389,refute_0_390]) ).

cnf(refute_0_392,plain,
    cons(X_34,append(cons(X_33,nil),cons(Y,nil))) = cons(X_34,cons(X_33,cons(Y,nil))),
    inference(resolve,[$cnf( $equal(append(cons(X_33,nil),cons(Y,nil)),cons(X_33,cons(Y,nil))) )],[refute_0_388,refute_0_391]) ).

cnf(refute_0_393,plain,
    append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) = cons(X_34,append(cons(X_33,nil),cons(Y,nil))),
    inference(subst,[],[axiom_016:[bind(Xs,$fot(cons(X_33,nil))),bind(Y,$fot(cons(Y,nil))),bind(Z,$fot(X_34))]]) ).

cnf(refute_0_394,plain,
    ( cons(X_34,append(cons(X_33,nil),cons(Y,nil))) != cons(X_34,cons(X_33,cons(Y,nil)))
    | append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) != cons(X_34,append(cons(X_33,nil),cons(Y,nil)))
    | append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) = cons(X_34,cons(X_33,cons(Y,nil))) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(append(cons(X_34,cons(X_33,nil)),cons(Y,nil)))),bind(Y0,$fot(cons(X_34,append(cons(X_33,nil),cons(Y,nil))))),bind(Z0,$fot(cons(X_34,cons(X_33,cons(Y,nil)))))]]) ).

cnf(refute_0_395,plain,
    ( cons(X_34,append(cons(X_33,nil),cons(Y,nil))) != cons(X_34,cons(X_33,cons(Y,nil)))
    | append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) = cons(X_34,cons(X_33,cons(Y,nil))) ),
    inference(resolve,[$cnf( $equal(append(cons(X_34,cons(X_33,nil)),cons(Y,nil)),cons(X_34,append(cons(X_33,nil),cons(Y,nil)))) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) = cons(X_34,cons(X_33,cons(Y,nil))),
    inference(resolve,[$cnf( $equal(cons(X_34,append(cons(X_33,nil),cons(Y,nil))),cons(X_34,cons(X_33,cons(Y,nil)))) )],[refute_0_392,refute_0_395]) ).

cnf(refute_0_397,plain,
    cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) = cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))),
    introduced(tautology,[refl,[$fot(cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))))]]) ).

cnf(refute_0_398,plain,
    ( cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) != cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil)))
    | append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) != cons(X_34,cons(X_33,cons(Y,nil)))
    | cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))) ),
    introduced(tautology,[equality,[$cnf( $equal(cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))),cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil)))) ),[1,1],$fot(cons(X_34,cons(X_33,cons(Y,nil))))]]) ).

cnf(refute_0_399,plain,
    ( append(cons(X_34,cons(X_33,nil)),cons(Y,nil)) != cons(X_34,cons(X_33,cons(Y,nil)))
    | cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))) ),
    inference(resolve,[$cnf( $equal(cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))),cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil)))) )],[refute_0_397,refute_0_398]) ).

cnf(refute_0_400,plain,
    cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))),
    inference(resolve,[$cnf( $equal(append(cons(X_34,cons(X_33,nil)),cons(Y,nil)),cons(X_34,cons(X_33,cons(Y,nil)))) )],[refute_0_396,refute_0_399]) ).

cnf(refute_0_401,plain,
    append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) = cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))),
    inference(subst,[],[axiom_016:[bind(Xs,$fot(cons(X_34,cons(X_33,nil)))),bind(Y,$fot(cons(Y,nil))),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_402,plain,
    ( cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) != cons(X_35,cons(X_34,cons(X_33,cons(Y,nil))))
    | append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) != cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil)))
    | append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)))),bind(Y0,$fot(cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))))),bind(Z0,$fot(cons(X_35,cons(X_34,cons(X_33,cons(Y,nil))))))]]) ).

cnf(refute_0_403,plain,
    ( cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))) != cons(X_35,cons(X_34,cons(X_33,cons(Y,nil))))
    | append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))) ),
    inference(resolve,[$cnf( $equal(append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)),cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil)))) )],[refute_0_401,refute_0_402]) ).

cnf(refute_0_404,plain,
    append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))),
    inference(resolve,[$cnf( $equal(cons(X_35,append(cons(X_34,cons(X_33,nil)),cons(Y,nil))),cons(X_35,cons(X_34,cons(X_33,cons(Y,nil))))) )],[refute_0_400,refute_0_403]) ).

cnf(refute_0_405,plain,
    ( append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)) != cons(X_35,cons(X_34,cons(X_33,cons(Y,nil))))
    | rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) != append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil))
    | rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))) ),
    introduced(tautology,[equality,[$cnf( $equal(rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))),append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil))) ),[1],$fot(cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))))]]) ).

cnf(refute_0_406,plain,
    ( rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) != append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil))
    | rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))) ),
    inference(resolve,[$cnf( $equal(append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil)),cons(X_35,cons(X_34,cons(X_33,cons(Y,nil))))) )],[refute_0_404,refute_0_405]) ).

cnf(refute_0_407,plain,
    rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))) = cons(X_35,cons(X_34,cons(X_33,cons(Y,nil)))),
    inference(resolve,[$cnf( $equal(rev(cons(Y,cons(X_33,cons(X_34,cons(X_35,nil))))),append(cons(X_35,cons(X_34,cons(X_33,nil))),cons(Y,nil))) )],[refute_0_380,refute_0_406]) ).

cnf(refute_0_408,plain,
    rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil)))),
    inference(subst,[],[refute_0_407:[bind(Y,$fot(s(s(s(X_3137))))),bind(X_33,$fot(s(s(z)))),bind(X_34,$fot(s(z))),bind(X_35,$fot(z))]]) ).

cnf(refute_0_409,plain,
    sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),
    introduced(tautology,[refl,[$fot(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))))]]) ).

cnf(refute_0_410,plain,
    ( rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) != sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))))
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) ),
    introduced(tautology,[equality,[$cnf( $equal(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))))) ),[1,0],$fot(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil)))))]]) ).

cnf(refute_0_411,plain,
    ( rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) ),
    inference(resolve,[$cnf( $equal(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))))) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))),
    inference(resolve,[$cnf( $equal(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) )],[refute_0_408,refute_0_411]) ).

cnf(refute_0_413,plain,
    ( sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) != btrue
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) != sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil)))))
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))))),bind(Y0,$fot(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_414,plain,
    ( sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))) != btrue
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = btrue ),
    inference(resolve,[$cnf( $equal(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil)))))) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = btrue,
    inference(resolve,[$cnf( $equal(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X_3137))),nil))))),btrue) )],[refute_0_326,refute_0_414]) ).

cnf(refute_0_416,plain,
    eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),
    introduced(tautology,[refl,[$fot(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue))]]) ).

cnf(refute_0_417,plain,
    ( eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) != eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue)
    | sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) != btrue
    | eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = eq2(btrue,btrue) ),
    introduced(tautology,[equality,[$cnf( $equal(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue)) ),[1,0],$fot(btrue)]]) ).

cnf(refute_0_418,plain,
    ( sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) != btrue
    | eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = eq2(btrue,btrue) ),
    inference(resolve,[$cnf( $equal(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue)) )],[refute_0_416,refute_0_417]) ).

cnf(refute_0_419,plain,
    eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = eq2(btrue,btrue),
    inference(resolve,[$cnf( $equal(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) )],[refute_0_415,refute_0_418]) ).

cnf(refute_0_420,plain,
    ( eq2(btrue,btrue) != btrue
    | eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) != eq2(btrue,btrue)
    | eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = btrue ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue))),bind(Y0,$fot(eq2(btrue,btrue))),bind(Z0,$fot(btrue))]]) ).

cnf(refute_0_421,plain,
    ( eq2(btrue,btrue) != btrue
    | eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = btrue ),
    inference(resolve,[$cnf( $equal(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),eq2(btrue,btrue)) )],[refute_0_419,refute_0_420]) ).

cnf(refute_0_422,plain,
    eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = btrue,
    inference(resolve,[$cnf( $equal(eq2(btrue,btrue),btrue) )],[refute_0_226,refute_0_421]) ).

cnf(refute_0_423,plain,
    impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
    introduced(tautology,[refl,[$fot(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))))]]) ).

cnf(refute_0_424,plain,
    ( eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) != btrue
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) ),
    introduced(tautology,[equality,[$cnf( $equal(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) ),[1,0],$fot(btrue)]]) ).

cnf(refute_0_425,plain,
    ( eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) != btrue
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) ),
    inference(resolve,[$cnf( $equal(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) )],[refute_0_423,refute_0_424]) ).

cnf(refute_0_426,plain,
    impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
    inference(resolve,[$cnf( $equal(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),btrue) )],[refute_0_422,refute_0_425]) ).

cnf(refute_0_427,plain,
    ( impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != impl(btrue,bfalse)
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,bfalse) ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))))),bind(Y0,$fot(impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))))),bind(Z0,$fot(impl(btrue,bfalse)))]]) ).

cnf(refute_0_428,plain,
    ( impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != impl(btrue,bfalse)
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,bfalse) ),
    inference(resolve,[$cnf( $equal(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) )],[refute_0_426,refute_0_427]) ).

cnf(refute_0_429,plain,
    impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,bfalse),
    inference(resolve,[$cnf( $equal(impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(btrue,bfalse)) )],[refute_0_240,refute_0_428]) ).

cnf(refute_0_430,plain,
    ( impl(btrue,bfalse) != bfalse
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != impl(btrue,bfalse)
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse ),
    inference(subst,[],[refute_0_111:[bind(X0,$fot(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))))),bind(Y0,$fot(impl(btrue,bfalse))),bind(Z0,$fot(bfalse))]]) ).

cnf(refute_0_431,plain,
    ( impl(btrue,bfalse) != bfalse
    | impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse ),
    inference(resolve,[$cnf( $equal(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),impl(btrue,bfalse)) )],[refute_0_429,refute_0_430]) ).

cnf(refute_0_432,plain,
    impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
    inference(resolve,[$cnf( $equal(impl(btrue,bfalse),bfalse) )],[refute_0_162,refute_0_431]) ).

cnf(refute_0_433,plain,
    ( impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) != bfalse
    | psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = bfalse ),
    introduced(tautology,[equality,[$cnf( $equal(psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) ),[1],$fot(bfalse)]]) ).

cnf(refute_0_434,plain,
    ( psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))
    | psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = bfalse ),
    inference(resolve,[$cnf( $equal(impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),bfalse) )],[refute_0_432,refute_0_433]) ).

cnf(refute_0_435,plain,
    psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = bfalse,
    inference(resolve,[$cnf( $equal(psorted_rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),impl(eq2(sorted(rev(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X_3137))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)))) )],[refute_0_161,refute_0_434]) ).

cnf(refute_0_436,plain,
    psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = bfalse,
    inference(subst,[],[refute_0_435:[bind(X_3137,$fot(X_3138))]]) ).

cnf(refute_0_437,plain,
    ( eq2(bfalse,bfalse) != btrue
    | psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))) != bfalse
    | eq2(psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse) = btrue ),
    introduced(tautology,[equality,[$cnf( ~ $equal(eq2(psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse),btrue) ),[0,0],$fot(bfalse)]]) ).

cnf(refute_0_438,plain,
    ( eq2(bfalse,bfalse) != btrue
    | eq2(psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse) = btrue ),
    inference(resolve,[$cnf( $equal(psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse) )],[refute_0_436,refute_0_437]) ).

cnf(refute_0_439,plain,
    eq2(bfalse,bfalse) != btrue,
    inference(resolve,[$cnf( $equal(eq2(psorted_rev(cons(s(s(s(X_3138))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse),btrue) )],[refute_0_438,refute_0_0]) ).

cnf(refute_0_440,plain,
    eq2(bfalse,bfalse) = btrue,
    inference(subst,[],[axiom_031:[bind(X,$fot(bfalse))]]) ).

cnf(refute_0_441,plain,
    ( btrue != btrue
    | eq2(bfalse,bfalse) != btrue
    | eq2(bfalse,bfalse) = btrue ),
    introduced(tautology,[equality,[$cnf( $equal(eq2(bfalse,bfalse),btrue) ),[1],$fot(btrue)]]) ).

cnf(refute_0_442,plain,
    ( btrue != btrue
    | eq2(bfalse,bfalse) = btrue ),
    inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_440,refute_0_441]) ).

cnf(refute_0_443,plain,
    btrue != btrue,
    inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_442,refute_0_439]) ).

cnf(refute_0_444,plain,
    btrue = btrue,
    introduced(tautology,[refl,[$fot(btrue)]]) ).

cnf(refute_0_445,plain,
    $false,
    inference(resolve,[$cnf( $equal(btrue,btrue) )],[refute_0_444,refute_0_443]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWX203-1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.16/0.34  % Computer : n023.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue May  5 11:27:38 EDT 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.96/8.19  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.96/8.19  
% 7.96/8.19  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.03/8.29  
%------------------------------------------------------------------------------