0.11/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.12/0.33	% Computer : n018.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 960
0.12/0.33	% WCLimit  : 120
0.12/0.33	% DateTime : Tue Aug  9 06:33:15 EDT 2022
0.12/0.33	% CPUTime  : 
19.85/19.80	% SZS status Theorem
19.85/19.80	% Mode: cade22grackle2xfaf3
19.85/19.80	% Steps: 12035
19.85/19.80	% SZS output start Proof
19.85/19.80	thf(ty_union, type, union : ($i>$i)).
19.85/19.80	thf(ty_eigen__1, type, eigen__1 : $i).
19.85/19.80	thf(ty_eigen__0, type, eigen__0 : $i).
19.85/19.80	thf(ty_emptyset, type, emptyset : $i).
19.85/19.80	thf(ty_repl, type, repl : ($i>($i>$i)>$i)).
19.85/19.80	thf(ty_eps, type, eps : (($i>$o)>$i)).
19.85/19.80	thf(ty_power, type, power : ($i>$i)).
19.85/19.80	thf(ty_univof, type, univof : ($i>$i)).
19.85/19.80	thf(ty_in, type, in : ($i>$i>$o)).
19.85/19.80	thf(sP1,plain,sP1 <=> (![X1:$i]:(((union @ ((repl @ (power @ (power @ emptyset))) @ (^[X2:$i]:(eps @ (^[X3:$i]:((((in @ emptyset) @ X2) => (~((X3 = eigen__0)))) => (~(((~(((in @ emptyset) @ X2))) => (~((X3 = ((repl @ (power @ (power @ emptyset))) @ (^[X4:$i]:(eps @ (^[X5:$i]:((((in @ emptyset) @ X4) => (~((X5 = eigen__0)))) => (~(((~(((in @ emptyset) @ X4))) => (~((X5 = eigen__0))))))))))))))))))))))) = (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X2:$i]:(eps @ (^[X3:$i]:((((in @ emptyset) @ X2) => (~((X3 = X1)))) => (~(((~(((in @ emptyset) @ X2))) => (~((X3 = ((repl @ (power @ (power @ emptyset))) @ (^[X4:$i]:(eps @ (^[X5:$i]:((((in @ emptyset) @ X4) => (~((X5 = X1)))) => (~(((~(((in @ emptyset) @ X4))) => (~((X5 = X1)))))))))))))))))))))))) => (eigen__0 = X1))),introduced(definition,[new_symbols(definition,[sP1])])).
19.85/19.80	thf(sP2,plain,sP2 <=> (((union @ ((repl @ (power @ (power @ emptyset))) @ (^[X1:$i]:(eps @ (^[X2:$i]:((((in @ emptyset) @ X1) => (~((X2 = eigen__0)))) => (~(((~(((in @ emptyset) @ X1))) => (~((X2 = ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = eigen__0)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = eigen__0))))))))))))))))))))))) = (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X1:$i]:(eps @ (^[X2:$i]:((((in @ emptyset) @ X1) => (~((X2 = eigen__1)))) => (~(((~(((in @ emptyset) @ X1))) => (~((X2 = ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = eigen__1)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = eigen__1)))))))))))))))))))))))) => (eigen__0 = eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])).
19.85/19.80	thf(sP3,plain,sP3 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP3])])).
19.85/19.80	thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:(((union @ ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = X1)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = ((repl @ (power @ (power @ emptyset))) @ (^[X5:$i]:(eps @ (^[X6:$i]:((((in @ emptyset) @ X5) => (~((X6 = X1)))) => (~(((~(((in @ emptyset) @ X5))) => (~((X6 = X1))))))))))))))))))))))) = (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = X2)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = ((repl @ (power @ (power @ emptyset))) @ (^[X5:$i]:(eps @ (^[X6:$i]:((((in @ emptyset) @ X5) => (~((X6 = X2)))) => (~(((~(((in @ emptyset) @ X5))) => (~((X6 = X2)))))))))))))))))))))))) => (X1 = X2)))),introduced(definition,[new_symbols(definition,[sP4])])).
19.85/19.80	thf(sP5,plain,sP5 <=> ((union @ ((repl @ (power @ (power @ emptyset))) @ (^[X1:$i]:(eps @ (^[X2:$i]:((((in @ emptyset) @ X1) => (~((X2 = eigen__0)))) => (~(((~(((in @ emptyset) @ X1))) => (~((X2 = ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = eigen__0)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = eigen__0))))))))))))))))))))))) = (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X1:$i]:(eps @ (^[X2:$i]:((((in @ emptyset) @ X1) => (~((X2 = eigen__1)))) => (~(((~(((in @ emptyset) @ X1))) => (~((X2 = ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = eigen__1)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = eigen__1)))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
19.85/19.80	thf(def_is_of,definition,(is_of = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
19.85/19.80	thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((is_of @ X3) @ X1)) @ (X2 @ X3))))))).
19.85/19.80	thf(def_d_Subq,definition,(d_Subq = (^[X1:$i]:(^[X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((in @ X3) @ X1)) @ ((in @ X3) @ X2))))))).
19.85/19.80	thf(def_d_Union_closed,definition,(d_Union_closed = (^[X1:$i]:(![X2:$i]:(((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ ((in @ X2) @ X1)) @ ((in @ (union @ X2)) @ X1)))))).
19.85/19.80	thf(def_d_Power_closed,definition,(d_Power_closed = (^[X1:$i]:(![X2:$i]:(((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ ((in @ X2) @ X1)) @ ((in @ (power @ X2)) @ X1)))))).
19.85/19.80	thf(def_d_Repl_closed,definition,(d_Repl_closed = (^[X1:$i]:(![X2:$i]:(((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ ((in @ X2) @ X1)) @ (![X3:$i>$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ (![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((in @ X4) @ X2)) @ ((in @ (X3 @ X4)) @ X1)))) @ ((in @ ((repl @ X2) @ X3)) @ X1)))))))).
19.85/19.80	thf(def_d_ZF_closed,definition,(d_ZF_closed = (^[X1:$i]:(((d_Union_closed @ X1) & (d_Power_closed @ X1)) & (d_Repl_closed @ X1))))).
19.85/19.80	thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(eps @ (^[X4:$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))).
19.85/19.80	thf(def_nIn,definition,(nIn = (^[X1:$i]:(^[X2:$i]:((~) @ ((in @ X1) @ X2)))))).
19.85/19.80	thf(def_d_UPair,definition,(d_UPair = (^[X1:$i]:(^[X2:$i]:((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(((if @ ((in @ emptyset) @ X3)) @ X1) @ X2))))))).
19.85/19.80	thf(def_d_Sing,definition,(d_Sing = (^[X1:$i]:((d_UPair @ X1) @ X1)))).
19.85/19.80	thf(def_binunion,definition,(binunion = (^[X1:$i]:(^[X2:$i]:(union @ ((d_UPair @ X1) @ X2)))))).
19.85/19.80	thf(def_famunion,definition,(famunion = (^[X1:$i]:(^[X2:$i>$i]:(union @ ((repl @ X1) @ X2)))))).
19.85/19.80	thf(def_d_Sep,definition,(d_Sep = (^[X1:$i]:(^[X2:$i>$o]:(((if @ (?[X3:$i]:(((in @ X3) @ X1) & (X2 @ X3)))) @ ((repl @ X1) @ (^[X3:$i]:(((if @ (X2 @ X3)) @ X3) @ (eps @ (^[X4:$i]:(((in @ X4) @ X1) & (X2 @ X4)))))))) @ emptyset))))).
19.85/19.80	thf(def_d_ReplSep,definition,(d_ReplSep = (^[X1:$i]:(^[X2:$i>$o]:(repl @ ((d_Sep @ X1) @ X2)))))).
19.85/19.80	thf(def_setminus,definition,(setminus = (^[X1:$i]:(^[X2:$i]:((d_Sep @ X1) @ (^[X3:$i]:((nIn @ X3) @ X2))))))).
19.85/19.80	thf(def_d_In_rec_G,definition,(d_In_rec_G = (^[X1:$i>($i>$i)>$i]:(^[X2:$i]:(^[X3:$i]:(![X4:$i>$i>$o]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (![X5:$i]:(![X6:$i>$i]:(((^[X7:$o]:(^[X8:$o]:(X7 => X8))) @ (![X7:$i]:(((^[X8:$o]:(^[X9:$o]:(X8 => X9))) @ ((in @ X7) @ X5)) @ ((X4 @ X7) @ (X6 @ X7))))) @ ((X4 @ X5) @ ((X1 @ X5) @ X6)))))) @ ((X4 @ X2) @ X3)))))))).
19.85/19.80	thf(def_d_In_rec,definition,(d_In_rec = (^[X1:$i>($i>$i)>$i]:(^[X2:$i]:(eps @ ((d_In_rec_G @ X1) @ X2)))))).
19.85/19.80	thf(def_ordsucc,definition,(ordsucc = (^[X1:$i]:((binunion @ X1) @ (d_Sing @ X1))))).
19.85/19.80	thf(def_nat_p,definition,(nat_p = (^[X1:$i]:(![X2:$i>$o]:(((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ (X2 @ emptyset)) @ (((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ (![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ (X2 @ X3)) @ (X2 @ (ordsucc @ X3))))) @ (X2 @ X1))))))).
19.85/19.80	thf(def_omega,definition,(omega = ((d_Sep @ (univof @ emptyset)) @ nat_p))).
19.85/19.80	thf(def_d_Inj1,definition,(d_Inj1 = (d_In_rec @ (^[X1:$i]:(^[X2:$i>$i]:((binunion @ (d_Sing @ emptyset)) @ ((repl @ X1) @ X2))))))).
19.85/19.80	thf(def_d_Inj0,definition,(d_Inj0 = (^[X1:$i]:((repl @ X1) @ d_Inj1)))).
19.85/19.80	thf(def_d_Unj,definition,(d_Unj = (d_In_rec @ (^[X1:$i]:(repl @ ((setminus @ X1) @ (d_Sing @ emptyset))))))).
19.85/19.80	thf(def_pair,definition,(pair = (^[X1:$i]:(^[X2:$i]:((binunion @ ((repl @ X1) @ d_Inj0)) @ ((repl @ X2) @ d_Inj1)))))).
19.85/19.80	thf(def_proj0,definition,(proj0 = (^[X1:$i]:(((d_ReplSep @ X1) @ (^[X2:$i]:(?[X3:$i]:((d_Inj0 @ X3) = X2)))) @ d_Unj)))).
19.85/19.80	thf(def_proj1,definition,(proj1 = (^[X1:$i]:(((d_ReplSep @ X1) @ (^[X2:$i]:(?[X3:$i]:((d_Inj1 @ X3) = X2)))) @ d_Unj)))).
19.85/19.80	thf(def_d_Sigma,definition,(d_Sigma = (^[X1:$i]:(^[X2:$i>$i]:((famunion @ X1) @ (^[X3:$i]:((repl @ (X2 @ X3)) @ (pair @ X3)))))))).
19.85/19.80	thf(def_setprod,definition,(setprod = (^[X1:$i]:(^[X2:$i]:((d_Sigma @ X1) @ (^[X3:$i]:X2)))))).
19.85/19.80	thf(def_ap,definition,(ap = (^[X1:$i]:(^[X2:$i]:(((d_ReplSep @ X1) @ (^[X3:$i]:(?[X4:$i]:(X3 = ((pair @ X2) @ X4))))) @ proj1))))).
19.85/19.80	thf(def_pair_p,definition,(pair_p = (^[X1:$i]:(((pair @ ((ap @ X1) @ emptyset)) @ ((ap @ X1) @ (ordsucc @ emptyset))) = X1)))).
19.85/19.80	thf(def_d_Pi,definition,(d_Pi = (^[X1:$i]:(^[X2:$i>$i]:((d_Sep @ (power @ ((d_Sigma @ X1) @ (^[X3:$i]:(union @ (X2 @ X3)))))) @ (^[X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((in @ X4) @ X1)) @ ((in @ ((ap @ X3) @ X4)) @ (X2 @ X4)))))))))).
19.85/19.80	thf(def_imp,definition,(imp = (^[X1:$o]:(^[X2:$o]:(((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ X1) @ X2))))).
19.85/19.80	thf(def_d_not,definition,(d_not = (^[X1:$o]:((imp @ X1) @ $false)))).
19.85/19.80	thf(def_wel,definition,(wel = (^[X1:$o]:(d_not @ (d_not @ X1))))).
19.85/19.80	thf(def_obvious,definition,(obvious = ((imp @ $false) @ $false))).
19.85/19.80	thf(def_l_ec,definition,(l_ec = (^[X1:$o]:(^[X2:$o]:((imp @ X1) @ (d_not @ X2)))))).
19.85/19.80	thf(def_d_and,definition,(d_and = (^[X1:$o]:(^[X2:$o]:(d_not @ ((l_ec @ X1) @ X2)))))).
19.85/19.80	thf(def_l_or,definition,(l_or = (^[X1:$o]:(imp @ (d_not @ X1))))).
19.85/19.80	thf(def_orec,definition,(orec = (^[X1:$o]:(^[X2:$o]:((d_and @ ((l_or @ X1) @ X2)) @ ((l_ec @ X1) @ X2)))))).
19.85/19.80	thf(def_l_iff,definition,(l_iff = (^[X1:$o]:(^[X2:$o]:((d_and @ ((imp @ X1) @ X2)) @ ((imp @ X2) @ X1)))))).
19.85/19.80	thf(def_all,definition,(all = (^[X1:$i]:(all_of @ (^[X2:$i]:((in @ X2) @ X1)))))).
19.85/19.80	thf(def_non,definition,(non = (^[X1:$i]:(^[X2:$i>$o]:(^[X3:$i]:(d_not @ (X2 @ X3))))))).
19.85/19.80	thf(def_l_some,definition,(l_some = (^[X1:$i]:(^[X2:$i>$o]:(d_not @ ((all_of @ (^[X3:$i]:((in @ X3) @ X1))) @ ((non @ X1) @ X2))))))).
19.85/19.80	thf(def_or3,definition,(or3 = (^[X1:$o]:(^[X2:$o]:(^[X3:$o]:((l_or @ X1) @ ((l_or @ X2) @ X3))))))).
19.85/19.80	thf(def_and3,definition,(and3 = (^[X1:$o]:(^[X2:$o]:(^[X3:$o]:((d_and @ X1) @ ((d_and @ X2) @ X3))))))).
19.85/19.80	thf(def_ec3,definition,(ec3 = (^[X1:$o]:(^[X2:$o]:(^[X3:$o]:(((and3 @ ((l_ec @ X1) @ X2)) @ ((l_ec @ X2) @ X3)) @ ((l_ec @ X3) @ X1))))))).
19.85/19.80	thf(def_orec3,definition,(orec3 = (^[X1:$o]:(^[X2:$o]:(^[X3:$o]:((d_and @ (((or3 @ X1) @ X2) @ X3)) @ (((ec3 @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_e_is,definition,(e_is = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(X2 = X3)))))).
19.85/19.80	thf(def_amone,definition,(amone = (^[X1:$i]:(^[X2:$i>$o]:((all_of @ (^[X3:$i]:((in @ X3) @ X1))) @ (^[X3:$i]:((all_of @ (^[X4:$i]:((in @ X4) @ X1))) @ (^[X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (X2 @ X3)) @ (((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (X2 @ X4)) @ (((e_is @ X1) @ X3) @ X4))))))))))).
19.85/19.80	thf(def_one,definition,(one = (^[X1:$i]:(^[X2:$i>$o]:((d_and @ ((amone @ X1) @ X2)) @ ((l_some @ X1) @ X2)))))).
19.85/19.80	thf(def_ind,definition,(ind = (^[X1:$i]:(^[X2:$i>$o]:(eps @ (^[X3:$i]:(((in @ X3) @ X1) & (X2 @ X3)))))))).
19.85/19.80	thf(def_injective,definition,(injective = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((all @ X1) @ (^[X4:$i]:((all @ X1) @ (^[X5:$i]:((imp @ (((e_is @ X2) @ ((ap @ X3) @ X4)) @ ((ap @ X3) @ X5))) @ (((e_is @ X1) @ X4) @ X5))))))))))).
19.85/19.80	thf(def_image,definition,(image = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((l_some @ X1) @ (^[X5:$i]:(((e_is @ X2) @ X4) @ ((ap @ X3) @ X5)))))))))).
19.85/19.80	thf(def_tofs,definition,(tofs = (^[X1:$i]:(^[X2:$i]:ap)))).
19.85/19.80	thf(def_soft,definition,(soft = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((ind @ X1) @ (^[X5:$i]:(((e_is @ X2) @ X4) @ ((ap @ X3) @ X5)))))))))).
19.85/19.80	thf(def_inverse,definition,(inverse = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((d_Sigma @ X2) @ (^[X4:$i]:(((if @ ((((image @ X1) @ X2) @ X3) @ X4)) @ ((((soft @ X1) @ X2) @ X3) @ X4)) @ emptyset)))))))).
19.85/19.80	thf(def_surjective,definition,(surjective = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((all @ X2) @ (((image @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_bijective,definition,(bijective = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((d_and @ (((injective @ X1) @ X2) @ X3)) @ (((surjective @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_invf,definition,(invf = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((d_Sigma @ X2) @ (((soft @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_inj_h,definition,(inj_h = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:((d_Sigma @ X1) @ (^[X6:$i]:((ap @ X5) @ ((ap @ X4) @ X6))))))))))).
19.85/19.80	thf(def_e_in,definition,(e_in = (^[X1:$i]:(^[X2:$i>$o]:(^[X3:$i]:X3))))).
19.85/19.80	thf(def_out,definition,(out = (^[X1:$i]:(^[X2:$i>$o]:(((soft @ ((d_Sep @ X1) @ X2)) @ X1) @ ((d_Sigma @ ((d_Sep @ X1) @ X2)) @ ((e_in @ X1) @ X2))))))).
19.85/19.80	thf(def_d_pair,definition,(d_pair = (^[X1:$i]:(^[X2:$i]:pair)))).
19.85/19.80	thf(def_first,definition,(first = (^[X1:$i]:(^[X2:$i]:proj0)))).
19.85/19.80	thf(def_second,definition,(second = (^[X1:$i]:(^[X2:$i]:proj1)))).
19.85/19.80	thf(def_prop1,definition,(prop1 = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:((d_and @ ((imp @ X1) @ (((e_is @ X2) @ X5) @ X3))) @ ((imp @ (d_not @ X1)) @ (((e_is @ X2) @ X5) @ X4)))))))))).
19.85/19.80	thf(def_ite,definition,(ite = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((ind @ X2) @ ((((prop1 @ X1) @ X2) @ X3) @ X4)))))))).
19.85/19.80	thf(def_wissel_wa,definition,(wissel_wa = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((((ite @ (((e_is @ X1) @ X4) @ X2)) @ X1) @ X3) @ X4))))))).
19.85/19.80	thf(def_wissel_wb,definition,(wissel_wb = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((((ite @ (((e_is @ X1) @ X4) @ X3)) @ X1) @ X2) @ ((((wissel_wa @ X1) @ X2) @ X3) @ X4)))))))).
19.85/19.80	thf(def_wissel,definition,(wissel = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((d_Sigma @ X1) @ (((wissel_wb @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_changef,definition,(changef = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:((d_Sigma @ X1) @ (^[X6:$i]:((ap @ X3) @ ((ap @ (((wissel @ X1) @ X4) @ X5)) @ X6))))))))))).
19.85/19.80	thf(def_r_ec,definition,(r_ec = (^[X1:$o]:(^[X2:$o]:(((^[X3:$o]:(^[X4:$o]:(X3 => X4))) @ X1) @ (d_not @ X2)))))).
19.85/19.80	thf(def_esti,definition,(esti = (^[X1:$i]:in))).
19.85/19.80	thf(def_empty,definition,(empty = (^[X1:$i]:(^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ X1))) @ ((non @ X1) @ (^[X3:$i]:(((esti @ X1) @ X3) @ X2)))))))).
19.85/19.80	thf(def_nonempty,definition,(nonempty = (^[X1:$i]:(^[X2:$i]:((l_some @ X1) @ (^[X3:$i]:(((esti @ X1) @ X3) @ X2))))))).
19.85/19.80	thf(def_incl,definition,(incl = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((all @ X1) @ (^[X4:$i]:((imp @ (((esti @ X1) @ X4) @ X2)) @ (((esti @ X1) @ X4) @ X3))))))))).
19.85/19.80	thf(def_st_disj,definition,(st_disj = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((all @ X1) @ (^[X4:$i]:((l_ec @ (((esti @ X1) @ X4) @ X2)) @ (((esti @ X1) @ X4) @ X3))))))))).
19.85/19.80	thf(def_nissetprop,definition,(nissetprop = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((d_and @ (((esti @ X1) @ X4) @ X2)) @ (d_not @ (((esti @ X1) @ X4) @ X3))))))))).
19.85/19.80	thf(def_unmore,definition,(unmore = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((d_Sep @ X1) @ (^[X4:$i]:((l_some @ X2) @ (^[X5:$i]:(((esti @ X1) @ X4) @ ((ap @ X3) @ X5))))))))))).
19.85/19.80	thf(def_ecelt,definition,(ecelt = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:((d_Sep @ X1) @ (X2 @ X3))))))).
19.85/19.80	thf(def_ecp,definition,(ecp = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(((e_is @ (power @ X1)) @ X3) @ (((ecelt @ X1) @ X2) @ X4)))))))).
19.85/19.80	thf(def_anec,definition,(anec = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:((l_some @ X1) @ (((ecp @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_ect,definition,(ect = (^[X1:$i]:(^[X2:$i>$i>$o]:((d_Sep @ (power @ X1)) @ ((anec @ X1) @ X2)))))).
19.85/19.80	thf(def_ectset,definition,(ectset = (^[X1:$i]:(^[X2:$i>$i>$o]:((out @ (power @ X1)) @ ((anec @ X1) @ X2)))))).
19.85/19.80	thf(def_ectelt,definition,(ectelt = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(((ectset @ X1) @ X2) @ (((ecelt @ X1) @ X2) @ X3))))))).
19.85/19.80	thf(def_ecect,definition,(ecect = (^[X1:$i]:(^[X2:$i>$i>$o]:((e_in @ (power @ X1)) @ ((anec @ X1) @ X2)))))).
19.85/19.80	thf(def_fixfu,definition,(fixfu = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:((all_of @ (^[X5:$i]:((in @ X5) @ X1))) @ (^[X5:$i]:((all_of @ (^[X6:$i]:((in @ X6) @ X1))) @ (^[X6:$i]:(((^[X7:$o]:(^[X8:$o]:(X7 => X8))) @ ((X2 @ X5) @ X6)) @ (((e_is @ X3) @ ((ap @ X4) @ X5)) @ ((ap @ X4) @ X6))))))))))))).
19.85/19.80	thf(def_d_10_prop1,definition,(d_10_prop1 = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:(^[X6:$i]:(^[X7:$i]:((d_and @ (((esti @ X1) @ X7) @ (((ecect @ X1) @ X2) @ X5))) @ (((e_is @ X3) @ ((ap @ X4) @ X7)) @ X6))))))))))).
19.85/19.80	thf(def_prop2,definition,(prop2 = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:(^[X6:$i]:((l_some @ X1) @ ((((((d_10_prop1 @ X1) @ X2) @ X3) @ X4) @ X5) @ X6)))))))))).
19.85/19.80	thf(def_indeq,definition,(indeq = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:((ind @ X3) @ (((((prop2 @ X1) @ X2) @ X3) @ X4) @ X5))))))))).
19.85/19.80	thf(def_fixfu2,definition,(fixfu2 = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:((all_of @ (^[X5:$i]:((in @ X5) @ X1))) @ (^[X5:$i]:((all_of @ (^[X6:$i]:((in @ X6) @ X1))) @ (^[X6:$i]:((all_of @ (^[X7:$i]:((in @ X7) @ X1))) @ (^[X7:$i]:((all_of @ (^[X8:$i]:((in @ X8) @ X1))) @ (^[X8:$i]:(((^[X9:$o]:(^[X10:$o]:(X9 => X10))) @ ((X2 @ X5) @ X6)) @ (((^[X9:$o]:(^[X10:$o]:(X9 => X10))) @ ((X2 @ X7) @ X8)) @ (((e_is @ X3) @ ((ap @ ((ap @ X4) @ X5)) @ X7)) @ ((ap @ ((ap @ X4) @ X6)) @ X8)))))))))))))))))).
19.85/19.80	thf(def_d_11_i,definition,(d_11_i = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(((indeq @ X1) @ X2) @ ((d_Pi @ X1) @ (^[X4:$i]:X3)))))))).
19.85/19.80	thf(def_indeq2,definition,(indeq2 = (^[X1:$i]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:((((indeq @ X1) @ X2) @ X3) @ (((((d_11_i @ X1) @ X2) @ X3) @ X4) @ X5))))))))).
19.85/19.80	thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:((~) @ (X1 = emptyset)))))).
19.85/19.80	thf(def_n_is,definition,(n_is = (e_is @ nat))).
19.85/19.80	thf(def_nis,definition,(nis = (^[X1:$i]:(^[X2:$i]:(d_not @ ((n_is @ X1) @ X2)))))).
19.85/19.80	thf(def_n_in,definition,(n_in = (esti @ nat))).
19.85/19.80	thf(def_n_some,definition,(n_some = (l_some @ nat))).
19.85/19.80	thf(def_n_all,definition,(n_all = (all @ nat))).
19.85/19.80	thf(def_n_one,definition,(n_one = (one @ nat))).
19.85/19.80	thf(def_n_1,definition,(n_1 = (ordsucc @ emptyset))).
19.85/19.80	thf(def_cond1,definition,(cond1 = (n_in @ n_1))).
19.85/19.80	thf(def_cond2,definition,(cond2 = (^[X1:$i]:(n_all @ (^[X2:$i]:((imp @ ((n_in @ X2) @ X1)) @ ((n_in @ (ordsucc @ X2)) @ X1))))))).
19.85/19.80	thf(def_i1_s,definition,(i1_s = (d_Sep @ nat))).
19.85/19.80	thf(satz1,conjecture,(![X1:$i]:(((in @ X1) @ (eps @ (^[X2:$i]:(((~((![X3:$i]:(((in @ X3) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))))) => (~((X4 = ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X5)))) => (~((X6 = X5)))) => (~(((~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X5)))))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X9)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = X9)))))))))))))))))))))))))) => (X8 @ X7)))))))))))))))))))))))))) => (~(((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))) => (~((X4 = emptyset)))))))))) => (X3 = emptyset))))) => (~((X2 = ((repl @ (eps @ (^[X3:$i]:(((~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X4)))))))))) => (~((X3 = ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(eps @ (^[X5:$i]:(((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X4)))) => (~((X5 = X4)))) => (~(((~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X4)))))) => (~((X5 = (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X6)))))))))))))))))))))))))) => (~(((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X4)))))))) => (~((X3 = emptyset)))))))))) @ (^[X3:$i]:(eps @ (^[X4:$i]:(((~((X3 = emptyset))) => (~((X4 = X3)))) => (~(((X3 = emptyset) => (~((X4 = (eps @ (^[X5:$i]:(~((((in @ X5) @ (eps @ (^[X6:$i]:(((~((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X9)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = X9)))))))))))))))))))))))))) => (X8 @ X7)))))))))) => (~((X6 = ((repl @ (univof @ emptyset)) @ (^[X7:$i]:(eps @ (^[X8:$i]:(((![X9:$i>$o]:((X9 @ emptyset) => ((![X10:$i]:((X9 @ X10) => (X9 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X10)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = ((repl @ (power @ (power @ emptyset))) @ (^[X13:$i]:(eps @ (^[X14:$i]:((((in @ emptyset) @ X13) => (~((X14 = X10)))) => (~(((~(((in @ emptyset) @ X13))) => (~((X14 = X10)))))))))))))))))))))))))) => (X9 @ X7)))) => (~((X8 = X7)))) => (~(((~((![X9:$i>$o]:((X9 @ emptyset) => ((![X10:$i]:((X9 @ X10) => (X9 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X10)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = ((repl @ (power @ (power @ emptyset))) @ (^[X13:$i]:(eps @ (^[X14:$i]:((((in @ emptyset) @ X13) => (~((X14 = X10)))) => (~(((~(((in @ emptyset) @ X13))) => (~((X14 = X10)))))))))))))))))))))))))) => (X9 @ X7)))))) => (~((X8 = (eps @ (^[X9:$i]:(~((((in @ X9) @ (univof @ emptyset)) => (~((![X10:$i>$o]:((X10 @ emptyset) => ((![X11:$i]:((X10 @ X11) => (X10 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X11)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = ((repl @ (power @ (power @ emptyset))) @ (^[X14:$i]:(eps @ (^[X15:$i]:((((in @ emptyset) @ X14) => (~((X15 = X11)))) => (~(((~(((in @ emptyset) @ X14))) => (~((X15 = X11)))))))))))))))))))))))))) => (X10 @ X9)))))))))))))))))))))))))) => (~(((![X7:$i]:(((in @ X7) @ (univof @ emptyset)) => (~((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X9)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = X9)))))))))))))))))))))))))) => (X8 @ X7)))))))) => (~((X6 = emptyset)))))))))) => (X5 = emptyset))))))))))))))))))))) => (~(((![X3:$i]:(((in @ X3) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))))) => (~((X4 = ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X5)))) => (~((X6 = X5)))) => (~(((~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X5)))))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => 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19.85/19.81	thf(h2,assumption,((in @ eigen__0) @ (eps @ (^[X1:$i]:(((~((![X2:$i]:(((in @ X2) @ (eps @ (^[X3:$i]:(((~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X4)))))))))) => (~((X3 = ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(eps @ (^[X5:$i]:(((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ 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=> (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X3)))))) => (~((X4 = (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))))))))))))))))))))) => (~(((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((![X4:$i>$o]:((X4 @ emptyset) => ((![X5:$i]:((X4 @ X5) => (X4 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X6:$i]:(eps @ (^[X7:$i]:((((in @ emptyset) @ X6) => (~((X7 = X5)))) => (~(((~(((in @ emptyset) @ X6))) => (~((X7 = ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X5)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = X5)))))))))))))))))))))))))) => (X4 @ X3)))))))) => (~((X2 = emptyset)))))))))) @ (^[X2:$i]:(eps @ (^[X3:$i]:(((~((X2 = emptyset))) => (~((X3 = X2)))) => (~(((X2 = emptyset) => (~((X3 = (eps @ (^[X4:$i]:(~((((in @ X4) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X6)))))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ 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emptyset) @ X6))) => (~((X7 = ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X5)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = X5)))))))))))))))))))))))))) => (X4 @ X3)))))))))) => (~((X2 = ((repl @ (univof @ emptyset)) @ (^[X3:$i]:(eps @ (^[X4:$i]:(((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X3)))) => (~((X4 = X3)))) => (~(((~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X3)))))) => (~((X4 = (eps @ (^[X5:$i]:(~((((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))))))))))))))))))))) => (~(((![X3:$i]:(((in @ X3) @ (univof @ emptyset)) => (~((![X4:$i>$o]:((X4 @ emptyset) => ((![X5:$i]:((X4 @ X5) => (X4 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X6:$i]:(eps @ (^[X7:$i]:((((in @ emptyset) @ X6) => (~((X7 = X5)))) => (~(((~(((in @ emptyset) @ X6))) => (~((X7 = ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X5)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = X5)))))))))))))))))))))))))) => (X4 @ X3)))))))) => (~((X2 = emptyset)))))))))) @ (^[X2:$i]:(eps @ (^[X3:$i]:(((~((X2 = emptyset))) => (~((X3 = X2)))) => (~(((X2 = emptyset) => (~((X3 = (eps @ (^[X4:$i]:(~((((in @ X4) @ (eps @ (^[X5:$i]:(((~((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X6)))))))))) => (~((X5 = ((repl @ (univof @ emptyset)) @ (^[X6:$i]:(eps @ (^[X7:$i]:(((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X9)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = X9)))))))))))))))))))))))))) => (X8 @ X6)))) => (~((X7 = X6)))) => (~(((~((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X9)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = X9)))))))))))))))))))))))))) => (X8 @ X6)))))) => (~((X7 = (eps @ (^[X8:$i]:(~((((in @ X8) 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X6)))))))) => (~((X5 = emptyset)))))))))) => (X4 = emptyset))))))))))))))))))))) => (~(((![X2:$i]:(((in @ X2) @ (eps @ (^[X3:$i]:(((~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X4)))))))))) => (~((X3 = ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(eps @ (^[X5:$i]:(((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X4)))) => (~((X5 = X4)))) => (~(((~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X4)))))) => (~((X5 = (eps @ (^[X6:$i]:(~((((in @ X6) @ (univof @ emptyset)) => (~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X6)))))))))))))))))))))))))) => (~(((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X4)))))))) => (~((X3 = emptyset)))))))))) => (X2 = emptyset))) => (~((X1 = emptyset)))))))))),introduced(assumption,[])).
19.85/19.81	thf(h6,assumption,(~(((~(sP3)) => (~(sP5))))),introduced(assumption,[])).
19.85/19.81	thf(h7,assumption,(~(sP3)),introduced(assumption,[])).
19.85/19.81	thf(h8,assumption,sP5,introduced(assumption,[])).
19.85/19.81	thf(1,plain,((~(sP2) | ~(sP5)) | sP3),inference(prop_rule,[status(thm)],[])).
19.85/19.81	thf(2,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])).
19.85/19.81	thf(3,plain,(~(sP4) | sP1),inference(all_rule,[status(thm)],[])).
19.85/19.81	thf(ordsucc_inj,axiom,sP4).
19.85/19.81	thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,h7,h8,ordsucc_inj])).
19.85/19.81	thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,4,h7,h8])).
19.85/19.81	thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,5,h5,h6])).
19.85/19.81	thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,6,h4])).
19.85/19.81	thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,7,h2,h3])).
19.85/19.81	thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1])).
19.85/19.81	thf(0,theorem,(![X1:$i]:(((in @ X1) @ (eps @ (^[X2:$i]:(((~((![X3:$i]:(((in @ X3) @ (eps @ (^[X4:$i]:(((~((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))))) => (~((X4 = ((repl @ (univof @ emptyset)) @ (^[X5:$i]:(eps @ (^[X6:$i]:(((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X5)))) => (~((X6 = X5)))) => (~(((~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X5)))))) => (~((X6 = (eps @ (^[X7:$i]:(~((((in @ X7) @ (univof @ emptyset)) => (~((![X8:$i>$o]:((X8 @ emptyset) => ((![X9:$i]:((X8 @ X9) => (X8 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X9)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = ((repl @ (power @ (power @ emptyset))) @ (^[X12:$i]:(eps @ (^[X13:$i]:((((in @ emptyset) @ X12) => (~((X13 = X9)))) => (~(((~(((in @ emptyset) @ X12))) => (~((X13 = X9)))))))))))))))))))))))))) => (X8 @ X7)))))))))))))))))))))))))) => (~(((![X5:$i]:(((in @ X5) @ (univof @ emptyset)) => (~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X5)))))))) => (~((X4 = emptyset)))))))))) => (X3 = emptyset))))) => (~((X2 = ((repl @ (eps @ (^[X3:$i]:(((~((![X4:$i]:(((in @ X4) @ (univof @ emptyset)) => (~((![X5:$i>$o]:((X5 @ emptyset) => ((![X6:$i]:((X5 @ X6) => (X5 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X7:$i]:(eps @ (^[X8:$i]:((((in @ emptyset) @ X7) => (~((X8 = X6)))) => (~(((~(((in @ emptyset) @ X7))) => (~((X8 = ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X6)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = X6)))))))))))))))))))))))))) => (X5 @ X4)))))))))) => (~((X3 = ((repl @ (univof @ emptyset)) @ (^[X4:$i]:(eps @ (^[X5:$i]:(((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => (~(((~(((in @ emptyset) @ X8))) => (~((X9 = ((repl @ (power @ (power @ emptyset))) @ (^[X10:$i]:(eps @ (^[X11:$i]:((((in @ emptyset) @ X10) => (~((X11 = X7)))) => (~(((~(((in @ emptyset) @ X10))) => (~((X11 = X7)))))))))))))))))))))))))) => (X6 @ X4)))) => (~((X5 = X4)))) => (~(((~((![X6:$i>$o]:((X6 @ emptyset) => ((![X7:$i]:((X6 @ X7) => (X6 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X8:$i]:(eps @ (^[X9:$i]:((((in @ emptyset) @ X8) => (~((X9 = X7)))) => 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@ (^[X14:$i]:((((in @ emptyset) @ X13) => (~((X14 = X10)))) => (~(((~(((in @ emptyset) @ X13))) => (~((X14 = X10)))))))))))))))))))))))))) => (X9 @ X8)))))))))))))))))))))))))) => (~(((![X6:$i]:(((in @ X6) @ (univof @ emptyset)) => (~((![X7:$i>$o]:((X7 @ emptyset) => ((![X8:$i]:((X7 @ X8) => (X7 @ (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X9:$i]:(eps @ (^[X10:$i]:((((in @ emptyset) @ X9) => (~((X10 = X8)))) => (~(((~(((in @ emptyset) @ X9))) => (~((X10 = ((repl @ (power @ (power @ emptyset))) @ (^[X11:$i]:(eps @ (^[X12:$i]:((((in @ emptyset) @ X11) => (~((X12 = X8)))) => (~(((~(((in @ emptyset) @ X11))) => (~((X12 = X8)))))))))))))))))))))))))) => (X7 @ X6)))))))) => (~((X5 = emptyset)))))))))) => (X4 = emptyset))) => (~((X3 = emptyset)))))))))) => ((~((X1 = X2))) => (~(((union @ ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = X1)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = ((repl @ (power @ (power @ emptyset))) @ (^[X5:$i]:(eps @ (^[X6:$i]:((((in @ emptyset) @ X5) => (~((X6 = X1)))) => (~(((~(((in @ emptyset) @ X5))) => (~((X6 = X1))))))))))))))))))))))) = (union @ ((repl @ (power @ (power @ emptyset))) @ (^[X3:$i]:(eps @ (^[X4:$i]:((((in @ emptyset) @ X3) => (~((X4 = X2)))) => (~(((~(((in @ emptyset) @ X3))) => (~((X4 = ((repl @ (power @ (power @ emptyset))) @ (^[X5:$i]:(eps @ (^[X6:$i]:((((in @ emptyset) @ X5) => (~((X6 = X2)))) => (~(((~(((in @ emptyset) @ X5))) => (~((X6 = X2))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])).
19.94/19.83	% SZS output end Proof
19.94/19.83	EOF