%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, is_of: ($i > ($i > $o) > $o)).
thf(func_def_2, type, all_of: (($i > $o) > ($i > $o) > $o)).
thf(func_def_3, type, eps: (($i > $o) > $i)).
thf(func_def_4, type, in: ($i > $i > $o)).
thf(func_def_5, type, d_Subq: ($i > $i > $o)).
thf(func_def_7, type, union: ($i > $i)).
thf(func_def_8, type, power: ($i > $i)).
thf(func_def_9, type, repl: ($i > ($i > $i) > $i)).
thf(func_def_10, type, d_Union_closed: ($i > $o)).
thf(func_def_11, type, d_Power_closed: ($i > $o)).
thf(func_def_12, type, d_Repl_closed: ($i > $o)).
thf(func_def_13, type, d_ZF_closed: ($i > $o)).
thf(func_def_14, type, univof: ($i > $i)).
thf(func_def_15, type, if: ($o > $i > $i > $i)).
thf(func_def_16, type, nIn: ($i > $i > $o)).
thf(func_def_17, type, d_UPair: ($i > $i > $i)).
thf(func_def_18, type, d_Sing: ($i > $i)).
thf(func_def_19, type, binunion: ($i > $i > $i)).
thf(func_def_20, type, famunion: ($i > ($i > $i) > $i)).
thf(func_def_21, type, d_Sep: ($i > ($i > $o) > $i)).
thf(func_def_22, type, d_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)).
thf(func_def_23, type, setminus: ($i > $i > $i)).
thf(func_def_24, type, d_In_rec_G: (($i > ($i > $i) > $i) > $i > $i > $o)).
thf(func_def_25, type, d_In_rec: (($i > ($i > $i) > $i) > $i > $i)).
thf(func_def_26, type, ordsucc: ($i > $i)).
thf(func_def_27, type, nat_p: ($i > $o)).
thf(func_def_29, type, d_Inj1: ($i > $i)).
thf(func_def_30, type, d_Inj0: ($i > $i)).
thf(func_def_31, type, d_Unj: ($i > $i)).
thf(func_def_32, type, pair: ($i > $i > $i)).
thf(func_def_33, type, proj0: ($i > $i)).
thf(func_def_34, type, proj1: ($i > $i)).
thf(func_def_35, type, d_Sigma: ($i > ($i > $i) > $i)).
thf(func_def_36, type, setprod: ($i > $i > $i)).
thf(func_def_37, type, ap: ($i > $i > $i)).
thf(func_def_38, type, pair_p: ($i > $o)).
thf(func_def_39, type, d_Pi: ($i > ($i > $i) > $i)).
thf(func_def_40, type, imp: ($o > $o > $o)).
thf(func_def_41, type, d_not: ($o > $o)).
thf(func_def_42, type, wel: ($o > $o)).
thf(func_def_43, type, obvious: $o).
thf(func_def_44, type, l_ec: ($o > $o > $o)).
thf(func_def_45, type, d_and: ($o > $o > $o)).
thf(func_def_46, type, l_or: ($o > $o > $o)).
thf(func_def_47, type, orec: ($o > $o > $o)).
thf(func_def_48, type, l_iff: ($o > $o > $o)).
thf(func_def_49, type, all: ($i > ($i > $o) > $o)).
thf(func_def_50, type, non: ($i > ($i > $o) > $i > $o)).
thf(func_def_51, type, l_some: ($i > ($i > $o) > $o)).
thf(func_def_52, type, or3: ($o > $o > $o > $o)).
thf(func_def_53, type, and3: ($o > $o > $o > $o)).
thf(func_def_54, type, ec3: ($o > $o > $o > $o)).
thf(func_def_55, type, orec3: ($o > $o > $o > $o)).
thf(func_def_56, type, e_is: ($i > $i > $i > $o)).
thf(func_def_57, type, amone: ($i > ($i > $o) > $o)).
thf(func_def_58, type, one: ($i > ($i > $o) > $o)).
thf(func_def_59, type, ind: ($i > ($i > $o) > $i)).
thf(func_def_60, type, injective: ($i > $i > $i > $o)).
thf(func_def_61, type, image: ($i > $i > $i > $i > $o)).
thf(func_def_62, type, tofs: ($i > $i > $i > $i > $i)).
thf(func_def_63, type, soft: ($i > $i > $i > $i > $i)).
thf(func_def_64, type, inverse: ($i > $i > $i > $i)).
thf(func_def_65, type, surjective: ($i > $i > $i > $o)).
thf(func_def_66, type, bijective: ($i > $i > $i > $o)).
thf(func_def_67, type, invf: ($i > $i > $i > $i)).
thf(func_def_68, type, inj_h: ($i > $i > $i > $i > $i > $i)).
thf(func_def_69, type, e_in: ($i > ($i > $o) > $i > $i)).
thf(func_def_70, type, out: ($i > ($i > $o) > $i > $i)).
thf(func_def_71, type, d_pair: ($i > $i > $i > $i > $i)).
thf(func_def_72, type, first: ($i > $i > $i > $i)).
thf(func_def_73, type, second: ($i > $i > $i > $i)).
thf(func_def_74, type, prop1: ($o > $i > $i > $i > $i > $o)).
thf(func_def_75, type, ite: ($o > $i > $i > $i > $i)).
thf(func_def_76, type, wissel_wa: ($i > $i > $i > $i > $i)).
thf(func_def_77, type, wissel_wb: ($i > $i > $i > $i > $i)).
thf(func_def_78, type, wissel: ($i > $i > $i > $i)).
thf(func_def_79, type, changef: ($i > $i > $i > $i > $i > $i)).
thf(func_def_80, type, r_ec: ($o > $o > $o)).
thf(func_def_81, type, esti: ($i > $i > $i > $o)).
thf(func_def_82, type, empty: ($i > $i > $o)).
thf(func_def_83, type, nonempty: ($i > $i > $o)).
thf(func_def_84, type, incl: ($i > $i > $i > $o)).
thf(func_def_85, type, st_disj: ($i > $i > $i > $o)).
thf(func_def_86, type, nissetprop: ($i > $i > $i > $i > $o)).
thf(func_def_87, type, unmore: ($i > $i > $i > $i)).
thf(func_def_88, type, ecelt: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_89, type, ecp: ($i > ($i > $i > $o) > $i > $i > $o)).
thf(func_def_90, type, anec: ($i > ($i > $i > $o) > $i > $o)).
thf(func_def_91, type, ect: ($i > ($i > $i > $o) > $i)).
thf(func_def_92, type, ectset: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_93, type, ectelt: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_94, type, ecect: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_95, type, fixfu: ($i > ($i > $i > $o) > $i > $i > $o)).
thf(func_def_96, type, d_10_prop1: ($i > ($i > $i > $o) > $i > $i > $i > $i > $i > $o)).
thf(func_def_97, type, prop2: ($i > ($i > $i > $o) > $i > $i > $i > $i > $o)).
thf(func_def_98, type, indeq: ($i > ($i > $i > $o) > $i > $i > $i > $i)).
thf(func_def_99, type, fixfu2: ($i > ($i > $i > $o) > $i > $i > $o)).
thf(func_def_100, type, d_11_i: ($i > ($i > $i > $o) > $i > $i > $i > $i)).
thf(func_def_101, type, indeq2: ($i > ($i > $i > $o) > $i > $i > $i > $i > $i)).
thf(func_def_103, type, n_is: ($i > $i > $o)).
thf(func_def_104, type, nis: ($i > $i > $o)).
thf(func_def_105, type, n_in: ($i > $i > $o)).
thf(func_def_106, type, n_some: (($i > $o) > $o)).
thf(func_def_107, type, n_all: (($i > $o) > $o)).
thf(func_def_108, type, n_one: (($i > $o) > $o)).
thf(func_def_110, type, cond1: ($i > $o)).
thf(func_def_111, type, cond2: ($i > $o)).
thf(func_def_112, type, i1_s: (($i > $o) > $i)).
thf(func_def_113, type, d_22_prop1: ($i > $o)).
thf(func_def_114, type, d_23_prop1: ($i > $o)).
thf(func_def_115, type, d_24_prop1: ($i > $o)).
thf(func_def_116, type, d_24_prop2: ($i > $i > $o)).
thf(func_def_117, type, prop3: ($i > $i > $i > $o)).
thf(func_def_118, type, prop4: ($i > $o)).
thf(func_def_119, type, d_24_g: ($i > $i)).
thf(func_def_120, type, plus: ($i > $i)).
thf(func_def_121, type, n_pl: ($i > $i > $i)).
thf(func_def_122, type, d_25_prop1: ($i > $i > $i > $o)).
thf(func_def_123, type, d_26_prop1: ($i > $i > $o)).
thf(func_def_124, type, d_27_prop1: ($i > $i > $o)).
thf(func_def_125, type, d_28_prop1: ($i > $i > $i > $o)).
thf(func_def_126, type, diffprop: ($i > $i > $i > $o)).
thf(func_def_127, type, d_29_ii: ($i > $i > $o)).
thf(func_def_128, type, iii: ($i > $i > $o)).
thf(func_def_129, type, d_29_prop1: ($i > $i > $o)).
thf(func_def_130, type, moreis: ($i > $i > $o)).
thf(func_def_131, type, lessis: ($i > $i > $o)).
thf(func_def_134, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_135, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_136, type, vIMP: ($o > $o > $o)).
thf(func_def_137, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_138, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_139, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_140, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_141, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_142, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_143, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_144, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_145, type, vNOT: ($o > $o)).
thf(func_def_146, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_147, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_148, type, vAND: ($o > $o > $o)).
thf(func_def_149, type, vOR: ($o > $o > $o)).
thf(func_def_150, type, sP0: (($i > $o) > $o)).
thf(func_def_151, type, sP1: ($i > ($i > $i) > $i > $o)).
thf(func_def_152, type, sK2: ($i > $i)).
thf(func_def_153, type, sK3: (($i > $o) > $i)).
thf(func_def_154, type, sK4: ($i > ($i > $i) > ($i > $i) > $i)).
thf(func_def_155, type, sK5: ($i > $i > $i > $i)).
thf(func_def_156, type, sK6: (($i > $o) > $i)).
thf(func_def_157, type, sK7: (($i > $i) > ($i > $i) > $i > $i)).
thf(func_def_158, type, sK8: (($i > $o) > $i)).
thf(func_def_162, type, sK12: ($i > $i > $o)).
thf(func_def_163, type, sK13: ($i > $i > $i > $i)).
thf(func_def_164, type, sK14: ($i > $i > $o)).
thf(func_def_165, type, sK15: ($i > $i > $o)).
thf(func_def_166, type, sK16: (($i > $o) > $i)).
thf(func_def_167, type, sK17: ($i > $i > $o)).
thf(func_def_168, type, sK18: (($i > $o) > $i)).
thf(func_def_169, type, sK19: (($i > $o) > $i)).
thf(func_def_170, type, sK20: (($i > $o) > $i)).
thf(func_def_171, type, sK21: ($i > $i > $o)).
thf(func_def_172, type, sK22: (($i > $o) > $i)).
thf(func_def_173, type, sK23: (($i > $o) > $i)).
thf(func_def_174, type, sK24: (($i > $o) > $i)).
thf(func_def_175, type, sK25: (($i > $o) > $i)).
thf(func_def_177, type, sK27: (($i > $i > $i) > ($i > $i) > ($i > $i > $i) > $i)).
thf(func_def_178, type, sK28: (($i > $i > $i) > ($i > $i) > ($i > $i > $i) > $i)).
thf(func_def_179, type, sK29: (($i > $i > $i) > ($i > $i) > ($i > $i > $i) > $i)).
thf(func_def_180, type, sK30: (($i > $i > $i) > ($i > $i) > ($i > $i > $i) > $i)).
thf(func_def_181, type, sK31: (($i > $i > $i) > ($i > $i) > $i)).
thf(func_def_182, type, sK32: (($i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i)).
thf(func_def_183, type, sK33: (($i > $i > $i) > ($i > $i) > $i)).
thf(f1,axiom,(
  ((^[X0 : $i, X1 : ($i > $o)] : ((X1 @ X0))) = is_of)),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of)).
thf(f2,axiom,(
  (all_of = (^[X0 : ($i > $o), X1 : ($i > $o)] : (! [X2 : $i] : ((is_of @ X2 @ X0) => (X1 @ X2)))))),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of)).
thf(f33,axiom,(
  (imp = (^[X0 : $o, X1 : $o] : (X0 => X1)))),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_imp)).
thf(f34,axiom,(
  (d_not = (^[X0 : $o] : ((imp @ X0 @ $false))))),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_d_not)).
thf(f39,axiom,(
  ((^[X0 : $o] : ((imp @ (d_not @ X0)))) = l_or)),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_l_or)).
thf(f49,axiom,(
  ((^[X0 : $i, X1 : $i, X2 : $i] : ((X1 = X2))) = e_is)),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is)).
thf(f96,axiom,(
  (n_is = ((e_is @ nat)))),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is)).
thf(f99,axiom,(
  (n_some = ((l_some @ nat)))),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some)).
thf(f148,axiom,(
  ! [X0 : ($i > $o)] : (! [X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X1 : $i] : (X0 @ X1))),
  file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',k_In_ind)).
thf(f185,axiom,(
  (diffprop = (^[X0 : $i, X1 : $i, X2 : $i] : ((n_is @ X0 @ (n_pl @ X1 @ X2)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_diffprop)).
thf(f186,axiom,(
  ((^[X0 : $i, X1 : $i] : ((n_some @ (diffprop @ X0 @ X1)))) = d_29_ii)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii)).
thf(f187,axiom,(
  ((^[X0 : $i, X1 : $i] : ((n_some @ (diffprop @ X1 @ X0)))) = iii)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii)).
thf(f189,axiom,(
  (moreis = (^[X0 : $i, X1 : $i] : ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_moreis)).
thf(f217,axiom,(
  (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((iii @ X0 @ X1) => ((iii @ X1 @ X2) => (iii @ X0 @ X2)))))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz15)).
thf(f219,conjecture,(
  (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((moreis @ X0 @ X1) => ((d_29_ii @ X1 @ X2) => (d_29_ii @ X0 @ X2)))))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16c)).
thf(f220,negated_conjecture,(
  ~(all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X0 : $i] : ((all_of @ (^[X1 : $i] : ((in @ X1 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X2 : $i] : ((moreis @ X0 @ X1) => ((d_29_ii @ X1 @ X2) => (d_29_ii @ X0 @ X2)))))))))))),
  inference(negated_conjecture,[status(cth)],[f219])).
thf(f271,plain,(
  (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))),
  inference(fool_elimination,[],[f187])).
thf(f324,plain,(
  (is_of = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (Y1 @ Y0)))))),
  inference(fool_elimination,[],[f1])).
thf(f405,plain,(
  (imp = (^[X0 : $o, X1 : $o] : (X0 => X1)))),
  inference(rectify,[],[f33])).
thf(f406,plain,(
  (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))),
  inference(fool_elimination,[],[f405])).
thf(f427,plain,(
  (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))),
  inference(fool_elimination,[],[f185])).
thf(f498,plain,(
  (all_of = (^[X0 : ($i > $o), X1 : ($i > $o)] : (! [X2 : $i] : ((is_of @ X2 @ X0) => (X1 @ X2)))))),
  inference(rectify,[],[f2])).
thf(f499,plain,(
  (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))),
  inference(fool_elimination,[],[f498])).
thf(f518,plain,(
  (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (d_29_ii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))),
  inference(fool_elimination,[],[f189])).
thf(f540,plain,(
  (d_not = (^[X0 : $o] : ((imp @ X0 @ $false))))),
  inference(rectify,[],[f34])).
thf(f541,plain,(
  (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))),
  inference(fool_elimination,[],[f540])).
thf(f549,plain,(
  (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))),
  inference(fool_elimination,[],[f186])).
thf(f550,plain,(
  (all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((all_of @ (^[X4 : $i] : ((in @ X4 @ nat))) @ (^[X5 : $i] : ((iii @ X1 @ X3) => ((iii @ X3 @ X5) => (iii @ X1 @ X5)))))))))))),
  inference(rectify,[],[f217])).
thf(f551,plain,(
  (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((iii @ Y0 @ Y1) => ((iii @ Y1 @ Y2) => (iii @ Y0 @ Y2)))))))))) = $true)),
  inference(fool_elimination,[],[f550])).
thf(f563,plain,(
  (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))),
  inference(fool_elimination,[],[f39])).
thf(f564,plain,(
  (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))),
  inference(fool_elimination,[],[f49])).
thf(f568,plain,(
  ! [X0 : ($i > $o)] : (! [X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X3 : $i] : (X0 @ X3))),
  inference(rectify,[],[f148])).
thf(f569,plain,(
  ! [X0 : ($i > $o)] : (! [X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((X0 @ X2)) = $true)) => (((X0 @ X1)) = $true)) => ! [X3 : $i] : (((X0 @ X3)) = $true))),
  inference(fool_elimination,[],[f568])).
thf(f584,plain,(
  ~(all_of @ (^[X0 : $i] : ((in @ X0 @ nat))) @ (^[X1 : $i] : ((all_of @ (^[X2 : $i] : ((in @ X2 @ nat))) @ (^[X3 : $i] : ((all_of @ (^[X4 : $i] : ((in @ X4 @ nat))) @ (^[X5 : $i] : ((moreis @ X1 @ X3) => ((d_29_ii @ X3 @ X5) => (d_29_ii @ X1 @ X5)))))))))))),
  inference(rectify,[],[f220])).
thf(f585,plain,(
  ~ (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((moreis @ Y0 @ Y1) => ((d_29_ii @ Y1 @ Y2) => (d_29_ii @ Y0 @ Y2)))))))))) = $true)),
  inference(fool_elimination,[],[f584])).
thf(f602,plain,(
  (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((moreis @ Y0 @ Y1) => ((d_29_ii @ Y1 @ Y2) => (d_29_ii @ Y0 @ Y2)))))))))) != $true)),
  inference(flattening,[],[f585])).
thf(f622,plain,(
  ! [X0 : ($i > $o)] : (! [X3 : $i] : (((X0 @ X3)) = $true) | ? [X1 : $i] : ((((X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((X0 @ X2)) = $true))))),
  inference(ennf_transformation,[],[f569])).
thf(f641,plain,(
  ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | ? [X2 : $i] : ((((X0 @ X2)) != $true) & ! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((X0 @ X3)) = $true))))),
  inference(rectify,[],[f622])).
thf(f642,plain,(
  ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | ((((X0 @ (sK3 @ X0))) != $true) & ! [X3 : $i] : ((((in @ X3 @ (sK3 @ X0))) != $true) | (((X0 @ X3)) = $true))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK2 @ X0))],[f641])).
thf(f672,plain,(
  (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f427])).
thf(f686,plain,(
  (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (d_29_ii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))),
  inference(cnf_transformation,[],[f518])).
thf(f689,plain,(
  (n_is = ((e_is @ nat)))),
  inference(cnf_transformation,[],[f96])).
thf(f704,plain,(
  (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))),
  inference(cnf_transformation,[],[f563])).
thf(f705,plain,(
  (n_some = ((l_some @ nat)))),
  inference(cnf_transformation,[],[f99])).
thf(f710,plain,(
  (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((iii @ Y0 @ Y1) => ((iii @ Y1 @ Y2) => (iii @ Y0 @ Y2)))))))))) = $true)),
  inference(cnf_transformation,[],[f551])).
thf(f716,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (sK3 @ X0))) != $true) | (((X0 @ X1)) = $true)) )),
  inference(cnf_transformation,[],[f642])).
thf(f726,plain,(
  (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))),
  inference(cnf_transformation,[],[f564])).
thf(f731,plain,(
  (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))),
  inference(cnf_transformation,[],[f406])).
thf(f735,plain,(
  (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))),
  inference(cnf_transformation,[],[f549])).
thf(f739,plain,(
  (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))),
  inference(cnf_transformation,[],[f541])).
thf(f785,plain,(
  (is_of = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (Y1 @ Y0)))))),
  inference(cnf_transformation,[],[f324])).
thf(f806,plain,(
  (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f499])).
thf(f808,plain,(
  (((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: ((moreis @ Y0 @ Y1) => ((d_29_ii @ Y1 @ Y2) => (d_29_ii @ Y0 @ Y2)))))))))) != $true)),
  inference(cnf_transformation,[],[f602])).
thf(f810,plain,(
  (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))),
  inference(cnf_transformation,[],[f271])).
thf(f814,plain,(
  (n_is = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))) @ nat)))),
  inference(definition_unfolding,[],[f689,f726])).
thf(f815,plain,(
  (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4 = Y5)))))) @ nat @ Y0 @ (n_pl @ Y1 @ Y2))))))))),
  inference(definition_unfolding,[],[f672,f814])).
thf(f816,plain,(
  (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ nat @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y0 @ Y1))))))),
  inference(definition_unfolding,[],[f735,f705,f815])).
thf(f817,plain,(
  (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ nat @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y1 @ Y0))))))),
  inference(definition_unfolding,[],[f810,f705,f815])).
thf(f818,plain,(
  (d_not = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ Y0 @ $false)))),
  inference(definition_unfolding,[],[f739,f731])).
thf(f819,plain,(
  (l_or = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y1 @ $false)) @ Y0))))),
  inference(definition_unfolding,[],[f704,f731,f818])).
thf(f822,plain,(
  (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y3 @ $false)) @ Y2))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ nat @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ nat @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ nat @ Y0 @ Y1))))))),
  inference(definition_unfolding,[],[f686,f819,f816,f814])).
thf(f835,plain,(
  (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))))),
  inference(definition_unfolding,[],[f806,f785])).
thf(f873,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((^[Y5 : $i]: ((^[Y6 : $i > $o]: (Y6 @ Y5)))) @ Y4 @ Y2) => (Y3 @ Y4))))))) @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y0 @ Y1) => (((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y1 @ Y2) => ((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y4 @ Y3))))) @ Y0 @ Y2)))))))))) = $true)),
  inference(definition_unfolding,[],[f710,f835,f835,f835,f817,f817,f817])).
thf(f922,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((^[Y5 : $i]: ((^[Y6 : $i > $o]: (Y6 @ Y5)))) @ Y4 @ Y2) => (Y3 @ Y4))))))) @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (l_some @ nat @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11 = Y12)))))) @ nat @ Y7 @ (n_pl @ Y8 @ Y9))))))) @ Y5 @ Y6))))) @ Y3 @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ nat @ Y3 @ Y4))))) @ Y0 @ Y1) => (((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y3 @ Y4))))) @ Y1 @ Y2) => ((^[Y3 : $i]: ((^[Y4 : $i]: (l_some @ nat @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ nat @ Y5 @ (n_pl @ Y6 @ Y7))))))) @ Y3 @ Y4))))) @ Y0 @ Y2)))))))))) != $true)),
  inference(definition_unfolding,[],[f808,f835,f835,f835,f822,f816,f816])).
thf(f996,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((((l_some @ nat @ (^[Y3 : $i]: (Y0 = (n_pl @ Y1 @ Y3)))) => $false) => (Y0 = Y1)) => ((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y2 @ Y3)))) => (l_some @ nat @ (^[Y3 : $i]: (Y0 = (n_pl @ Y2 @ Y3)))))))))))))))) != $true)),
  inference(beta-eta_normalization,[],[f922])).
thf(f997,plain,(
  ($false = (((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((((l_some @ nat @ (^[Y3 : $i]: (Y0 = (n_pl @ Y1 @ Y3)))) => $false) => (Y0 = Y1)) => ((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y2 @ Y3)))) => (l_some @ nat @ (^[Y3 : $i]: (Y0 = (n_pl @ Y2 @ Y3)))))))))))))) @ sK9)))),
  inference(sigma_proxy_clausification,[],[f996])).
thf(f998,plain,(
  ($false = (((in @ sK9 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (sK9 = (n_pl @ Y0 @ Y2)))) => $false) => (sK9 = Y0)) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (sK9 = (n_pl @ Y1 @ Y2)))))))))))))))),
  inference(beta-eta_normalization,[],[f997])).
thf(f999,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (sK9 = (n_pl @ Y0 @ Y2)))) => $false) => (sK9 = Y0)) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (sK9 = (n_pl @ Y1 @ Y2))))))))))))))),
  inference(imp_proxy_clausification,[],[f998])).
thf(f1000,plain,(
  ($true = ((in @ sK9 @ nat)))),
  inference(imp_proxy_clausification,[],[f998])).
thf(f1001,plain,(
  ($false = (((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((((l_some @ nat @ (^[Y2 : $i]: (sK9 = (n_pl @ Y0 @ Y2)))) => $false) => (sK9 = Y0)) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ Y1 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (sK9 = (n_pl @ Y1 @ Y2))))))))))) @ sK10)))),
  inference(sigma_proxy_clausification,[],[f999])).
thf(f1002,plain,(
  ($false = (((in @ sK10 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (sK9 = (n_pl @ sK10 @ Y1)))) => $false) => (sK9 = sK10)) => ((l_some @ nat @ (^[Y1 : $i]: (sK10 = (n_pl @ Y0 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (sK9 = (n_pl @ Y0 @ Y1))))))))))))),
  inference(beta-eta_normalization,[],[f1001])).
thf(f1003,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (sK9 = (n_pl @ sK10 @ Y1)))) => $false) => (sK9 = sK10)) => ((l_some @ nat @ (^[Y1 : $i]: (sK10 = (n_pl @ Y0 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (sK9 = (n_pl @ Y0 @ Y1)))))))))))),
  inference(imp_proxy_clausification,[],[f1002])).
thf(f1004,plain,(
  ($true = ((in @ sK10 @ nat)))),
  inference(imp_proxy_clausification,[],[f1002])).
thf(f1005,plain,(
  ($false = (((^[Y0 : $i]: ((in @ Y0 @ nat) => ((((l_some @ nat @ (^[Y1 : $i]: (sK9 = (n_pl @ sK10 @ Y1)))) => $false) => (sK9 = sK10)) => ((l_some @ nat @ (^[Y1 : $i]: (sK10 = (n_pl @ Y0 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (sK9 = (n_pl @ Y0 @ Y1)))))))) @ sK11)))),
  inference(sigma_proxy_clausification,[],[f1003])).
thf(f1006,plain,(
  ($false = (((in @ sK11 @ nat) => ((((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0)))) => $false) => (sK9 = sK10)) => ((l_some @ nat @ (^[Y0 : $i]: (sK10 = (n_pl @ sK11 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0)))))))))),
  inference(beta-eta_normalization,[],[f1005])).
thf(f1007,plain,(
  ($false = (((((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0)))) => $false) => (sK9 = sK10)) => ((l_some @ nat @ (^[Y0 : $i]: (sK10 = (n_pl @ sK11 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))))))),
  inference(imp_proxy_clausification,[],[f1006])).
thf(f1008,plain,(
  (((in @ sK11 @ nat)) = $true)),
  inference(imp_proxy_clausification,[],[f1006])).
thf(f1009,plain,(
  ((((l_some @ nat @ (^[Y0 : $i]: (sK10 = (n_pl @ sK11 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0)))))) = $false)),
  inference(imp_proxy_clausification,[],[f1007])).
thf(f1010,plain,(
  (((((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0)))) => $false) => (sK9 = sK10))) = $true)),
  inference(imp_proxy_clausification,[],[f1007])).
thf(f1011,plain,(
  ($false = (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0)))) => $false))) | ($true = ((sK9 = sK10)))),
  inference(imp_proxy_clausification,[],[f1010])).
thf(f1013,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0))))) = $true) | ($true = ((sK9 = sK10)))),
  inference(imp_proxy_clausification,[],[f1011])).
thf(f1014,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0))))) = $true) | (sK10 = sK9)),
  inference(equality_proxy_clausification,[],[f1013])).
thf(f1016,plain,(
  ($false = ((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))))),
  inference(imp_proxy_clausification,[],[f1009])).
thf(f1017,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK10 = (n_pl @ sK11 @ Y0))))) = $true)),
  inference(imp_proxy_clausification,[],[f1009])).
thf(f1643,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => ((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => (l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))))))))))))))) = $true)),
  inference(beta-eta_normalization,[],[f873])).
thf(f1644,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ nat) => ((l_some @ nat @ (^[Y3 : $i]: (Y1 = (n_pl @ Y0 @ Y3)))) => ((l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y1 @ Y3)))) => (l_some @ nat @ (^[Y3 : $i]: (Y2 = (n_pl @ Y0 @ Y3)))))))))))))) @ X1)) = $true)) )),
  inference(pi_proxy_clausification,[],[f1643])).
thf(f1645,plain,(
  ( ! [X1 : $i] : (((((in @ X1 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => ((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2)))))))))))))) = $true)) )),
  inference(beta-eta_normalization,[],[f1644])).
thf(f1646,plain,(
  ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => ((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2)))))))))))))) | (((in @ X1 @ nat)) = $false)) )),
  inference(imp_proxy_clausification,[],[f1645])).
thf(f1647,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ((((^[Y0 : $i]: ((in @ Y0 @ nat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ nat) => ((l_some @ nat @ (^[Y2 : $i]: (Y0 = (n_pl @ X1 @ Y2)))) => ((l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ Y0 @ Y2)))) => (l_some @ nat @ (^[Y2 : $i]: (Y1 = (n_pl @ X1 @ Y2))))))))))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f1646])).
thf(f1648,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ((((in @ X2 @ nat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => ((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1))))))))))) = $true)) )),
  inference(beta-eta_normalization,[],[f1647])).
thf(f1649,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ nat) => ((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => ((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1))))))))))) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
  inference(imp_proxy_clausification,[],[f1648])).
thf(f1650,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ nat)) = $false) | ((((^[Y0 : $i]: ((in @ Y0 @ nat) => ((l_some @ nat @ (^[Y1 : $i]: (X2 = (n_pl @ X1 @ Y1)))) => ((l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X2 @ Y1)))) => (l_some @ nat @ (^[Y1 : $i]: (Y0 = (n_pl @ X1 @ Y1)))))))) @ X3)) = $true) | (((in @ X1 @ nat)) = $false)) )),
  inference(pi_proxy_clausification,[],[f1649])).
thf(f1651,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | (((in @ X2 @ nat)) = $false) | ($true = (((in @ X3 @ nat) => ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))))))) )),
  inference(beta-eta_normalization,[],[f1650])).
thf(f1652,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))) => ((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))))) | (((in @ X2 @ nat)) = $false) | (((in @ X3 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
  inference(imp_proxy_clausification,[],[f1651])).
thf(f1653,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ nat)) = $false) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((in @ X3 @ nat)) = $false) | ((((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0)))) => (l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0)))))) = $true) | (((in @ X2 @ nat)) = $false)) )),
  inference(imp_proxy_clausification,[],[f1652])).
thf(f1654,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X2 = (n_pl @ X1 @ Y0)))))) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X1 @ Y0))))) = $true) | (((in @ X3 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X3 = (n_pl @ X2 @ Y0))))) = $false) | (((in @ X2 @ nat)) = $false) | (((in @ X1 @ nat)) = $false)) )),
  inference(imp_proxy_clausification,[],[f1653])).
thf(f1689,definition,(
  spl26_1 <=> (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition])).
thf(f1691,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK10 @ Y0))))) = $true) | ~spl26_1),
  inference(avatar_component_clause,[],[f1689])).
thf(f1693,definition,(
  spl26_2 <=> (sK10 = sK9)),
  introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition])).
thf(f1695,plain,(
  (sK10 = sK9) | ~spl26_2),
  inference(avatar_component_clause,[],[f1693])).
thf(f1696,plain,(
  spl26_1 | spl26_2),
  inference(avatar_split_clause,[],[f1014,f1693,f1689])).
thf(f1718,plain,(
  ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((((n_pl @ sK11)) != ((X2 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK10))) | ($true != $true) | ((((^[Y0 : $i]: (l_some @ (X0 @ Y0) @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((X1 @ Y1 @ Y2) = (X2 @ Y1 @ Y2))))) @ Y0))) @ X3)) = $true) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))))) )),
  inference(constrained_superposition,[],[f716,f1017])).
thf(f1719,plain,(
  ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : (((((^[Y0 : $i]: (l_some @ (X0 @ Y0) @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((X1 @ Y1 @ Y2) = (X2 @ Y1 @ Y2))))) @ Y0))) @ X3)) = $true) | (((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK10))) | (((n_pl @ sK11)) != ((X2 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))))) )),
  inference(trivial_inequality_removal,[],[f1718])).
thf(f1720,plain,(
  ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((((n_pl @ sK11)) != ((X2 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK10))) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (X2 @ Y0 @ Y1))))))))) | (((l_some @ (X0 @ X3) @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) = (X2 @ X3 @ Y0))))) = $true)) )),
  inference(beta-eta_normalization,[],[f1719])).
thf(f1865,plain,(
  ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i > $i),X1 : ($i > $i)] : ((nat != ((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = ((^[Y2 : $i]: ((^[Y3 : $i]: (n_pl @ (X2 @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3))))) @ Y0 @ Y1))))))))) | (((X2 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK11))) | (((l_some @ (X1 @ X3) @ (^[Y0 : $i]: ((X0 @ X3 @ Y0) = ((^[Y1 : $i]: ((^[Y2 : $i]: (n_pl @ (X2 @ Y1 @ Y2) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (Y4)))) @ Y1 @ Y2))))) @ X3 @ Y0))))) = $true) | (((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = ((^[Y2 : $i]: ((^[Y3 : $i]: (n_pl @ (X2 @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3))))) @ Y0 @ Y1)))))))) != (^[Y0 : $i]: (sK10)))) )),
  inference(equality_resolution,[],[f1720])).
thf(f1866,plain,(
  ( ! [X2 : ($i > $i > $i),X3 : $i,X0 : ($i > $i > $i),X1 : ($i > $i)] : ((((X2 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK11))) | (nat != ((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1))))))))) | (((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X1 @ Y0) @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) = (n_pl @ (X2 @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK10))) | (((l_some @ (X1 @ X3) @ (^[Y0 : $i]: ((X0 @ X3 @ Y0) = (n_pl @ (X2 @ X3 @ Y0) @ Y0))))) = $true)) )),
  inference(beta-eta_normalization,[],[f1865])).
thf(f1938,plain,(
  ( ! [X0 : $i] : (($false = $true) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK10 @ Y0)))))) | (((in @ X0 @ nat)) = $false) | ($false = ((in @ sK11 @ nat))) | (((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK11 @ Y0))))) = $true) | ($false = ((in @ sK10 @ nat)))) )),
  inference(constrained_superposition,[],[f1017,f1654])).
thf(f1942,plain,(
  ( ! [X0 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK10 @ Y0)))))) | ($false = ((in @ sK11 @ nat))) | (((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK11 @ Y0))))) = $true) | ($false = ((in @ sK10 @ nat))) | (((in @ X0 @ nat)) = $false)) )),
  inference(trivial_inequality_removal,[],[f1938])).
thf(f1948,plain,(
  ( ! [X0 : $i] : (($false = $true) | (((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK11 @ Y0))))) = $true) | (((in @ X0 @ nat)) = $false) | ($false = ((in @ sK10 @ nat))) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK10 @ Y0))))))) )),
  inference(forward_demodulation,[],[f1942,f1008])).
thf(f1949,plain,(
  ( ! [X0 : $i] : (($false = ((in @ sK10 @ nat))) | (((in @ X0 @ nat)) = $false) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK10 @ Y0)))))) | (((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK11 @ Y0))))) = $true)) )),
  inference(trivial_inequality_removal,[],[f1948])).
thf(f1956,plain,(
  ( ! [X0 : $i] : (($false = $true) | ($false = ((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK10 @ Y0)))))) | (((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK11 @ Y0))))) = $true) | (((in @ X0 @ nat)) = $false)) )),
  inference(forward_demodulation,[],[f1949,f1004])).
thf(f1957,plain,(
  ( ! [X0 : $i] : (($false = ((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK10 @ Y0)))))) | (((in @ X0 @ nat)) = $false) | (((l_some @ nat @ (^[Y0 : $i]: (X0 = (n_pl @ sK11 @ Y0))))) = $true)) )),
  inference(trivial_inequality_removal,[],[f1956])).
thf(f1967,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true) | ($false = ((in @ sK9 @ nat))) | ($false = $true) | ~spl26_1),
  inference(constrained_superposition,[],[f1691,f1957])).
thf(f1969,plain,(
  ($false = ((in @ sK9 @ nat))) | (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true) | ~spl26_1),
  inference(trivial_inequality_removal,[],[f1967])).
thf(f1973,plain,(
  ($false = $true) | (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true) | ~spl26_1),
  inference(forward_demodulation,[],[f1969,f1000])).
thf(f1974,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true) | ~spl26_1),
  inference(trivial_inequality_removal,[],[f1973])).
thf(f1977,plain,(
  ($false = $true) | ~spl26_1),
  inference(forward_demodulation,[],[f1974,f1016])).
thf(f1978,plain,(
  $false | ~spl26_1),
  inference(trivial_inequality_removal,[],[f1977])).
thf(f1979,plain,(
  ~spl26_1),
  inference(avatar_contradiction_clause,[],[f1978])).
thf(f2014,plain,(
  ( ! [X2 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ ((^[Y2 : $i]: ((^[Y3 : $i]: (sK11)))) @ Y0 @ Y1) @ Y1)))))))) != (^[Y0 : $i]: (sK10))) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ ((^[Y2 : $i]: ((^[Y3 : $i]: (sK11)))) @ Y0 @ Y1) @ Y1))))))))) | (((l_some @ (X0 @ X2) @ (^[Y0 : $i]: ((X1 @ X2 @ Y0) = (n_pl @ ((^[Y1 : $i]: ((^[Y2 : $i]: (sK11)))) @ X2 @ Y0) @ Y0))))) = $true)) )),
  inference(equality_resolution,[],[f1866])).
thf(f2016,plain,(
  ( ! [X2 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1)))))))) != (^[Y0 : $i]: (sK10))) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1))))))))) | ($true = ((l_some @ (X0 @ X2) @ (^[Y0 : $i]: ((X1 @ X2 @ Y0) = (n_pl @ sK11 @ Y0))))))) )),
  inference(beta-eta_normalization,[],[f2014])).
thf(f2017,plain,(
  ( ! [X2 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : (($true = ((l_some @ (X0 @ X2) @ (^[Y0 : $i]: ((X1 @ X2 @ Y0) = (n_pl @ sK11 @ Y0)))))) | (((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1)))))) @ (sK33 @ X1 @ X0))) != (((^[Y0 : $i]: (sK10)) @ (sK33 @ X1 @ X0)))) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1)))))))))) )),
  inference(negative_extensionality,[],[f2016])).
thf(f2019,plain,(
  ( ! [X2 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1))))))))) | ($true = ((l_some @ (X0 @ X2) @ (^[Y0 : $i]: ((X1 @ X2 @ Y0) = (n_pl @ sK11 @ Y0)))))) | (((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1)))))) @ (sK33 @ X1 @ X0))) != sK10)) )),
  inference(beta-eta_normalization,[],[f2017])).
thf(f2021,plain,(
  ( ! [X2 : $i,X0 : ($i > $i),X1 : ($i > $i > $i)] : ((((X1 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1)))))) @ (sK33 @ X1 @ X0))) != sK9) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) = (n_pl @ sK11 @ Y1))))))))) | ($true = ((l_some @ (X0 @ X2) @ (^[Y0 : $i]: ((X1 @ X2 @ Y0) = (n_pl @ sK11 @ Y0))))))) ) | ~spl26_2),
  inference(forward_demodulation,[],[f2019,f1695])).
thf(f2046,plain,(
  ( ! [X0 : ($i > $i),X1 : $i] : ((((l_some @ (X0 @ X1) @ (^[Y0 : $i]: (((^[Y1 : $i]: ((^[Y2 : $i]: (sK9)))) @ X1 @ Y0) = (n_pl @ sK11 @ Y0))))) = $true) | (nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (sK9)))) @ Y0 @ Y1) = (n_pl @ sK11 @ Y1)))))))))) ) | ~spl26_2),
  inference(equality_resolution,[],[f2021])).
thf(f2050,plain,(
  ( ! [X0 : ($i > $i),X1 : $i] : ((nat != ((X0 @ (sK3 @ (^[Y0 : $i]: (l_some @ (X0 @ Y0) @ (^[Y1 : $i]: (sK9 = (n_pl @ sK11 @ Y1))))))))) | (((l_some @ (X0 @ X1) @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true)) ) | ~spl26_2),
  inference(beta-eta_normalization,[],[f2046])).
thf(f2053,plain,(
  ( ! [X0 : $i] : ((((l_some @ ((^[Y0 : $i]: (nat)) @ X0) @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true)) ) | ~spl26_2),
  inference(equality_resolution,[],[f2050])).
thf(f2054,plain,(
  (((l_some @ nat @ (^[Y0 : $i]: (sK9 = (n_pl @ sK11 @ Y0))))) = $true) | ~spl26_2),
  inference(beta-eta_normalization,[],[f2053])).
thf(f2057,plain,(
  ($false = $true) | ~spl26_2),
  inference(forward_demodulation,[],[f2054,f1016])).
thf(f2058,plain,(
  $false | ~spl26_2),
  inference(trivial_inequality_removal,[],[f2057])).
thf(f2059,plain,(
  ~spl26_2),
  inference(avatar_contradiction_clause,[],[f2058])).
cnf(s1, plain, spl26_1 | spl26_2, inference(sat_conversion,[],[f1696])).
cnf(s15, plain, ~spl26_1, inference(sat_conversion,[],[f1979])).
cnf(s19, plain, ~spl26_2, inference(sat_conversion,[],[f2059])).
cnf(s20, plain, $false, inference(rat,[],[s1,s19,s15])).
thf(f2060,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s20])).
% SZS output end Proof for theBenchmark