%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, in: ($i > $i > $o)).
thf(func_def_1, type, exu: (($i > $o) > $o)).
thf(func_def_3, type, setextAx: $o).
thf(func_def_5, type, emptysetAx: $o).
thf(func_def_6, type, setadjoin: ($i > $i > $i)).
thf(func_def_7, type, setadjoinAx: $o).
thf(func_def_8, type, powerset: ($i > $i)).
thf(func_def_9, type, powersetAx: $o).
thf(func_def_10, type, setunion: ($i > $i)).
thf(func_def_11, type, setunionAx: $o).
thf(func_def_13, type, omega0Ax: $o).
thf(func_def_14, type, omegaSAx: $o).
thf(func_def_15, type, omegaIndAx: $o).
thf(func_def_16, type, replAx: $o).
thf(func_def_17, type, foundationAx: $o).
thf(func_def_18, type, wellorderingAx: $o).
thf(func_def_19, type, descr: (($i > $o) > $i)).
thf(func_def_20, type, descrp: $o).
thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
thf(func_def_22, type, dsetconstrI: $o).
thf(func_def_23, type, dsetconstrEL: $o).
thf(func_def_24, type, dsetconstrER: $o).
thf(func_def_25, type, exuE1: $o).
thf(func_def_26, type, prop2set: ($o > $i)).
thf(func_def_27, type, prop2setE: $o).
thf(func_def_28, type, emptysetE: $o).
thf(func_def_29, type, emptysetimpfalse: $o).
thf(func_def_30, type, notinemptyset: $o).
thf(func_def_31, type, exuE3e: $o).
thf(func_def_32, type, setext: $o).
thf(func_def_33, type, emptyI: $o).
thf(func_def_34, type, noeltsimpempty: $o).
thf(func_def_35, type, setbeta: $o).
thf(func_def_36, type, nonempty: ($i > $o)).
thf(func_def_37, type, nonemptyE1: $o).
thf(func_def_38, type, nonemptyI: $o).
thf(func_def_39, type, nonemptyI1: $o).
thf(func_def_40, type, setadjoinIL: $o).
thf(func_def_41, type, emptyinunitempty: $o).
thf(func_def_42, type, setadjoinIR: $o).
thf(func_def_43, type, setadjoinE: $o).
thf(func_def_44, type, setadjoinOr: $o).
thf(func_def_45, type, setoftrueEq: $o).
thf(func_def_46, type, powersetI: $o).
thf(func_def_47, type, emptyinPowerset: $o).
thf(func_def_48, type, emptyInPowerset: $o).
thf(func_def_49, type, powersetE: $o).
thf(func_def_50, type, setunionI: $o).
thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_56, type, vAND: ($o > $o > $o)).
thf(func_def_57, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_59, type, vIMP: ($o > $o > $o)).
thf(func_def_60, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_61, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_62, type, vNOT: ($o > $o)).
thf(func_def_63, type, sP0: ($i > $i > $o)).
thf(func_def_64, type, sP1: ($i > $o)).
thf(func_def_65, type, sP2: ($i > $i > $o)).
thf(func_def_66, type, sP3: ($i > $i > $o)).
thf(func_def_67, type, sP4: $o).
thf(func_def_70, type, sK7: ($i > $i > $i)).
thf(func_def_74, type, sK11: $o).
thf(func_def_75, type, sK12: ($i > $o)).
thf(func_def_78, type, sK15: ($i > $o)).
thf(func_def_84, type, sK21: ($i > $o)).
thf(func_def_86, type, sK23: ($i > $i)).
thf(func_def_90, type, sK27: ($i > $i > $i)).
thf(func_def_94, type, sK31: (($i > $o) > $i)).
thf(func_def_95, type, sK32: ($i > $o)).
thf(func_def_96, type, sK33: ($i > $i)).
thf(func_def_97, type, sK34: ($i > $i > $i)).
thf(func_def_101, type, sK38: ($i > $i > $i)).
thf(func_def_102, type, sK39: ($i > $i > $i)).
thf(func_def_105, type, sK42: ($i > $i > $i)).
thf(func_def_106, type, sK43: ($i > $i > $i)).
thf(func_def_107, type, sK44: ($i > $i > $i)).
thf(func_def_108, type, sK45: ($i > $i > $i)).
thf(func_def_109, type, sK46: ($i > $i > $i)).
thf(func_def_110, type, sK47: ($i > $i > $i > $i)).
thf(func_def_111, type, sK48: ($i > $i)).
thf(func_def_112, type, sK49: ($i > $i)).
thf(func_def_113, type, sK50: ($i > $i)).
thf(func_def_114, type, sK51: ($i > $i)).
thf(func_def_115, type, sK52: ($i > $i > $i > $i)).
thf(func_def_116, type, sK53: ($i > $i > $i > $i)).
thf(func_def_117, type, sK54: ($i > $i > $i)).
thf(func_def_118, type, sK55: ($i > $i > $i)).
thf(func_def_119, type, sK56: ($i > $i > $i)).
thf(func_def_120, type, sK57: ($i > $i)).
thf(func_def_122, type, sK59: ($i > $i)).
thf(func_def_123, type, sK60: ($i > $i)).
thf(func_def_131, type, sK68: $o).
thf(func_def_132, type, sK69: ($i > $i)).
thf(func_def_137, type, sK74: ($i > $i > $i)).
thf(func_def_141, type, sK78: $o).
thf(func_def_143, type, sK80: ($i > $i)).
thf(func_def_144, type, sK81: $o).
thf(func_def_150, type, sK87: ($i > $i)).
thf(func_def_152, type, sK89: ($i > $i)).
thf(func_def_153, type, sK90: ($i > $o)).
thf(func_def_154, type, sK91: (($i > $o) > $i)).
thf(func_def_156, type, sK93: ($i > $i)).
thf(func_def_158, type, sK95: ($i > $o)).
thf(func_def_171, type, sK108: ($i > $o)).
thf(func_def_173, type, sK110: ($i > $i > $o)).
thf(func_def_175, type, sK112: ($i > $i)).
thf(func_def_176, type, sK113: ($i > $i)).
thf(func_def_177, type, sK114: ($i > ($i > $i > $o) > $i)).
thf(func_def_178, type, sK115: ($i > ($i > $i > $o) > $i)).
thf(func_def_179, type, sK116: ($i > $i > ($i > $i > $o) > $i)).
thf(func_def_180, type, sK117: ($i > $o)).
thf(func_def_183, type, sK120: ($i > ($i > $o) > $i)).
thf(func_def_184, type, sK121: ($i > $i)).
thf(func_def_185, type, sK122: ($i > $i > ($i > $i > $o) > $i)).
thf(func_def_186, type, sK123: ($i > ($i > $o) > $i)).
thf(func_def_187, type, sK124: ($i > ($i > $o) > $i)).
thf(func_def_188, type, sK125: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_189, type, sK126: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_190, type, sK127: ($i > ($i > $o) > $i)).
thf(f6,axiom,(
  (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)).
thf(f43,conjecture,(
  setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2))))))))))))))))))))))))))))))))))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)).
thf(f44,negated_conjecture,(
  ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))))))))))))))))))))))))))))))))))))))))),
  inference(negated_conjecture,[status(cth)],[f43])).
thf(f51,plain,(
  ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))))))))))))))))))))))))))))))))))))))))),
  inference(rectify,[],[f44])).
thf(f52,plain,(
  ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) => ! [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) = $true) => ((((in @ X3 @ X0)) = $true) => ($true = X2))) => ($true = X2))))))))))))))))))))))))))))))))))))))))))),
  inference(fool_elimination,[],[f51])).
thf(f53,plain,(
  (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
  inference(rectify,[],[f6])).
thf(f54,plain,(
  ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (setunion @ X0))) = $true)) <=> (setunionAx = $true)),
  inference(fool_elimination,[],[f53])).
thf(f148,plain,(
  ((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((($true = X2) | (((in @ X3 @ X0)) != $true)) | (((in @ X1 @ X3)) != $true))) & (((in @ X1 @ (setunion @ X0))) = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
  inference(ennf_transformation,[],[f52])).
thf(f149,plain,(
  (powersetI = $true) & (replAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (prop2setE = $true) & (descrp = $true) & ? [X1 : $i,X0 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) & ? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((((in @ X1 @ X3)) != $true) | ($true = X2) | (((in @ X3 @ X0)) != $true)))) & (setextAx = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (setunionI = $true) & (dsetconstrI = $true) & (powersetE = $true) & (setadjoinOr = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (setext = $true) & (foundationAx = $true) & (exuE1 = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (exuE3e = $true) & (emptyI = $true) & (setbeta = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (notinemptyset = $true) & (setoftrueEq = $true) & (dsetconstrEL = $true) & (dsetconstrER = $true) & (nonemptyE1 = $true) & (emptyInPowerset = $true) & (omegaSAx = $true) & (setunionAx = $true) & (emptysetAx = $true) & (setadjoinIL = $true)),
  inference(flattening,[],[f148])).
thf(f208,plain,(
  (! [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (setunion @ X0))) != $true)) & ((((in @ X1 @ (setunion @ X0))) = $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true)))) | (setunionAx != $true)) & ((setunionAx = $true) | ? [X1 : $i,X0 : $i] : (((((in @ X1 @ (setunion @ X0))) != $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true))) & ((((in @ X1 @ (setunion @ X0))) = $true) | ? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)))))),
  inference(nnf_transformation,[],[f54])).
thf(f209,plain,(
  (! [X0 : $i,X1 : $i] : ((? [X2 : $i] : (($true = ((in @ X0 @ X2))) & (((in @ X2 @ X1)) = $true)) | ($true != ((in @ X0 @ (setunion @ X1))))) & (($true = ((in @ X0 @ (setunion @ X1)))) | ! [X3 : $i] : (($true != ((in @ X0 @ X3))) | (((in @ X3 @ X1)) != $true)))) | (setunionAx != $true)) & ((setunionAx = $true) | ? [X4 : $i,X5 : $i] : ((($true != ((in @ X4 @ (setunion @ X5)))) | ! [X6 : $i] : ((((in @ X4 @ X6)) != $true) | (((in @ X6 @ X5)) != $true))) & (($true = ((in @ X4 @ (setunion @ X5)))) | ? [X7 : $i] : ((((in @ X4 @ X7)) = $true) & ($true = ((in @ X7 @ X5)))))))),
  inference(rectify,[],[f208])).
thf(f210,plain,(
  (! [X0 : $i,X1 : $i] : (((($true = ((in @ X0 @ (sK27 @ X1 @ X0)))) & ($true = ((in @ (sK27 @ X1 @ X0) @ X1)))) | ($true != ((in @ X0 @ (setunion @ X1))))) & (($true = ((in @ X0 @ (setunion @ X1)))) | ! [X3 : $i] : (($true != ((in @ X0 @ X3))) | (((in @ X3 @ X1)) != $true)))) | (setunionAx != $true)) & ((setunionAx = $true) | ((($true != ((in @ sK28 @ (setunion @ sK29)))) | ! [X6 : $i] : (($true != ((in @ sK28 @ X6))) | ($true != ((in @ X6 @ sK29))))) & (($true = ((in @ sK28 @ (setunion @ sK29)))) | (($true = ((in @ sK28 @ sK30))) & ($true = ((in @ sK30 @ sK29)))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK28,sK29,sK30]),skolemize(X5,$thf(sK7 @ X4 @ X3)),skolemize(X4,$thf(sK28)),skolemize(X5,$thf(sK29)),skolemize(X7,$thf(sK30))],[f209])).
thf(f244,plain,(
  (powersetI = $true) & (replAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (prop2setE = $true) & (descrp = $true) & ? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X1)))) & ? [X2 : $o] : (($true != X2) & ! [X3 : $i] : (($true != ((in @ X0 @ X3))) | ($true = X2) | (((in @ X3 @ X1)) != $true)))) & (setextAx = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (setunionI = $true) & (dsetconstrI = $true) & (powersetE = $true) & (setadjoinOr = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (setext = $true) & (foundationAx = $true) & (exuE1 = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (exuE3e = $true) & (emptyI = $true) & (setbeta = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (notinemptyset = $true) & (setoftrueEq = $true) & (dsetconstrEL = $true) & (dsetconstrER = $true) & (nonemptyE1 = $true) & (emptyInPowerset = $true) & (omegaSAx = $true) & (setunionAx = $true) & (emptysetAx = $true) & (setadjoinIL = $true)),
  inference(rectify,[],[f149])).
thf(f245,plain,(
  (powersetI = $true) & (replAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (prop2setE = $true) & (descrp = $true) & ((((in @ sK66 @ (setunion @ sK67))) = $true) & (($true != sK68) & ! [X3 : $i] : (($true != ((in @ sK66 @ X3))) | ($true = sK68) | (((in @ X3 @ sK67)) != $true)))) & (setextAx = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (setunionI = $true) & (dsetconstrI = $true) & (powersetE = $true) & (setadjoinOr = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (setext = $true) & (foundationAx = $true) & (exuE1 = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (exuE3e = $true) & (emptyI = $true) & (setbeta = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (notinemptyset = $true) & (setoftrueEq = $true) & (dsetconstrEL = $true) & (dsetconstrER = $true) & (nonemptyE1 = $true) & (emptyInPowerset = $true) & (omegaSAx = $true) & (setunionAx = $true) & (emptysetAx = $true) & (setadjoinIL = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK66,sK67,sK68]),skolemize(X0,$thf(sK66)),skolemize(X1,$thf(sK67)),skolemize(X2,$thf(sK68))],[f244])).
thf(f344,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK27 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (setunion @ X1)))) | (setunionAx != $true)) )),
  inference(cnf_transformation,[],[f210])).
thf(f345,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (sK27 @ X1 @ X0)))) | ($true != ((in @ X0 @ (setunion @ X1)))) | (setunionAx != $true)) )),
  inference(cnf_transformation,[],[f210])).
thf(f412,plain,(
  (setunionAx = $true)),
  inference(cnf_transformation,[],[f245])).
thf(f443,plain,(
  ( ! [X3 : $i] : ((((in @ X3 @ sK67)) != $true) | ($true != ((in @ sK66 @ X3))) | ($true = sK68)) )),
  inference(cnf_transformation,[],[f245])).
thf(f444,plain,(
  ($true != sK68)),
  inference(cnf_transformation,[],[f245])).
thf(f445,plain,(
  (((in @ sK66 @ (setunion @ sK67))) = $true)),
  inference(cnf_transformation,[],[f245])).
thf(f567,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ X0 @ (sK27 @ X1 @ X0)))) | ($true != ((in @ X0 @ (setunion @ X1))))) )),
  inference(definition_unfolding,[],[f345,f412])).
thf(f568,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ (sK27 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (setunion @ X1))))) )),
  inference(definition_unfolding,[],[f344,f412])).
thf(f685,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | ($true = ((in @ X0 @ (sK27 @ X1 @ X0))))) )),
  inference(trivial_inequality_removal,[],[f567])).
thf(f722,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | ($true = ((in @ (sK27 @ X1 @ X0) @ X1)))) )),
  inference(trivial_inequality_removal,[],[f568])).
thf(f854,definition,(
  spl128_3 <=> ! [X3 : $i] : ((((in @ X3 @ sK67)) != $true) | ($true != ((in @ sK66 @ X3))))),
  introduced(definition,[new_symbols(definition,[spl128_3])],[avatar_definition])).
thf(f855,plain,(
  ( ! [X3 : $i] : (($true != ((in @ sK66 @ X3))) | (((in @ X3 @ sK67)) != $true)) ) | ~spl128_3),
  inference(avatar_component_clause,[],[f854])).
thf(f857,definition,(
  spl128_4 <=> ($true = sK68)),
  introduced(definition,[new_symbols(definition,[spl128_4])],[avatar_definition])).
thf(f858,plain,(
  ($true = sK68) | ~spl128_4),
  inference(avatar_component_clause,[],[f857])).
thf(f859,plain,(
  spl128_3 | spl128_4),
  inference(avatar_split_clause,[],[f443,f857,f854])).
thf(f989,plain,(
  ($true != $true) | ($true = ((in @ sK66 @ (sK27 @ sK67 @ sK66))))),
  inference(constrained_superposition,[],[f685,f445])).
thf(f995,plain,(
  ($true = ((in @ sK66 @ (sK27 @ sK67 @ sK66))))),
  inference(trivial_inequality_removal,[],[f989])).
thf(f1000,plain,(
  ($true != $true) | ($true != ((in @ (sK27 @ sK67 @ sK66) @ sK67))) | ~spl128_3),
  inference(constrained_superposition,[],[f855,f995])).
thf(f1004,plain,(
  ($true != ((in @ (sK27 @ sK67 @ sK66) @ sK67))) | ~spl128_3),
  inference(trivial_inequality_removal,[],[f1000])).
thf(f1009,plain,(
  ($true = ((in @ (sK27 @ sK67 @ sK66) @ sK67))) | ($true != $true)),
  inference(constrained_superposition,[],[f722,f445])).
thf(f1014,plain,(
  ($true = ((in @ (sK27 @ sK67 @ sK66) @ sK67)))),
  inference(trivial_inequality_removal,[],[f1009])).
thf(f1020,plain,(
  $false | ~spl128_3),
  inference(forward_subsumption_resolution,[],[f1014,f1004])).
thf(f1021,plain,(
  ~spl128_3),
  inference(avatar_contradiction_clause,[],[f1020])).
thf(f1022,plain,(
  $false | ~spl128_4),
  inference(forward_subsumption_resolution,[],[f858,f444])).
thf(f1023,plain,(
  ~spl128_4),
  inference(avatar_contradiction_clause,[],[f1022])).
cnf(s2, plain, spl128_3 | spl128_4, inference(sat_conversion,[],[f859])).
cnf(s4, plain, ~spl128_3, inference(sat_conversion,[],[f1021])).
cnf(s5, plain, ~spl128_4, inference(sat_conversion,[],[f1023])).
cnf(s6, plain, $false, inference(rat,[],[s2,s5,s4])).
thf(f1024,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s6])).
% SZS output end Proof for theBenchmark