%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, a: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, vAND: ($o > $o > $o)).
thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_5, type, vIMP: ($o > $o > $o)).
thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_8, type, vIFF: ($o > $o > $o)).
thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_11, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_12, type, sK0: ((a > $o) > $o)).
thf(func_def_13, type, sK1: ((a > $o) > a)).
thf(func_def_14, type, sK2: ((a > a > $o) > a)).
thf(func_def_15, type, sK3: ((a > a > $o) > a)).
thf(func_def_16, type, sK4: ((a > a > $o) > a)).
thf(func_def_17, type, sK5: ((a > a > $o) > a)).
thf(func_def_18, type, sK6: ((a > a > $o) > a)).
thf(func_def_19, type, sK7: ((a > a > $o) > a)).
thf(func_def_20, type, sK8: (a > a > $o)).
thf(func_def_21, type, sK9: ((a > $o) > (a > $o) > a)).
thf(func_def_23, type, sK11: ((a > a > $o) > a > $o)).
thf(func_def_24, type, sK12: ((a > a > $o) > a)).
thf(func_def_25, type, sK13: ((a > a > $o) > a)).
thf(func_def_26, type, sK14: ((a > a > $o) > a)).
thf(func_def_27, type, sK15: ((a > a > $o) > a > $o)).
thf(func_def_28, type, sK16: ((a > a > $o) > a)).
thf(func_def_29, type, sK17: ((a > a > $o) > a)).
thf(func_def_30, type, sK18: ((a > a > $o) > a)).
thf(func_def_31, type, sK19: (a > $o)).
thf(func_def_32, type, sK20: a).
thf(func_def_33, type, sK21: a).
thf(func_def_34, type, sK22: a).
thf(func_def_35, type, sK23: ((a > a > $o) > a > $o)).
thf(func_def_36, type, sK24: ((a > a > $o) > a)).
thf(func_def_37, type, sK25: ((a > a > $o) > a)).
thf(func_def_38, type, sK26: ((a > a > $o) > a)).
thf(func_def_39, type, sK27: (a > $o)).
thf(func_def_40, type, sK28: a).
thf(func_def_41, type, sK29: a).
thf(func_def_42, type, sK30: a).
thf(func_def_43, type, sK31: ((a > a > $o) > a > $o)).
thf(func_def_44, type, sK32: ((a > a > $o) > a)).
thf(func_def_45, type, sK33: ((a > a > $o) > a)).
thf(func_def_46, type, sK34: ((a > a > $o) > a)).
thf(func_def_47, type, sK35: ((a > $o) > a)).
thf(func_def_48, type, sK36: ((a > $o) > a)).
thf(func_def_49, type, sK37: ((a > $o) > a)).
thf(func_def_50, type, sK38: ((a > a > $o) > a > $o)).
thf(func_def_51, type, sK39: ((a > a > $o) > a)).
thf(func_def_52, type, sK40: ((a > a > $o) > a)).
thf(func_def_53, type, sK41: ((a > a > $o) > a)).
thf(func_def_54, type, sK42: ((a > a > $o) > a > $o)).
thf(func_def_55, type, sK43: ((a > a > $o) > a)).
thf(func_def_56, type, sK44: ((a > a > $o) > a)).
thf(func_def_57, type, sK45: ((a > a > $o) > a)).
thf(func_def_58, type, sK46: (a > $o)).
thf(func_def_59, type, sK47: a).
thf(func_def_60, type, sK48: a).
thf(func_def_61, type, sK49: a).
thf(func_def_62, type, sK50: ((a > $o) > a)).
thf(func_def_63, type, sK51: ((a > $o) > a)).
thf(func_def_64, type, sK52: ((a > $o) > a)).
thf(func_def_65, type, sK53: (a > $o)).
thf(func_def_66, type, sK54: a).
thf(func_def_67, type, sK55: a).
thf(func_def_68, type, sK56: a).
thf(func_def_69, type, sK57: a).
thf(func_def_70, type, sK58: (a > $o)).
thf(func_def_71, type, sK59: a).
thf(func_def_72, type, sK60: a).
thf(func_def_73, type, sK61: a).
thf(func_def_74, type, sK62: ((a > a > $o) > a > $o)).
thf(func_def_75, type, sK63: ((a > a > $o) > a)).
thf(func_def_76, type, sK64: ((a > a > $o) > a)).
thf(func_def_77, type, sK65: ((a > a > $o) > a)).
thf(func_def_78, type, sK66: ((a > a > $o) > a > $o)).
thf(func_def_79, type, sK67: ((a > a > $o) > a)).
thf(func_def_80, type, sK68: ((a > a > $o) > a)).
thf(func_def_81, type, sK69: ((a > a > $o) > a)).
thf(func_def_82, type, sK70: ((a > a > $o) > a > $o)).
thf(func_def_83, type, sK71: ((a > a > $o) > a)).
thf(func_def_84, type, sK72: ((a > a > $o) > a)).
thf(func_def_85, type, sK73: ((a > a > $o) > a)).
thf(func_def_86, type, sK74: ((a > a > $o) > a > $o)).
thf(func_def_87, type, sK75: ((a > a > $o) > a)).
thf(func_def_88, type, sK76: ((a > a > $o) > a)).
thf(func_def_89, type, sK77: ((a > a > $o) > a)).
thf(func_def_90, type, sK78: ((a > a > $o) > a > $o)).
thf(func_def_91, type, sK79: ((a > a > $o) > a)).
thf(func_def_92, type, sK80: ((a > a > $o) > a)).
thf(func_def_93, type, sK81: ((a > a > $o) > a)).
thf(func_def_94, type, sK82: ((a > a > $o) > a > $o)).
thf(func_def_95, type, sK83: ((a > a > $o) > a)).
thf(func_def_96, type, sK84: ((a > a > $o) > a)).
thf(func_def_97, type, sK85: ((a > a > $o) > a)).
thf(func_def_98, type, sK86: ((a > a > $o) > a > $o)).
thf(func_def_99, type, sK87: ((a > a > $o) > a)).
thf(func_def_100, type, sK88: ((a > a > $o) > a)).
thf(func_def_101, type, sK89: ((a > a > $o) > a)).
thf(func_def_102, type, sK90: a).
thf(func_def_103, type, sK91: ((a > a > $o) > a > $o)).
thf(func_def_104, type, sK92: ((a > a > $o) > a)).
thf(func_def_105, type, sK93: ((a > a > $o) > a)).
thf(func_def_106, type, sK94: ((a > a > $o) > a)).
thf(func_def_107, type, sK95: ((a > a > $o) > a > $o)).
thf(func_def_108, type, sK96: ((a > a > $o) > a)).
thf(func_def_109, type, sK97: ((a > a > $o) > a)).
thf(func_def_110, type, sK98: ((a > a > $o) > a)).
thf(func_def_111, type, sK99: ((a > a > $o) > a > $o)).
thf(func_def_112, type, sK100: ((a > a > $o) > a)).
thf(func_def_113, type, sK101: ((a > a > $o) > a)).
thf(func_def_114, type, sK102: ((a > a > $o) > a)).
thf(func_def_115, type, sK103: ((a > a > $o) > a > $o)).
thf(func_def_116, type, sK104: ((a > a > $o) > a)).
thf(func_def_117, type, sK105: ((a > a > $o) > a)).
thf(func_def_118, type, sK106: ((a > a > $o) > a)).
thf(func_def_119, type, sK107: ((a > $o) > a)).
thf(func_def_120, type, sK108: ((a > $o) > a)).
thf(func_def_121, type, sK109: ((a > $o) > a)).
thf(func_def_122, type, sK110: a).
thf(func_def_123, type, sK111: a).
thf(func_def_124, type, sK112: (a > $o)).
thf(func_def_125, type, sK113: a).
thf(func_def_126, type, sK114: a).
thf(func_def_127, type, sK115: a).
thf(func_def_128, type, sK116: a).
thf(func_def_129, type, sK117: ((a > a > $o) > a > $o)).
thf(func_def_130, type, sK118: ((a > a > $o) > a)).
thf(func_def_131, type, sK119: ((a > a > $o) > a)).
thf(func_def_132, type, sK120: ((a > a > $o) > a)).
thf(func_def_133, type, sK121: a).
thf(func_def_134, type, sK122: a).
thf(func_def_135, type, sK123: ((a > a > $o) > a > $o)).
thf(func_def_136, type, sK124: ((a > a > $o) > a)).
thf(func_def_137, type, sK125: ((a > a > $o) > a)).
thf(func_def_138, type, sK126: ((a > a > $o) > a)).
thf(func_def_139, type, sK127: ((a > a > $o) > a > $o)).
thf(func_def_140, type, sK128: ((a > a > $o) > a)).
thf(func_def_141, type, sK129: ((a > a > $o) > a)).
thf(func_def_142, type, sK130: ((a > a > $o) > a)).
thf(func_def_143, type, sK131: a).
thf(func_def_144, type, sK132: ((a > a > $o) > a > $o)).
thf(func_def_145, type, sK133: ((a > a > $o) > a)).
thf(func_def_146, type, sK134: ((a > a > $o) > a)).
thf(func_def_147, type, sK135: ((a > a > $o) > a)).
thf(func_def_148, type, sK136: ((a > a > $o) > a > $o)).
thf(func_def_149, type, sK137: ((a > a > $o) > a)).
thf(func_def_150, type, sK138: ((a > a > $o) > a)).
thf(func_def_151, type, sK139: ((a > a > $o) > a)).
thf(func_def_152, type, sK140: a).
thf(f1,conjecture,(
  ! [X1 : (a > $o),X8 : (a > $o)] : (! [X9 : a] : (((X1 @ X9)) = ((X8 @ X9))) => ! [X0 : ((a > $o) > $o)] : ((X0 @ X1) => (X0 @ X8))) => ! [X0 : ((a > $o) > $o)] : ((! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X1 : (a > $o)] : ((X1 @ X3) & ! [X4 : (a > $o)] : (((X0 @ X4) & (X4 @ X3)) => (X4 = X1)) & (X0 @ X1))) => ? [X5 : (a > a > $o)] : (! [X6 : a,X3 : a,X2 : a] : (((X5 @ X6 @ X2) & (X5 @ X3 @ X6)) => (X5 @ X3 @ X2)) & ! [X6 : a,X3 : a] : ((X5 @ X3 @ X6) => (X5 @ X6 @ X3)) & ! [X3 : a] : (X5 @ X3 @ X3) & (X0 = (^[X7 : (a > $o)] : (? [X2 : a] : (X7 @ X2) & ! [X3 : a] : ((X7 @ X3) => ! [X6 : a] : ((X5 @ X3 @ X6) <=> (X7 @ X6))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM262_EXT_pme)).
thf(f2,negated_conjecture,(
  ~(! [X1 : (a > $o),X8 : (a > $o)] : (! [X9 : a] : (((X1 @ X9)) = ((X8 @ X9))) => ! [X0 : ((a > $o) > $o)] : ((X0 @ X1) => (X0 @ X8))) => ! [X0 : ((a > $o) > $o)] : ((! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X1 : (a > $o)] : ((X1 @ X3) & ! [X4 : (a > $o)] : (((X0 @ X4) & (X4 @ X3)) => (X4 = X1)) & (X0 @ X1))) => ? [X5 : (a > a > $o)] : (! [X6 : a,X3 : a,X2 : a] : (((X5 @ X6 @ X2) & (X5 @ X3 @ X6)) => (X5 @ X3 @ X2)) & ! [X6 : a,X3 : a] : ((X5 @ X3 @ X6) => (X5 @ X6 @ X3)) & ! [X3 : a] : (X5 @ X3 @ X3) & (X0 = (^[X7 : (a > $o)] : (? [X2 : a] : (X7 @ X2) & ! [X3 : a] : ((X7 @ X3) => ! [X6 : a] : ((X5 @ X3 @ X6) <=> (X7 @ X6)))))))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : (((X1 @ X2)) = ((X0 @ X2))) => ! [X3 : ((a > $o) > $o)] : ((X3 @ X0) => (X3 @ X1))) => ! [X4 : ((a > $o) > $o)] : ((! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) & ! [X7 : a] : ? [X8 : (a > $o)] : ((X8 @ X7) & ! [X9 : (a > $o)] : (((X4 @ X9) & (X9 @ X7)) => (X8 = X9)) & (X4 @ X8))) => ? [X10 : (a > a > $o)] : (! [X11 : a,X12 : a,X13 : a] : (((X10 @ X11 @ X13) & (X10 @ X12 @ X11)) => (X10 @ X12 @ X13)) & ! [X14 : a,X15 : a] : ((X10 @ X15 @ X14) => (X10 @ X14 @ X15)) & ! [X16 : a] : (X10 @ X16 @ X16) & (X4 = (^[X17 : (a > $o)] : (? [X18 : a] : (X17 @ X18) & ! [X19 : a] : ((X17 @ X19) => ! [X20 : a] : ((X10 @ X19 @ X20) <=> (X17 @ X20)))))))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~(! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : (((X1 @ X2)) = ((X0 @ X2))) => ! [X3 : ((a > $o) > $o)] : ((((X3 @ X0)) = $true) => (((X3 @ X1)) = $true))) => ! [X4 : ((a > $o) > $o)] : ((! [X5 : (a > $o)] : ((((X4 @ X5)) = $true) => ? [X6 : a] : (((X5 @ X6)) = $true)) & ! [X7 : a] : ? [X8 : (a > $o)] : (($true = ((X8 @ X7))) & ($true = ((X4 @ X8))) & ! [X9 : (a > $o)] : ((($true = ((X4 @ X9))) & (((X9 @ X7)) = $true)) => (X8 = X9)))) => ? [X10 : (a > a > $o)] : (! [X12 : a,X11 : a,X13 : a] : (((((X10 @ X12 @ X11)) = $true) & ($true = ((X10 @ X11 @ X13)))) => (((X10 @ X12 @ X13)) = $true)) & ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X10 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1))))) = X4) & ! [X16 : a] : (((X10 @ X16 @ X16)) = $true) & ! [X15 : a,X14 : a] : ((((X10 @ X15 @ X14)) = $true) => ($true = ((X10 @ X14 @ X15)))))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X4 : ((a > $o) > $o)] : (! [X10 : (a > a > $o)] : (? [X12 : a,X11 : a,X13 : a] : ((((X10 @ X12 @ X13)) != $true) & ((((X10 @ X12 @ X11)) = $true) & ($true = ((X10 @ X11 @ X13))))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X10 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1))))) != X4) | ? [X16 : a] : (((X10 @ X16 @ X16)) != $true) | ? [X15 : a,X14 : a] : (($true != ((X10 @ X14 @ X15))) & (((X10 @ X15 @ X14)) = $true))) & (! [X5 : (a > $o)] : (? [X6 : a] : (((X5 @ X6)) = $true) | (((X4 @ X5)) != $true)) & ! [X7 : a] : ? [X8 : (a > $o)] : (($true = ((X8 @ X7))) & ($true = ((X4 @ X8))) & ! [X9 : (a > $o)] : ((X8 = X9) | (($true != ((X4 @ X9))) | (((X9 @ X7)) != $true)))))) & ! [X0 : (a > $o),X1 : (a > $o)] : (? [X2 : a] : (((X1 @ X2)) != ((X0 @ X2))) | ! [X3 : ((a > $o) > $o)] : ((((X3 @ X1)) = $true) | (((X3 @ X0)) != $true)))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : (? [X6 : a] : (((X5 @ X6)) = $true) | (((X4 @ X5)) != $true)) & ! [X10 : (a > a > $o)] : (? [X11 : a,X13 : a,X12 : a] : (($true = ((X10 @ X11 @ X13))) & (((X10 @ X12 @ X13)) != $true) & (((X10 @ X12 @ X11)) = $true)) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X10 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1))))) != X4) | ? [X16 : a] : (((X10 @ X16 @ X16)) != $true) | ? [X15 : a,X14 : a] : (($true != ((X10 @ X14 @ X15))) & (((X10 @ X15 @ X14)) = $true))) & ! [X7 : a] : ? [X8 : (a > $o)] : (($true = ((X4 @ X8))) & ($true = ((X8 @ X7))) & ! [X9 : (a > $o)] : ((X8 = X9) | (((X9 @ X7)) != $true) | ($true != ((X4 @ X9)))))) & ! [X0 : (a > $o),X1 : (a > $o)] : (? [X2 : a] : (((X1 @ X2)) != ((X0 @ X2))) | ! [X3 : ((a > $o) > $o)] : ((((X3 @ X1)) = $true) | (((X3 @ X0)) != $true)))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ? [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : (? [X2 : a] : (((X1 @ X2)) = $true) | (((X0 @ X1)) != $true)) & ! [X3 : (a > a > $o)] : (? [X4 : a,X5 : a,X6 : a] : (($true = ((X3 @ X4 @ X5))) & ($true != ((X3 @ X6 @ X5))) & (((X3 @ X6 @ X4)) = $true)) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1))))) != X0) | ? [X7 : a] : ($true != ((X3 @ X7 @ X7))) | ? [X8 : a,X9 : a] : ((((X3 @ X9 @ X8)) != $true) & (((X3 @ X8 @ X9)) = $true))) & ! [X10 : a] : ? [X11 : (a > $o)] : ((((X0 @ X11)) = $true) & ($true = ((X11 @ X10))) & ! [X12 : (a > $o)] : ((X11 = X12) | (((X12 @ X10)) != $true) | (((X0 @ X12)) != $true)))) & ! [X13 : (a > $o),X14 : (a > $o)] : (? [X15 : a] : (((X14 @ X15)) != ((X13 @ X15))) | ! [X16 : ((a > $o) > $o)] : ((((X16 @ X14)) = $true) | ($true != ((X16 @ X13)))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  (! [X1 : (a > $o)] : (($true = ((X1 @ (sK1 @ X1)))) | (((sK0 @ X1)) != $true)) & ! [X3 : (a > a > $o)] : ((($true = ((X3 @ (sK2 @ X3) @ (sK3 @ X3)))) & (((X3 @ (sK4 @ X3) @ (sK3 @ X3))) != $true) & (((X3 @ (sK4 @ X3) @ (sK2 @ X3))) = $true)) | (sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1)))))) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ((((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) & ($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3)))))) & ! [X10 : a] : (($true = ((sK0 @ (sK8 @ X10)))) & ($true = ((sK8 @ X10 @ X10))) & ! [X12 : (a > $o)] : ((((sK8 @ X10)) = X12) | (((X12 @ X10)) != $true) | ($true != ((sK0 @ X12)))))) & ! [X13 : (a > $o),X14 : (a > $o)] : ((((X13 @ (sK9 @ X14 @ X13))) != ((X14 @ (sK9 @ X14 @ X13)))) | ! [X16 : ((a > $o) > $o)] : ((((X16 @ X14)) = $true) | ($true != ((X16 @ X13)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13)),skolemize(X15,$thf(sK9 @ X14 @ X13))],[f7])).
thf(f9,plain,(
  ( ! [X16 : ((a > $o) > $o),X14 : (a > $o),X13 : (a > $o)] : (($true != ((X16 @ X13))) | (((X16 @ X14)) = $true) | (((X13 @ (sK9 @ X14 @ X13))) != ((X14 @ (sK9 @ X14 @ X13))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f10,plain,(
  ( ! [X10 : a,X12 : (a > $o)] : (($true != ((sK0 @ X12))) | (((X12 @ X10)) != $true) | (((sK8 @ X10)) = X12)) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X10 : a] : (($true = ((sK8 @ X10 @ X10)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f12,plain,(
  ( ! [X10 : a] : (($true = ((sK0 @ (sK8 @ X10))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f13,plain,(
  ( ! [X3 : (a > a > $o)] : (($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3)))) | (((X3 @ (sK4 @ X3) @ (sK2 @ X3))) = $true) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | (sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1))))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f14,plain,(
  ( ! [X3 : (a > a > $o)] : ((((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) | (sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1)))))) | (((X3 @ (sK4 @ X3) @ (sK2 @ X3))) = $true) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f15,plain,(
  ( ! [X3 : (a > a > $o)] : ((sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1)))))) | (((X3 @ (sK4 @ X3) @ (sK3 @ X3))) != $true) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f16,plain,(
  ( ! [X3 : (a > a > $o)] : (($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | (((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) | (((X3 @ (sK4 @ X3) @ (sK3 @ X3))) != $true) | (sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1))))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f17,plain,(
  ( ! [X3 : (a > a > $o)] : ((sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1)))))) | ($true = ((X3 @ (sK2 @ X3) @ (sK3 @ X3)))) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f18,plain,(
  ( ! [X3 : (a > a > $o)] : ((sK0 != (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ (^[Y1 : a]: (Y0 @ Y1)))))) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | (((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) | ($true = ((X3 @ (sK2 @ X3) @ (sK3 @ X3))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f19,plain,(
  ( ! [X1 : (a > $o)] : ((((sK0 @ X1)) != $true) | ($true = ((X1 @ (sK1 @ X1))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f21,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f22,plain,(
  ( ! [X3 : (a > a > $o)] : ((((X3 @ (sK4 @ X3) @ (sK3 @ X3))) != $true) | (((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0)) )),
  inference(beta-eta_normalization,[],[f16])).
thf(f23,plain,(
  ( ! [X3 : (a > a > $o)] : (((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ($true = ((X3 @ (sK2 @ X3) @ (sK3 @ X3)))) | ($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3))))) )),
  inference(beta-eta_normalization,[],[f17])).
thf(f24,plain,(
  ( ! [X16 : ((a > $o) > $o),X14 : (a > $o),X13 : (a > $o)] : (($true != ((X16 @ X13))) | ($true = ((X13 @ (sK9 @ X14 @ X13)))) | ($true = ((X14 @ (sK9 @ X14 @ X13)))) | (((X16 @ X14)) = $true)) )),
  inference(xor_proxy_clausification,[],[f9])).
thf(f25,plain,(
  ( ! [X16 : ((a > $o) > $o),X14 : (a > $o),X13 : (a > $o)] : (($true != ((X16 @ X13))) | (((X16 @ X14)) = $true) | ($false = ((X14 @ (sK9 @ X14 @ X13)))) | ($false = ((X13 @ (sK9 @ X14 @ X13))))) )),
  inference(xor_proxy_clausification,[],[f9])).
thf(f26,plain,(
  ( ! [X3 : (a > a > $o)] : (($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | (((X3 @ (sK4 @ X3) @ (sK2 @ X3))) = $true) | ($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3))))) )),
  inference(beta-eta_normalization,[],[f13])).
thf(f27,plain,(
  ( ! [X3 : (a > a > $o)] : (((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | (((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | ($true = ((X3 @ (sK2 @ X3) @ (sK3 @ X3))))) )),
  inference(beta-eta_normalization,[],[f18])).
thf(f28,plain,(
  ( ! [X3 : (a > a > $o)] : (($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | (((X3 @ (sK4 @ X3) @ (sK3 @ X3))) != $true) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true = ((X3 @ (sK6 @ X3) @ (sK7 @ X3))))) )),
  inference(beta-eta_normalization,[],[f15])).
thf(f29,plain,(
  ( ! [X3 : (a > a > $o)] : (((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X3 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true != ((X3 @ (sK5 @ X3) @ (sK5 @ X3)))) | (((X3 @ (sK7 @ X3) @ (sK6 @ X3))) != $true) | (((X3 @ (sK4 @ X3) @ (sK2 @ X3))) = $true)) )),
  inference(beta-eta_normalization,[],[f14])).
thf(f47,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((sK8 @ X1)) = X0) | ($true != ((sK0 @ X0))) | ($true != $true) | ($false = ((X0 @ X1)))) )),
  inference(constrained_superposition,[],[f10,f21])).
thf(f48,plain,(
  ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | (((X0 @ X1)) != $true) | ($false = ((sK0 @ X0))) | (((sK8 @ X1)) = X0)) )),
  inference(constrained_superposition,[],[f10,f21])).
thf(f49,plain,(
  ( ! [X0 : (a > $o)] : (($false = ((sK0 @ X0))) | ($true = ((X0 @ (sK1 @ X0)))) | ($true != $true)) )),
  inference(constrained_superposition,[],[f19,f21])).
thf(f57,plain,(
  ( ! [X0 : (a > $o)] : (($true = ((X0 @ (sK1 @ X0)))) | ($false = ((sK0 @ X0)))) )),
  inference(trivial_inequality_removal,[],[f49])).
thf(f58,plain,(
  ( ! [X0 : (a > $o),X1 : a] : (($true != ((sK0 @ X0))) | (((sK8 @ X1)) = X0) | ($false = ((X0 @ X1)))) )),
  inference(trivial_inequality_removal,[],[f47])).
thf(f59,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | ($false = ((sK0 @ X0))) | (((sK8 @ X1)) = X0)) )),
  inference(trivial_inequality_removal,[],[f48])).
thf(f74,plain,(
  ($true != $true) | ($true != ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | ($true != ((sK8 @ (sK7 @ sK8) @ (sK6 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0)),
  inference(constrained_superposition,[],[f22,f11])).
thf(f102,plain,(
  ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true != ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | ($true != ((sK8 @ (sK7 @ sK8) @ (sK6 @ sK8))))),
  inference(trivial_inequality_removal,[],[f74])).
thf(f122,definition,(
  spl10_3 <=> ($true = ((sK8 @ (sK7 @ sK8) @ (sK6 @ sK8))))),
  introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition])).
thf(f124,plain,(
  ($true != ((sK8 @ (sK7 @ sK8) @ (sK6 @ sK8)))) | spl10_3),
  inference(avatar_component_clause,[],[f122])).
thf(f126,definition,(
  spl10_4 <=> ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) = sK0)),
  introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition])).
thf(f127,plain,(
  ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) = sK0) | ~spl10_4),
  inference(avatar_component_clause,[],[f126])).
thf(f128,plain,(
  ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | spl10_4),
  inference(avatar_component_clause,[],[f126])).
thf(f130,definition,(
  spl10_5 <=> ($true = ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8))))),
  introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition])).
thf(f131,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | ~spl10_5),
  inference(avatar_component_clause,[],[f130])).
thf(f132,plain,(
  ($true != ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | spl10_5),
  inference(avatar_component_clause,[],[f130])).
thf(f133,plain,(
  ~spl10_3 | ~spl10_4 | ~spl10_5),
  inference(avatar_split_clause,[],[f102,f130,f126,f122])).
thf(f146,plain,(
  ($true != $true) | (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0)),
  inference(constrained_superposition,[],[f23,f11])).
thf(f174,plain,(
  ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true)),
  inference(trivial_inequality_removal,[],[f146])).
thf(f179,definition,(
  spl10_6 <=> ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8))))),
  introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition])).
thf(f181,plain,(
  ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | ~spl10_6),
  inference(avatar_component_clause,[],[f179])).
thf(f183,definition,(
  spl10_7 <=> (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition])).
thf(f184,plain,(
  (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) != $true) | spl10_7),
  inference(avatar_component_clause,[],[f183])).
thf(f185,plain,(
  (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ~spl10_7),
  inference(avatar_component_clause,[],[f183])).
thf(f186,plain,(
  ~spl10_4 | spl10_6 | spl10_7),
  inference(avatar_split_clause,[],[f174,f183,f179,f126])).
thf(f187,plain,(
  ((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) @ sK19)) != ((sK0 @ sK19))) | spl10_4),
  inference(negative_extensionality,[],[f128])).
thf(f188,plain,(
  ($true = ((sK0 @ sK19))) | ((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) @ sK19)) = $true) | spl10_4),
  inference(xor_proxy_clausification,[],[f187])).
thf(f189,plain,(
  ((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) @ sK19)) = $false) | ($false = ((sK0 @ sK19))) | spl10_4),
  inference(xor_proxy_clausification,[],[f187])).
thf(f190,plain,(
  ($false = (((!! @ a @ (^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1))))))) & (?? @ a @ sK19)))) | ($false = ((sK0 @ sK19))) | spl10_4),
  inference(beta-eta_normalization,[],[f189])).
thf(f191,plain,(
  ($false = ((sK0 @ sK19))) | ($false = ((?? @ a @ sK19))) | ($false = ((!! @ a @ (^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1))))))))) | spl10_4),
  inference(and_proxy_clausification,[],[f190])).
thf(f192,plain,(
  ( ! [X1 : a] : (($false = ((sK0 @ sK19))) | ($false = ((!! @ a @ (^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1))))))))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(pi_proxy_clausification,[],[f191])).
thf(f193,plain,(
  ( ! [X1 : a] : (($false = (((^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1)))))) @ sK20))) | ($false = ((sK0 @ sK19))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(sigma_proxy_clausification,[],[f192])).
thf(f194,plain,(
  ( ! [X1 : a] : (($false = ((sK0 @ sK19))) | ($false = ((sK19 @ X1))) | ($false = (((sK19 @ sK20) => (!! @ a @ (^[Y0 : a]: ((sK8 @ sK20 @ Y0) = (sK19 @ Y0)))))))) ) | spl10_4),
  inference(beta-eta_normalization,[],[f193])).
thf(f195,plain,(
  ( ! [X1 : a] : (($false = ((sK0 @ sK19))) | ($false = ((sK19 @ X1))) | (((!! @ a @ (^[Y0 : a]: ((sK8 @ sK20 @ Y0) = (sK19 @ Y0))))) = $false)) ) | spl10_4),
  inference(imp_proxy_clausification,[],[f194])).
thf(f196,plain,(
  ( ! [X1 : a] : (($false = ((sK0 @ sK19))) | (((sK19 @ sK20)) = $true) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(imp_proxy_clausification,[],[f194])).
thf(f197,plain,(
  ( ! [X1 : a] : (((((^[Y0 : a]: ((sK8 @ sK20 @ Y0) = (sK19 @ Y0))) @ sK21)) = $false) | ($false = ((sK0 @ sK19))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(sigma_proxy_clausification,[],[f195])).
thf(f198,plain,(
  ( ! [X1 : a] : (($false = (((sK8 @ sK20 @ sK21) = (sK19 @ sK21)))) | ($false = ((sK19 @ X1))) | ($false = ((sK0 @ sK19)))) ) | spl10_4),
  inference(beta-eta_normalization,[],[f197])).
thf(f199,plain,(
  ( ! [X1 : a] : (($false = ((sK19 @ X1))) | (((sK8 @ sK20 @ sK21)) != ((sK19 @ sK21))) | ($false = ((sK0 @ sK19)))) ) | spl10_4),
  inference(iff_proxy_clausification,[],[f198])).
thf(f200,plain,(
  ( ! [X1 : a] : (($false = ((sK0 @ sK19))) | ($true = ((sK8 @ sK20 @ sK21))) | ($true = ((sK19 @ sK21))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(xor_proxy_clausification,[],[f199])).
thf(f201,plain,(
  ( ! [X1 : a] : (($false = ((sK8 @ sK20 @ sK21))) | ($false = ((sK19 @ sK21))) | ($false = ((sK19 @ X1))) | ($false = ((sK0 @ sK19)))) ) | spl10_4),
  inference(xor_proxy_clausification,[],[f199])).
thf(f202,plain,(
  ((((!! @ a @ (^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1))))))) & (?? @ a @ sK19))) = $true) | ($true = ((sK0 @ sK19))) | spl10_4),
  inference(beta-eta_normalization,[],[f188])).
thf(f203,plain,(
  ($true = ((sK0 @ sK19))) | (((?? @ a @ sK19)) = $true) | spl10_4),
  inference(and_proxy_clausification,[],[f202])).
thf(f204,plain,(
  ($true = ((sK0 @ sK19))) | ($true = ((!! @ a @ (^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1))))))))) | spl10_4),
  inference(and_proxy_clausification,[],[f202])).
thf(f205,plain,(
  ( ! [X1 : a] : (((((^[Y0 : a]: ((sK19 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK8 @ Y0 @ Y1) = (sK19 @ Y1)))))) @ X1)) = $true) | ($true = ((sK0 @ sK19)))) ) | spl10_4),
  inference(pi_proxy_clausification,[],[f204])).
thf(f206,plain,(
  ( ! [X1 : a] : (((((sK19 @ X1) => (!! @ a @ (^[Y0 : a]: ((sK8 @ X1 @ Y0) = (sK19 @ Y0)))))) = $true) | ($true = ((sK0 @ sK19)))) ) | spl10_4),
  inference(beta-eta_normalization,[],[f205])).
thf(f207,plain,(
  ( ! [X1 : a] : (($true = ((sK0 @ sK19))) | ($true = ((!! @ a @ (^[Y0 : a]: ((sK8 @ X1 @ Y0) = (sK19 @ Y0)))))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(imp_proxy_clausification,[],[f206])).
thf(f208,plain,(
  ( ! [X2 : a,X1 : a] : (($true = (((^[Y0 : a]: ((sK8 @ X1 @ Y0) = (sK19 @ Y0))) @ X2))) | ($true = ((sK0 @ sK19))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(pi_proxy_clausification,[],[f207])).
thf(f209,plain,(
  ( ! [X2 : a,X1 : a] : (($true = ((sK0 @ sK19))) | ((((sK8 @ X1 @ X2) = (sK19 @ X2))) = $true) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(beta-eta_normalization,[],[f208])).
thf(f210,plain,(
  ( ! [X2 : a,X1 : a] : (($false = ((sK19 @ X1))) | (((sK8 @ X1 @ X2)) = ((sK19 @ X2))) | ($true = ((sK0 @ sK19)))) ) | spl10_4),
  inference(iff_proxy_clausification,[],[f209])).
thf(f211,plain,(
  ( ! [X2 : a,X1 : a] : (($false = ((sK19 @ X1))) | ($true = ((sK0 @ sK19))) | ($true = ((sK8 @ X1 @ X2))) | ($false = ((sK19 @ X2)))) ) | spl10_4),
  inference(iff_proxy_clausification,[],[f210])).
thf(f212,plain,(
  ( ! [X2 : a,X1 : a] : (($false = ((sK8 @ X1 @ X2))) | ($true = ((sK0 @ sK19))) | ($true = ((sK19 @ X2))) | ($false = ((sK19 @ X1)))) ) | spl10_4),
  inference(iff_proxy_clausification,[],[f210])).
thf(f213,plain,(
  ($true = ((sK0 @ sK19))) | ($true = ((sK19 @ sK22))) | spl10_4),
  inference(sigma_proxy_clausification,[],[f203])).
thf(f215,definition,(
  spl10_8 <=> ($false = ((sK0 @ sK19)))),
  introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition])).
thf(f216,plain,(
  ($false != ((sK0 @ sK19))) | spl10_8),
  inference(avatar_component_clause,[],[f215])).
thf(f217,plain,(
  ($false = ((sK0 @ sK19))) | ~spl10_8),
  inference(avatar_component_clause,[],[f215])).
thf(f219,definition,(
  spl10_9 <=> (((sK19 @ sK20)) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition])).
thf(f221,plain,(
  (((sK19 @ sK20)) = $true) | ~spl10_9),
  inference(avatar_component_clause,[],[f219])).
thf(f223,definition,(
  spl10_10 <=> ! [X1 : a] : ($false = ((sK19 @ X1)))),
  introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition])).
thf(f224,plain,(
  ( ! [X1 : a] : (($false = ((sK19 @ X1)))) ) | ~spl10_10),
  inference(avatar_component_clause,[],[f223])).
thf(f225,plain,(
  spl10_8 | spl10_9 | spl10_10 | spl10_4),
  inference(avatar_split_clause,[],[f196,f126,f223,f219,f215])).
thf(f227,definition,(
  spl10_11 <=> ($false = ((sK19 @ sK21)))),
  introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition])).
thf(f229,plain,(
  ($false = ((sK19 @ sK21))) | ~spl10_11),
  inference(avatar_component_clause,[],[f227])).
thf(f231,definition,(
  spl10_12 <=> ($false = ((sK8 @ sK20 @ sK21)))),
  introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition])).
thf(f232,plain,(
  ($false != ((sK8 @ sK20 @ sK21))) | spl10_12),
  inference(avatar_component_clause,[],[f231])).
thf(f233,plain,(
  ($false = ((sK8 @ sK20 @ sK21))) | ~spl10_12),
  inference(avatar_component_clause,[],[f231])).
thf(f234,plain,(
  spl10_8 | spl10_11 | spl10_10 | spl10_12 | spl10_4),
  inference(avatar_split_clause,[],[f201,f126,f231,f223,f227,f215])).
thf(f236,definition,(
  spl10_13 <=> ($true = ((sK8 @ sK20 @ sK21)))),
  introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition])).
thf(f238,plain,(
  ($true = ((sK8 @ sK20 @ sK21))) | ~spl10_13),
  inference(avatar_component_clause,[],[f236])).
thf(f240,definition,(
  spl10_14 <=> ($true = ((sK19 @ sK21)))),
  introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition])).
thf(f241,plain,(
  ($true != ((sK19 @ sK21))) | spl10_14),
  inference(avatar_component_clause,[],[f240])).
thf(f242,plain,(
  ($true = ((sK19 @ sK21))) | ~spl10_14),
  inference(avatar_component_clause,[],[f240])).
thf(f243,plain,(
  spl10_10 | spl10_13 | spl10_8 | spl10_14 | spl10_4),
  inference(avatar_split_clause,[],[f200,f126,f240,f215,f236,f223])).
thf(f245,definition,(
  spl10_15 <=> ! [X2 : a,X1 : a] : (($false = ((sK8 @ X1 @ X2))) | ($false = ((sK19 @ X1))) | ($true = ((sK19 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition])).
thf(f246,plain,(
  ( ! [X2 : a,X1 : a] : (($false = ((sK8 @ X1 @ X2))) | ($false = ((sK19 @ X1))) | ($true = ((sK19 @ X2)))) ) | ~spl10_15),
  inference(avatar_component_clause,[],[f245])).
thf(f248,definition,(
  spl10_16 <=> ($true = ((sK0 @ sK19)))),
  introduced(definition,[new_symbols(definition,[spl10_16])],[avatar_definition])).
thf(f250,plain,(
  ($true = ((sK0 @ sK19))) | ~spl10_16),
  inference(avatar_component_clause,[],[f248])).
thf(f251,plain,(
  spl10_15 | spl10_16 | spl10_4),
  inference(avatar_split_clause,[],[f212,f126,f248,f245])).
thf(f253,definition,(
  spl10_17 <=> ! [X2 : a,X1 : a] : (($false = ((sK19 @ X1))) | ($false = ((sK19 @ X2))) | ($true = ((sK8 @ X1 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl10_17])],[avatar_definition])).
thf(f254,plain,(
  ( ! [X2 : a,X1 : a] : (($true = ((sK8 @ X1 @ X2))) | ($false = ((sK19 @ X2))) | ($false = ((sK19 @ X1)))) ) | ~spl10_17),
  inference(avatar_component_clause,[],[f253])).
thf(f255,plain,(
  spl10_17 | spl10_16 | spl10_4),
  inference(avatar_split_clause,[],[f211,f126,f248,f253])).
thf(f257,definition,(
  spl10_18 <=> ($true = ((sK19 @ sK22)))),
  introduced(definition,[new_symbols(definition,[spl10_18])],[avatar_definition])).
thf(f259,plain,(
  ($true = ((sK19 @ sK22))) | ~spl10_18),
  inference(avatar_component_clause,[],[f257])).
thf(f260,plain,(
  spl10_16 | spl10_18 | spl10_4),
  inference(avatar_split_clause,[],[f213,f126,f257,f248])).
thf(f293,plain,(
  ($false = $true) | (~spl10_8 | ~spl10_16)),
  inference(forward_demodulation,[],[f217,f250])).
thf(f294,plain,(
  $false | (~spl10_8 | ~spl10_16)),
  inference(trivial_inequality_removal,[],[f293])).
thf(f295,plain,(
  ~spl10_8 | ~spl10_16),
  inference(avatar_contradiction_clause,[],[f294])).
thf(f309,plain,(
  ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true != $true) | (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8))))),
  inference(constrained_superposition,[],[f26,f11])).
thf(f312,plain,(
  (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0)),
  inference(trivial_inequality_removal,[],[f309])).
thf(f412,plain,(
  ($false = $true) | (~spl10_10 | ~spl10_18)),
  inference(constrained_superposition,[],[f224,f259])).
thf(f417,plain,(
  $false | (~spl10_10 | ~spl10_18)),
  inference(trivial_inequality_removal,[],[f412])).
thf(f418,plain,(
  ~spl10_10 | ~spl10_18),
  inference(avatar_contradiction_clause,[],[f417])).
thf(f455,plain,(
  ($false = $true) | ($false = ((sK0 @ sK19))) | ~spl10_10),
  inference(constrained_superposition,[],[f224,f57])).
thf(f461,plain,(
  ($false = ((sK0 @ sK19))) | ~spl10_10),
  inference(trivial_inequality_removal,[],[f455])).
thf(f465,plain,(
  ($false = $true) | (~spl10_10 | ~spl10_16)),
  inference(forward_demodulation,[],[f461,f250])).
thf(f466,plain,(
  $false | (~spl10_10 | ~spl10_16)),
  inference(trivial_inequality_removal,[],[f465])).
thf(f467,plain,(
  ~spl10_10 | ~spl10_16),
  inference(avatar_contradiction_clause,[],[f466])).
thf(f469,definition,(
  spl10_30 <=> ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8))))),
  introduced(definition,[new_symbols(definition,[spl10_30])],[avatar_definition])).
thf(f471,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | ~spl10_30),
  inference(avatar_component_clause,[],[f469])).
thf(f472,plain,(
  spl10_30 | spl10_7 | ~spl10_4),
  inference(avatar_split_clause,[],[f312,f126,f183,f469])).
thf(f477,plain,(
  ($true != ((sK0 @ (sK8 @ (sK6 @ sK8))))) | (((sK8 @ (sK6 @ sK8))) = ((sK8 @ (sK7 @ sK8)))) | ($true != $true) | ~spl10_7),
  inference(constrained_superposition,[],[f10,f185])).
thf(f478,plain,(
  (((sK8 @ (sK6 @ sK8))) = ((sK8 @ (sK7 @ sK8)))) | ($true != ((sK0 @ (sK8 @ (sK6 @ sK8))))) | ~spl10_7),
  inference(trivial_inequality_removal,[],[f477])).
thf(f479,plain,(
  (((sK8 @ (sK6 @ sK8))) = ((sK8 @ (sK7 @ sK8)))) | ~spl10_7),
  inference(forward_subsumption_resolution,[],[f478,f12])).
thf(f521,plain,(
  ($false = ((sK8 @ (sK7 @ sK8) @ (sK6 @ sK8)))) | ($true != $true) | spl10_3),
  inference(constrained_superposition,[],[f124,f21])).
thf(f522,plain,(
  ($false = ((sK8 @ (sK7 @ sK8) @ (sK6 @ sK8)))) | spl10_3),
  inference(trivial_inequality_removal,[],[f521])).
thf(f571,plain,(
  ( ! [X1 : a] : ((((sK8 @ (sK6 @ sK8) @ X1)) = ((sK8 @ (sK7 @ sK8) @ X1)))) ) | ~spl10_7),
  inference(argument_congruence,[],[f479])).
thf(f574,plain,(
  ( ! [X1 : a] : (($true = ((sK8 @ (sK7 @ sK8) @ X1))) | ($false = ((sK8 @ (sK6 @ sK8) @ X1)))) ) | ~spl10_7),
  inference(iff_proxy_clausification,[],[f571])).
thf(f579,plain,(
  (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ($true != $true) | ($true != ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0)),
  inference(constrained_superposition,[],[f28,f11])).
thf(f585,plain,(
  (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true != ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8))))),
  inference(trivial_inequality_removal,[],[f579])).
thf(f710,plain,(
  (((sK8 @ (sK5 @ sK8) @ (sK5 @ sK8))) != $true) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ($true != $true) | ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ~spl10_7),
  inference(constrained_superposition,[],[f27,f574])).
thf(f712,plain,(
  ($false = $true) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | (spl10_3 | ~spl10_7)),
  inference(constrained_superposition,[],[f522,f574])).
thf(f722,plain,(
  ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | (spl10_3 | ~spl10_7)),
  inference(trivial_inequality_removal,[],[f712])).
thf(f723,plain,(
  ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | (((sK8 @ (sK5 @ sK8) @ (sK5 @ sK8))) != $true) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ~spl10_7),
  inference(trivial_inequality_removal,[],[f710])).
thf(f731,plain,(
  ($false = $true) | (spl10_3 | ~spl10_7)),
  inference(forward_demodulation,[],[f722,f11])).
thf(f732,plain,(
  $false | (spl10_3 | ~spl10_7)),
  inference(trivial_inequality_removal,[],[f731])).
thf(f733,plain,(
  spl10_3 | ~spl10_7),
  inference(avatar_contradiction_clause,[],[f732])).
thf(f734,plain,(
  ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ~spl10_7),
  inference(forward_subsumption_resolution,[],[f723,f11])).
thf(f736,plain,(
  ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | (~spl10_4 | ~spl10_7)),
  inference(forward_subsumption_resolution,[],[f734,f127])).
thf(f737,plain,(
  ($false = $true) | ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | (~spl10_4 | ~spl10_7)),
  inference(forward_demodulation,[],[f736,f11])).
thf(f738,plain,(
  ($true = ((sK8 @ (sK2 @ sK8) @ (sK3 @ sK8)))) | (~spl10_4 | ~spl10_7)),
  inference(trivial_inequality_removal,[],[f737])).
thf(f739,plain,(
  spl10_6 | ~spl10_4 | ~spl10_7),
  inference(avatar_split_clause,[],[f738,f183,f126,f179])).
thf(f747,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ($true != $true) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | (((sK8 @ (sK5 @ sK8) @ (sK5 @ sK8))) != $true) | ~spl10_7),
  inference(constrained_superposition,[],[f29,f574])).
thf(f750,plain,(
  (((sK8 @ (sK5 @ sK8) @ (sK5 @ sK8))) != $true) | ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ~spl10_7),
  inference(trivial_inequality_removal,[],[f747])).
thf(f784,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ~spl10_7),
  inference(forward_subsumption_resolution,[],[f750,f11])).
thf(f786,plain,(
  ($false = ((sK8 @ (sK6 @ sK8) @ (sK6 @ sK8)))) | ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | (~spl10_4 | ~spl10_7)),
  inference(forward_subsumption_resolution,[],[f784,f127])).
thf(f788,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | ($false = $true) | (~spl10_4 | ~spl10_7)),
  inference(forward_demodulation,[],[f786,f11])).
thf(f789,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK2 @ sK8)))) | (~spl10_4 | ~spl10_7)),
  inference(trivial_inequality_removal,[],[f788])).
thf(f791,plain,(
  spl10_30 | ~spl10_4 | ~spl10_7),
  inference(avatar_split_clause,[],[f789,f183,f126,f469])).
thf(f982,plain,(
  ( ! [X0 : a,X1 : a] : (($true != $true) | (((sK8 @ X1)) = ((sK8 @ X0))) | ($false = ((sK8 @ X0 @ X1)))) )),
  inference(constrained_superposition,[],[f58,f12])).
thf(f986,plain,(
  ( ! [X0 : a,X1 : a] : (($false = ((sK8 @ X0 @ X1))) | (((sK8 @ X1)) = ((sK8 @ X0)))) )),
  inference(trivial_inequality_removal,[],[f982])).
thf(f1542,plain,(
  ( ! [X2 : (a > $o),X0 : ((a > $o) > $o),X1 : (a > $o)] : (($true != $true) | (((X2 @ (sK9 @ X2 @ X1))) = $true) | (((X0 @ X2)) = $true) | (((X1 @ (sK9 @ X2 @ X1))) = $true) | (((X0 @ X1)) = $false)) )),
  inference(constrained_superposition,[],[f24,f21])).
thf(f1548,plain,(
  ( ! [X2 : (a > $o),X0 : ((a > $o) > $o),X1 : (a > $o)] : ((((X0 @ X2)) = $true) | (((X1 @ (sK9 @ X2 @ X1))) = $true) | (((X2 @ (sK9 @ X2 @ X1))) = $true) | (((X0 @ X1)) = $false)) )),
  inference(trivial_inequality_removal,[],[f1542])).
thf(f2080,plain,(
  (((sK8 @ (sK6 @ sK8) @ (sK7 @ sK8))) = $true) | ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | ~spl10_5),
  inference(forward_subsumption_resolution,[],[f585,f131])).
thf(f2082,plain,(
  ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK8 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (?? @ a @ Y0))) != sK0) | (~spl10_5 | spl10_7)),
  inference(forward_subsumption_resolution,[],[f2080,f184])).
thf(f2083,plain,(
  $false | (~spl10_4 | ~spl10_5 | spl10_7)),
  inference(forward_subsumption_resolution,[],[f2082,f127])).
thf(f2084,plain,(
  ~spl10_4 | ~spl10_5 | spl10_7),
  inference(avatar_contradiction_clause,[],[f2083])).
thf(f2098,plain,(
  ( ! [X2 : (a > $o),X0 : ((a > $o) > $o),X1 : (a > $o)] : ((((X0 @ X1)) = $false) | (((X0 @ X2)) = $true) | ($false = ((X2 @ (sK9 @ X2 @ X1)))) | ($true != $true) | ($false = ((X1 @ (sK9 @ X2 @ X1))))) )),
  inference(constrained_superposition,[],[f25,f21])).
thf(f2101,plain,(
  ( ! [X2 : (a > $o),X0 : ((a > $o) > $o),X1 : (a > $o)] : ((((X0 @ X1)) = $false) | ($false = ((X1 @ (sK9 @ X2 @ X1)))) | (((X0 @ X2)) = $true) | ($false = ((X2 @ (sK9 @ X2 @ X1))))) )),
  inference(trivial_inequality_removal,[],[f2098])).
thf(f2216,plain,(
  ($false = ((sK0 @ sK19))) | (sK19 = ((sK8 @ sK20))) | ($true != $true) | ~spl10_9),
  inference(constrained_superposition,[],[f59,f221])).
thf(f2219,plain,(
  ($false = ((sK0 @ sK19))) | (sK19 = ((sK8 @ sK20))) | ~spl10_9),
  inference(trivial_inequality_removal,[],[f2216])).
thf(f2221,plain,(
  (sK19 = ((sK8 @ sK20))) | (spl10_8 | ~spl10_9)),
  inference(forward_subsumption_resolution,[],[f2219,f216])).
thf(f2685,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ X0))) | (sK19 = ((sK8 @ X0))) | ($true != $true)) ) | ~spl10_16),
  inference(constrained_superposition,[],[f58,f250])).
thf(f2692,plain,(
  ( ! [X0 : a] : ((sK19 = ((sK8 @ X0))) | ($false = ((sK19 @ X0)))) ) | ~spl10_16),
  inference(trivial_inequality_removal,[],[f2685])).
thf(f2746,plain,(
  ($true = ((sK0 @ sK19))) | (spl10_8 | ~spl10_9)),
  inference(constrained_superposition,[],[f12,f2221])).
thf(f3551,plain,(
  ( ! [X0 : a,X1 : a] : (($false = ((sK19 @ X0))) | (((sK19 @ X1)) = ((sK8 @ X0 @ X1)))) ) | ~spl10_16),
  inference(argument_congruence,[],[f2692])).
thf(f3572,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK19 @ X1)) = $true) | ($false = ((sK19 @ X0))) | ($false = ((sK8 @ X0 @ X1)))) ) | ~spl10_16),
  inference(iff_proxy_clausification,[],[f3551])).
thf(f3573,plain,(
  ( ! [X0 : a,X1 : a] : (($false = ((sK19 @ X1))) | ($true = ((sK8 @ X0 @ X1))) | ($false = ((sK19 @ X0)))) ) | ~spl10_16),
  inference(iff_proxy_clausification,[],[f3551])).
thf(f3579,plain,(
  spl10_17 | ~spl10_16),
  inference(avatar_split_clause,[],[f3573,f248,f253])).
thf(f3580,plain,(
  spl10_15 | ~spl10_16),
  inference(avatar_split_clause,[],[f3572,f248,f245])).
thf(f3599,plain,(
  spl10_16 | spl10_8 | ~spl10_9),
  inference(avatar_split_clause,[],[f2746,f219,f215,f248])).
thf(f3753,plain,(
  ($false = $true) | ($false = ((sK19 @ sK21))) | ($false = ((sK19 @ sK20))) | (~spl10_12 | ~spl10_17)),
  inference(constrained_superposition,[],[f233,f254])).
thf(f3768,plain,(
  ($false = ((sK19 @ sK20))) | ($false = ((sK19 @ sK21))) | (~spl10_12 | ~spl10_17)),
  inference(trivial_inequality_removal,[],[f3753])).
thf(f3816,plain,(
  ($false = ((sK19 @ sK21))) | ($false = $true) | (~spl10_9 | ~spl10_12 | ~spl10_17)),
  inference(forward_demodulation,[],[f3768,f221])).
thf(f3817,plain,(
  ($false = ((sK19 @ sK21))) | (~spl10_9 | ~spl10_12 | ~spl10_17)),
  inference(trivial_inequality_removal,[],[f3816])).
thf(f3844,plain,(
  spl10_11 | ~spl10_9 | ~spl10_12 | ~spl10_17),
  inference(avatar_split_clause,[],[f3817,f253,f231,f219,f227])).
thf(f3845,plain,(
  ($false = $true) | (~spl10_12 | ~spl10_13)),
  inference(forward_demodulation,[],[f238,f233])).
thf(f3846,plain,(
  $false | (~spl10_12 | ~spl10_13)),
  inference(trivial_inequality_removal,[],[f3845])).
thf(f3847,plain,(
  ~spl10_12 | ~spl10_13),
  inference(avatar_contradiction_clause,[],[f3846])).
thf(f3850,plain,(
  ($false = $true) | (~spl10_11 | ~spl10_14)),
  inference(forward_demodulation,[],[f229,f242])).
thf(f3851,plain,(
  $false | (~spl10_11 | ~spl10_14)),
  inference(trivial_inequality_removal,[],[f3850])).
thf(f3852,plain,(
  ~spl10_11 | ~spl10_14),
  inference(avatar_contradiction_clause,[],[f3851])).
thf(f3901,plain,(
  ($false = ((sK19 @ sK20))) | ($false != $false) | ($true = ((sK19 @ sK21))) | (spl10_12 | ~spl10_15)),
  inference(constrained_superposition,[],[f232,f246])).
thf(f3905,plain,(
  ($false = ((sK19 @ sK20))) | ($true = ((sK19 @ sK21))) | (spl10_12 | ~spl10_15)),
  inference(trivial_inequality_removal,[],[f3901])).
thf(f3908,plain,(
  ($false = ((sK19 @ sK20))) | (spl10_12 | spl10_14 | ~spl10_15)),
  inference(forward_subsumption_resolution,[],[f3905,f241])).
thf(f3915,plain,(
  ($false = $true) | (~spl10_9 | spl10_12 | spl10_14 | ~spl10_15)),
  inference(forward_demodulation,[],[f3908,f221])).
thf(f3916,plain,(
  $false | (~spl10_9 | spl10_12 | spl10_14 | ~spl10_15)),
  inference(trivial_inequality_removal,[],[f3915])).
thf(f3917,plain,(
  ~spl10_9 | spl10_12 | spl10_14 | ~spl10_15),
  inference(avatar_contradiction_clause,[],[f3916])).
thf(f6117,plain,(
  ($false = $true) | (((sK8 @ (sK2 @ sK8))) = ((sK8 @ (sK4 @ sK8)))) | ~spl10_30),
  inference(constrained_superposition,[],[f986,f471])).
thf(f6123,plain,(
  (((sK8 @ (sK2 @ sK8))) = ((sK8 @ (sK4 @ sK8)))) | ~spl10_30),
  inference(trivial_inequality_removal,[],[f6117])).
thf(f6580,plain,(
  ( ! [X1 : a] : ((((sK8 @ (sK4 @ sK8) @ X1)) = ((sK8 @ (sK2 @ sK8) @ X1)))) ) | ~spl10_30),
  inference(argument_congruence,[],[f6123])).
thf(f6596,plain,(
  ( ! [X1 : a] : (($false = ((sK8 @ (sK2 @ sK8) @ X1))) | (((sK8 @ (sK4 @ sK8) @ X1)) = $true)) ) | ~spl10_30),
  inference(iff_proxy_clausification,[],[f6580])).
thf(f8957,plain,(
  ($false = $true) | ($true = ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | (~spl10_6 | ~spl10_30)),
  inference(constrained_superposition,[],[f6596,f181])).
thf(f8985,plain,(
  ($true = ((sK8 @ (sK4 @ sK8) @ (sK3 @ sK8)))) | (~spl10_6 | ~spl10_30)),
  inference(trivial_inequality_removal,[],[f8957])).
thf(f9009,plain,(
  $false | (spl10_5 | ~spl10_6 | ~spl10_30)),
  inference(forward_subsumption_resolution,[],[f8985,f132])).
thf(f9010,plain,(
  spl10_5 | ~spl10_6 | ~spl10_30),
  inference(avatar_contradiction_clause,[],[f9009])).
thf(f10197,plain,(
  ( ! [X0 : (a > $o)] : (($false = ((sK0 @ X0))) | ($false = $true) | ($false = ((sK19 @ (sK9 @ sK19 @ X0)))) | ($false = ((X0 @ (sK9 @ sK19 @ X0))))) ) | ~spl10_8),
  inference(constrained_superposition,[],[f217,f2101])).
thf(f10198,plain,(
  ( ! [X0 : (a > $o)] : ((((sK19 @ (sK9 @ sK19 @ X0))) = $true) | ($false = ((sK0 @ X0))) | ($false = $true) | ($true = ((X0 @ (sK9 @ sK19 @ X0))))) ) | ~spl10_8),
  inference(constrained_superposition,[],[f217,f1548])).
thf(f10207,plain,(
  ( ! [X0 : (a > $o)] : ((((sK19 @ (sK9 @ sK19 @ X0))) = $true) | ($true = ((X0 @ (sK9 @ sK19 @ X0)))) | ($false = ((sK0 @ X0)))) ) | ~spl10_8),
  inference(trivial_inequality_removal,[],[f10198])).
thf(f10208,plain,(
  ( ! [X0 : (a > $o)] : (($false = ((X0 @ (sK9 @ sK19 @ X0)))) | ($false = ((sK19 @ (sK9 @ sK19 @ X0)))) | ($false = ((sK0 @ X0)))) ) | ~spl10_8),
  inference(trivial_inequality_removal,[],[f10197])).
thf(f11359,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ X0))) | ($false = ((sK0 @ (sK8 @ X0)))) | ($false = $true) | ($true = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($true = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0)))))) ) | (~spl10_8 | ~spl10_15)),
  inference(constrained_superposition,[],[f10207,f246])).
thf(f11418,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ X0))) | ($false = $true) | ($false = ((sK0 @ (sK8 @ X0)))) | ($true = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0)))))) ) | (~spl10_8 | ~spl10_15)),
  inference(duplicate_literal_removal,[],[f11359])).
thf(f11419,plain,(
  ( ! [X0 : a] : (($true = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($false = ((sK19 @ X0))) | ($false = ((sK0 @ (sK8 @ X0))))) ) | (~spl10_8 | ~spl10_15)),
  inference(trivial_inequality_removal,[],[f11418])).
thf(f11445,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ X0))) | ($false = $true) | ($true = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0)))))) ) | (~spl10_8 | ~spl10_15)),
  inference(forward_demodulation,[],[f11419,f12])).
thf(f11446,plain,(
  ( ! [X0 : a] : (($true = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($false = ((sK19 @ X0)))) ) | (~spl10_8 | ~spl10_15)),
  inference(trivial_inequality_removal,[],[f11445])).
thf(f11490,plain,(
  ( ! [X0 : a] : (($false = $true) | ($false = ((sK19 @ X0))) | ($false = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($false = ((sK0 @ (sK8 @ X0)))) | ($false = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0)))))) ) | (~spl10_8 | ~spl10_17)),
  inference(constrained_superposition,[],[f10208,f254])).
thf(f11547,plain,(
  ( ! [X0 : a] : (($false = ((sK0 @ (sK8 @ X0)))) | ($false = $true) | ($false = ((sK19 @ X0))) | ($false = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0)))))) ) | (~spl10_8 | ~spl10_17)),
  inference(duplicate_literal_removal,[],[f11490])).
thf(f11548,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($false = ((sK0 @ (sK8 @ X0)))) | ($false = ((sK19 @ X0)))) ) | (~spl10_8 | ~spl10_17)),
  inference(trivial_inequality_removal,[],[f11547])).
thf(f11579,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($false = ((sK19 @ X0))) | ($false = $true)) ) | (~spl10_8 | ~spl10_17)),
  inference(forward_demodulation,[],[f11548,f12])).
thf(f11580,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ (sK9 @ sK19 @ (sK8 @ X0))))) | ($false = ((sK19 @ X0)))) ) | (~spl10_8 | ~spl10_17)),
  inference(trivial_inequality_removal,[],[f11579])).
thf(f11631,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ X0))) | ($false = $true)) ) | (~spl10_8 | ~spl10_15 | ~spl10_17)),
  inference(forward_subsumption_demodulation,[],[f11446,f11580])).
thf(f11632,plain,(
  ( ! [X0 : a] : (($false = ((sK19 @ X0)))) ) | (~spl10_8 | ~spl10_15 | ~spl10_17)),
  inference(trivial_inequality_removal,[],[f11631])).
thf(f11637,plain,(
  spl10_10 | ~spl10_8 | ~spl10_15 | ~spl10_17),
  inference(avatar_split_clause,[],[f11632,f253,f245,f215,f223])).
cnf(s2, plain, ~spl10_3 | ~spl10_4 | ~spl10_5, inference(sat_conversion,[],[f133])).
cnf(s3, plain, ~spl10_4 | spl10_6 | spl10_7, inference(sat_conversion,[],[f186])).
cnf(s4, plain, spl10_4 | spl10_8 | spl10_9 | spl10_10, inference(sat_conversion,[],[f225])).
cnf(s5, plain, spl10_4 | spl10_8 | spl10_10 | spl10_11 | spl10_12, inference(sat_conversion,[],[f234])).
cnf(s6, plain, spl10_4 | spl10_8 | spl10_10 | spl10_13 | spl10_14, inference(sat_conversion,[],[f243])).
cnf(s7, plain, spl10_4 | spl10_15 | spl10_16, inference(sat_conversion,[],[f251])).
cnf(s8, plain, spl10_4 | spl10_16 | spl10_17, inference(sat_conversion,[],[f255])).
cnf(s9, plain, spl10_4 | spl10_16 | spl10_18, inference(sat_conversion,[],[f260])).
cnf(s12, plain, ~spl10_8 | ~spl10_16, inference(sat_conversion,[],[f295])).
cnf(s19, plain, ~spl10_10 | ~spl10_18, inference(sat_conversion,[],[f418])).
cnf(s28, plain, ~spl10_10 | ~spl10_16, inference(sat_conversion,[],[f467])).
cnf(s29, plain, ~spl10_4 | spl10_7 | spl10_30, inference(sat_conversion,[],[f472])).
cnf(s34, plain, spl10_3 | ~spl10_7, inference(sat_conversion,[],[f733])).
cnf(s35, plain, ~spl10_4 | spl10_6 | ~spl10_7, inference(sat_conversion,[],[f739])).
cnf(s37, plain, ~spl10_4 | ~spl10_7 | spl10_30, inference(sat_conversion,[],[f791])).
cnf(s71, plain, ~spl10_4 | ~spl10_5 | spl10_7, inference(sat_conversion,[],[f2084])).
cnf(s130, plain, ~spl10_16 | spl10_17, inference(sat_conversion,[],[f3579])).
cnf(s131, plain, spl10_15 | ~spl10_16, inference(sat_conversion,[],[f3580])).
cnf(s139, plain, spl10_8 | ~spl10_9 | spl10_16, inference(sat_conversion,[],[f3599])).
cnf(s154, plain, ~spl10_9 | spl10_11 | ~spl10_12 | ~spl10_17, inference(sat_conversion,[],[f3844])).
cnf(s155, plain, ~spl10_12 | ~spl10_13, inference(sat_conversion,[],[f3847])).
cnf(s157, plain, ~spl10_11 | ~spl10_14, inference(sat_conversion,[],[f3852])).
cnf(s159, plain, ~spl10_9 | spl10_12 | spl10_14 | ~spl10_15, inference(sat_conversion,[],[f3917])).
cnf(s422, plain, spl10_5 | ~spl10_6 | ~spl10_30, inference(sat_conversion,[],[f9010])).
cnf(s629, plain, ~spl10_8 | spl10_10 | ~spl10_15 | ~spl10_17, inference(sat_conversion,[],[f11637])).
cnf(s631, plain, ~spl10_10 | spl10_4, inference(rat,[],[s9,s19,s28])).
cnf(s632, plain, spl10_11 | spl10_8 | spl10_4, inference(rat,[],[s154,s5,s130,s139,s4,s631])).
cnf(s633, plain, spl10_10 | spl10_8 | spl10_4, inference(rat,[],[s155,s159,s6,s157,s632,s131,s139,s4])).
cnf(s634, plain, spl10_10 | spl10_4, inference(rat,[],[s629,s7,s8,s12,s633])).
cnf(s635, plain, spl10_4, inference(rat,[],[s634,s631])).
cnf(s636, plain, spl10_7, inference(rat,[],[s422,s3,s29,s71,s635])).
cnf(s637, plain, spl10_30, inference(rat,[],[s37,s635,s636])).
cnf(s638, plain, spl10_3, inference(rat,[],[s34,s636])).
cnf(s639, plain, spl10_6, inference(rat,[],[s35,s635,s636])).
cnf(s641, plain, ~spl10_5, inference(rat,[],[s2,s635,s638])).
cnf(s642, plain, $false, inference(rat,[],[s422,s637,s641,s639])).
thf(f11638,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s642])).
% SZS output end Proof for theBenchmark