%----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, vSIGMA: !>[X0: $tType]:(((X0 > $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, db0: !>[X0: $tType]:(X0)).
thf(func_def_7, type, vAND: ($o > $o > $o)).
thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
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, sK0: (((a > $o) > $o) > $o)).
thf(func_def_12, type, sK1: (((a > $o) > $o) > a > $o)).
thf(func_def_13, type, sK2: ((a > $o) > $o)).
thf(func_def_14, type, sK3: ((((a > $o) > $o) > $o) > (a > $o) > $o)).
thf(func_def_15, type, sK4: ((((a > $o) > $o) > $o) > ((a > $o) > $o) > a > $o)).
thf(func_def_16, type, sF5: (((a > $o) > $o) > $o)).
thf(func_def_17, type, sF6: (((a > $o) > $o) > $o)).
thf(func_def_18, type, sF7: $o).
thf(func_def_19, type, sF8: ((((a > $o) > $o) > $o) > $o)).
thf(func_def_20, type, sF9: ((((a > $o) > $o) > $o) > ((a > $o) > $o) > $o)).
thf(func_def_21, type, sF10: (((a > $o) > $o) > (((a > $o) > $o) > $o) > $o)).
thf(func_def_22, type, sF11: ((a > $o) > (((a > $o) > $o) > $o) > $o)).
thf(func_def_24, type, sK13: a).
thf(func_def_25, type, sK14: ((a > $o) > $o)).
thf(func_def_26, type, sK15: ((((a > $o) > $o) > a > $o) > (a > $o) > $o)).
thf(func_def_27, type, sK16: (((a > $o) > $o) > a > $o)).
thf(func_def_28, type, sK17: (((a > $o) > $o) > a > $o)).
thf(f1,conjecture,(
  ! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => ? [X2 : (a > $o)] : (X1 @ X2)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : (((a > $o) > $o) > $o)] : ((? [X1 : ((a > $o) > $o)] : (X4 @ X1) & ! [X1 : ((a > $o) > $o)] : ((X4 @ X1) => ? [X5 : (a > $o)] : (X1 @ X5))) => ((^[X6 : a] : (? [X3 : (((a > $o) > $o) > a > $o)] : ! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ((X3 @ X7 @ X6) & (X7 @ (X3 @ X7)))))) = (^[X6 : a] : (! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ? [X8 : (a > $o)] : ((X7 @ X8) & (X8 @ X6)))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM535)).
thf(f2,negated_conjecture,(
  ~(! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => ? [X2 : (a > $o)] : (X1 @ X2)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : (((a > $o) > $o) > $o)] : ((? [X1 : ((a > $o) > $o)] : (X4 @ X1) & ! [X1 : ((a > $o) > $o)] : ((X4 @ X1) => ? [X5 : (a > $o)] : (X1 @ X5))) => ((^[X6 : a] : (? [X3 : (((a > $o) > $o) > a > $o)] : ! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ((X3 @ X7 @ X6) & (X7 @ (X3 @ X7)))))) = (^[X6 : a] : (! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ? [X8 : (a > $o)] : ((X7 @ X8) & (X8 @ X6))))))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => ? [X2 : (a > $o)] : (X1 @ X2)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : ((X0 @ X4) => (X4 @ (X3 @ X4)))) => ! [X5 : (((a > $o) > $o) > $o)] : ((? [X6 : ((a > $o) > $o)] : (X5 @ X6) & ! [X7 : ((a > $o) > $o)] : ((X5 @ X7) => ? [X8 : (a > $o)] : (X7 @ X8))) => ((^[X9 : a] : (? [X10 : (((a > $o) > $o) > a > $o)] : ! [X11 : ((a > $o) > $o)] : ((X5 @ X11) => ((X10 @ X11 @ X9) & (X11 @ (X10 @ X11)))))) = (^[X12 : a] : (! [X13 : ((a > $o) > $o)] : ((X5 @ X13) => ? [X14 : (a > $o)] : ((X13 @ X14) & (X14 @ X12))))))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~(! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((((X0 @ X1)) = $true) => ? [X2 : (a > $o)] : (((X1 @ X2)) = $true)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : (($true = ((X0 @ X4))) => ($true = ((X4 @ (X3 @ X4)))))) => ! [X5 : (((a > $o) > $o) > $o)] : ((! [X7 : ((a > $o) > $o)] : (($true = ((X5 @ X7))) => ? [X8 : (a > $o)] : (((X7 @ X8)) = $true)) & ? [X6 : ((a > $o) > $o)] : ($true = ((X5 @ X6)))) => ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) = (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X5 : (((a > $o) > $o) > $o)] : (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0))))))))) & (! [X7 : ((a > $o) > $o)] : (($true != ((X5 @ X7))) | ? [X8 : (a > $o)] : (((X7 @ X8)) = $true)) & ? [X6 : ((a > $o) > $o)] : ($true = ((X5 @ X6))))) & ! [X0 : (((a > $o) > $o) > $o)] : (? [X1 : ((a > $o) > $o)] : ((((X0 @ X1)) = $true) & ! [X2 : (a > $o)] : (((X1 @ X2)) != $true)) | ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : (($true = ((X4 @ (X3 @ X4)))) | ($true != ((X0 @ X4)))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X5 : (((a > $o) > $o) > $o)] : (! [X7 : ((a > $o) > $o)] : (($true != ((X5 @ X7))) | ? [X8 : (a > $o)] : (((X7 @ X8)) = $true)) & ? [X6 : ((a > $o) > $o)] : ($true = ((X5 @ X6))) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))) & ! [X0 : (((a > $o) > $o) > $o)] : (? [X1 : ((a > $o) > $o)] : ((((X0 @ X1)) = $true) & ! [X2 : (a > $o)] : (((X1 @ X2)) != $true)) | ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : (($true = ((X4 @ (X3 @ X4)))) | ($true != ((X0 @ X4)))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ? [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((((X0 @ X1)) != $true) | ? [X2 : (a > $o)] : (((X1 @ X2)) = $true)) & ? [X3 : ((a > $o) > $o)] : ($true = ((X0 @ X3))) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))))) & ! [X4 : (((a > $o) > $o) > $o)] : (? [X5 : ((a > $o) > $o)] : (($true = ((X4 @ X5))) & ! [X6 : (a > $o)] : ($true != ((X5 @ X6)))) | ? [X7 : (((a > $o) > $o) > a > $o)] : ! [X8 : ((a > $o) > $o)] : (($true = ((X8 @ (X7 @ X8)))) | ($true != ((X4 @ X8)))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  (! [X1 : ((a > $o) > $o)] : (($true != ((sK0 @ X1))) | (((X1 @ (sK1 @ X1))) = $true)) & ($true = ((sK0 @ sK2))) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))) & ! [X4 : (((a > $o) > $o) > $o)] : ((($true = ((X4 @ (sK3 @ X4)))) & ! [X6 : (a > $o)] : (((sK3 @ X4 @ X6)) != $true)) | ! [X8 : ((a > $o) > $o)] : (($true = ((X8 @ (sK4 @ X4 @ X8)))) | ($true != ((X4 @ X8)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,sK2,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X7,$thf(sK4 @ X4)),skolemize(X3,$thf(sK2)),skolemize(X7,$thf(sK4 @ X4)),skolemize(X7,$thf(sK4 @ X4))],[f7])).
thf(f11,plain,(
  ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))),
  inference(cnf_transformation,[],[f8])).
thf(f92,plain,(
  ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) @ sK13)) != (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK13)))),
  inference(negative_extensionality,[],[f11])).
thf(f93,plain,(
  ($true = (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK13))) | ($true = (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) @ sK13)))),
  inference(xor_proxy_clausification,[],[f92])).
thf(f94,plain,(
  ($false = (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK13))) | ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) @ sK13)) = $false)),
  inference(xor_proxy_clausification,[],[f92])).
thf(f95,plain,(
  (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK13) & (Y0 @ Y1)))))))) = $false) | (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $false)),
  inference(beta-eta_normalization,[],[f94])).
thf(f96,plain,(
  (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $false) | ($false = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK13) & (Y0 @ Y1)))))) @ sK14)))),
  inference(sigma_proxy_clausification,[],[f95])).
thf(f97,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK13) & (Y0 @ Y1)))))) @ sK14))) | ($false = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f96])).
thf(f98,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13))))))) | ($false = (((sK0 @ sK14) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK13) & (sK14 @ Y0)))))))) )),
  inference(beta-eta_normalization,[],[f97])).
thf(f99,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (((((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))) = $false) | ($false = (((sK0 @ sK14) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK13) & (sK14 @ Y0)))))))) )),
  inference(sigma_proxy_clausification,[],[f98])).
thf(f100,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (((((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))) = $false) | ($false = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK13) & (sK14 @ Y0))))))) )),
  inference(imp_proxy_clausification,[],[f99])).
thf(f101,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (((((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))) = $false) | ($true = ((sK0 @ sK14)))) )),
  inference(imp_proxy_clausification,[],[f99])).
thf(f102,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ sK14))) | ((((sK0 @ (sK15 @ X1)) => ((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13)))) = $false)) )),
  inference(beta-eta_normalization,[],[f101])).
thf(f103,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ sK14))) | ((((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13))) = $false)) )),
  inference(imp_proxy_clausification,[],[f102])).
thf(f104,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ (sK15 @ X1)))) | ($true = ((sK0 @ sK14)))) )),
  inference(imp_proxy_clausification,[],[f102])).
thf(f105,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK15 @ X1 @ (X1 @ (sK15 @ X1)))) = $false) | (((X1 @ (sK15 @ X1) @ sK13)) = $false) | ($true = ((sK0 @ sK14)))) )),
  inference(and_proxy_clausification,[],[f103])).
thf(f106,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (((((^[Y0 : a > $o]: ((Y0 @ sK13) & (sK14 @ Y0))) @ X2)) = $false) | ((((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))) = $false)) )),
  inference(pi_proxy_clausification,[],[f100])).
thf(f107,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (((((sK0 @ (sK15 @ X1)) => ((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13)))) = $false) | ((((X2 @ sK13) & (sK14 @ X2))) = $false)) )),
  inference(beta-eta_normalization,[],[f106])).
thf(f108,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (((((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13))) = $false) | ((((X2 @ sK13) & (sK14 @ X2))) = $false)) )),
  inference(imp_proxy_clausification,[],[f107])).
thf(f109,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ (sK15 @ X1)))) | ((((X2 @ sK13) & (sK14 @ X2))) = $false)) )),
  inference(imp_proxy_clausification,[],[f107])).
thf(f110,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($false = ((X2 @ sK13))) | (((sK14 @ X2)) = $false) | ($true = ((sK0 @ (sK15 @ X1))))) )),
  inference(and_proxy_clausification,[],[f109])).
thf(f111,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : ((((sK15 @ X1 @ (X1 @ (sK15 @ X1)))) = $false) | ((((X2 @ sK13) & (sK14 @ X2))) = $false) | (((X1 @ (sK15 @ X1) @ sK13)) = $false)) )),
  inference(and_proxy_clausification,[],[f108])).
thf(f112,plain,(
  ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($false = ((X2 @ sK13))) | (((sK15 @ X1 @ (X1 @ (sK15 @ X1)))) = $false) | (((X1 @ (sK15 @ X1) @ sK13)) = $false) | (((sK14 @ X2)) = $false)) )),
  inference(and_proxy_clausification,[],[f111])).
thf(f113,plain,(
  ($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK13) & (Y0 @ Y1))))))))) | (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $true)),
  inference(beta-eta_normalization,[],[f93])).
thf(f114,plain,(
  ( ! [X1 : ((a > $o) > $o)] : (($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK13) & (Y0 @ Y1)))))) @ X1))) | (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $true)) )),
  inference(pi_proxy_clausification,[],[f113])).
thf(f115,plain,(
  ( ! [X1 : ((a > $o) > $o)] : (($true = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))) @ sK16))) | ($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK13) & (Y0 @ Y1)))))) @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f114])).
thf(f116,plain,(
  ( ! [X1 : ((a > $o) > $o)] : (($true = (((sK0 @ X1) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK13) & (X1 @ Y0))))))) | ($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13)))))))) )),
  inference(beta-eta_normalization,[],[f115])).
thf(f117,plain,(
  ( ! [X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | ($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13))))))) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK13) & (X1 @ Y0))))) = $true)) )),
  inference(imp_proxy_clausification,[],[f116])).
thf(f118,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | ($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13)))) @ X2))) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK13) & (X1 @ Y0))))) = $true)) )),
  inference(pi_proxy_clausification,[],[f117])).
thf(f119,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | ($true = (((^[Y0 : a > $o]: ((Y0 @ sK13) & (X1 @ Y0))) @ (sK17 @ X1)))) | ($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13)))) @ X2)))) )),
  inference(sigma_proxy_clausification,[],[f118])).
thf(f120,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((sK0 @ X2) => ((X2 @ (sK16 @ X2)) & (sK16 @ X2 @ sK13))))) | (((sK0 @ X1)) = $false) | ($true = (((sK17 @ X1 @ sK13) & (X1 @ (sK17 @ X1)))))) )),
  inference(beta-eta_normalization,[],[f119])).
thf(f121,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((sK17 @ X1 @ sK13) & (X1 @ (sK17 @ X1))))) | (((sK0 @ X1)) = $false) | (((sK0 @ X2)) = $false) | ($true = (((X2 @ (sK16 @ X2)) & (sK16 @ X2 @ sK13))))) )),
  inference(imp_proxy_clausification,[],[f120])).
thf(f122,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | (((sK0 @ X2)) = $false) | ($true = ((X1 @ (sK17 @ X1)))) | ($true = (((X2 @ (sK16 @ X2)) & (sK16 @ X2 @ sK13))))) )),
  inference(and_proxy_clausification,[],[f121])).
thf(f123,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((X2 @ (sK16 @ X2)) & (sK16 @ X2 @ sK13)))) | ($true = ((sK17 @ X1 @ sK13))) | (((sK0 @ X1)) = $false) | (((sK0 @ X2)) = $false)) )),
  inference(and_proxy_clausification,[],[f121])).
thf(f124,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | (((sK16 @ X2 @ sK13)) = $true) | (((sK0 @ X2)) = $false) | ($true = ((sK17 @ X1 @ sK13)))) )),
  inference(and_proxy_clausification,[],[f123])).
thf(f125,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = ((sK17 @ X1 @ sK13))) | (((sK0 @ X1)) = $false) | ($true = ((X2 @ (sK16 @ X2)))) | (((sK0 @ X2)) = $false)) )),
  inference(and_proxy_clausification,[],[f123])).
thf(f126,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | (((sK0 @ X2)) = $false) | ($true = ((X1 @ (sK17 @ X1)))) | (((sK16 @ X2 @ sK13)) = $true)) )),
  inference(and_proxy_clausification,[],[f122])).
thf(f127,plain,(
  ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = ((X1 @ (sK17 @ X1)))) | ($true = ((X2 @ (sK16 @ X2)))) | (((sK0 @ X2)) = $false) | (((sK0 @ X1)) = $false)) )),
  inference(and_proxy_clausification,[],[f122])).
thf(f129,definition,(
  spl12_5 <=> ($true = ((sK0 @ sK14)))),
  introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition])).
thf(f131,plain,(
  ($true = ((sK0 @ sK14))) | ~spl12_5),
  inference(avatar_component_clause,[],[f129])).
thf(f133,definition,(
  spl12_6 <=> ! [X1 : (((a > $o) > $o) > a > $o)] : ($true = ((sK0 @ (sK15 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition])).
thf(f134,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ (sK15 @ X1))))) ) | ~spl12_6),
  inference(avatar_component_clause,[],[f133])).
thf(f135,plain,(
  spl12_5 | spl12_6),
  inference(avatar_split_clause,[],[f104,f133,f129])).
thf(f137,definition,(
  spl12_7 <=> ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK15 @ X1 @ (X1 @ (sK15 @ X1)))) = $false) | (((X1 @ (sK15 @ X1) @ sK13)) = $false))),
  introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition])).
thf(f138,plain,(
  ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK15 @ X1 @ (X1 @ (sK15 @ X1)))) = $false) | (((X1 @ (sK15 @ X1) @ sK13)) = $false)) ) | ~spl12_7),
  inference(avatar_component_clause,[],[f137])).
thf(f139,plain,(
  spl12_5 | spl12_7),
  inference(avatar_split_clause,[],[f105,f137,f129])).
thf(f141,definition,(
  spl12_8 <=> ! [X2 : (a > $o)] : (($false = ((X2 @ sK13))) | (((sK14 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition])).
thf(f142,plain,(
  ( ! [X2 : (a > $o)] : ((((sK14 @ X2)) = $false) | ($false = ((X2 @ sK13)))) ) | ~spl12_8),
  inference(avatar_component_clause,[],[f141])).
thf(f143,plain,(
  spl12_6 | spl12_8),
  inference(avatar_split_clause,[],[f110,f141,f133])).
thf(f144,plain,(
  spl12_8 | spl12_7),
  inference(avatar_split_clause,[],[f112,f137,f141])).
thf(f146,definition,(
  spl12_9 <=> ! [X2 : ((a > $o) > $o)] : (($true = ((X2 @ (sK16 @ X2)))) | (((sK0 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition])).
thf(f147,plain,(
  ( ! [X2 : ((a > $o) > $o)] : (($true = ((X2 @ (sK16 @ X2)))) | (((sK0 @ X2)) = $false)) ) | ~spl12_9),
  inference(avatar_component_clause,[],[f146])).
thf(f149,definition,(
  spl12_10 <=> ! [X1 : ((a > $o) > $o)] : (($true = ((sK17 @ X1 @ sK13))) | (((sK0 @ X1)) = $false))),
  introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition])).
thf(f150,plain,(
  ( ! [X1 : ((a > $o) > $o)] : (($true = ((sK17 @ X1 @ sK13))) | (((sK0 @ X1)) = $false)) ) | ~spl12_10),
  inference(avatar_component_clause,[],[f149])).
thf(f151,plain,(
  spl12_9 | spl12_10),
  inference(avatar_split_clause,[],[f125,f149,f146])).
thf(f153,definition,(
  spl12_11 <=> ! [X2 : ((a > $o) > $o)] : ((((sK16 @ X2 @ sK13)) = $true) | (((sK0 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition])).
thf(f154,plain,(
  ( ! [X2 : ((a > $o) > $o)] : ((((sK16 @ X2 @ sK13)) = $true) | (((sK0 @ X2)) = $false)) ) | ~spl12_11),
  inference(avatar_component_clause,[],[f153])).
thf(f155,plain,(
  spl12_10 | spl12_11),
  inference(avatar_split_clause,[],[f124,f153,f149])).
thf(f157,definition,(
  spl12_12 <=> ! [X1 : ((a > $o) > $o)] : (($true = ((X1 @ (sK17 @ X1)))) | (((sK0 @ X1)) = $false))),
  introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition])).
thf(f158,plain,(
  ( ! [X1 : ((a > $o) > $o)] : (($true = ((X1 @ (sK17 @ X1)))) | (((sK0 @ X1)) = $false)) ) | ~spl12_12),
  inference(avatar_component_clause,[],[f157])).
thf(f159,plain,(
  spl12_9 | spl12_12),
  inference(avatar_split_clause,[],[f127,f157,f146])).
thf(f160,plain,(
  spl12_11 | spl12_12),
  inference(avatar_split_clause,[],[f126,f157,f153])).
thf(f163,plain,(
  (((sK0 @ (sK15 @ sK16))) = $false) | ($false = ((sK16 @ (sK15 @ sK16) @ sK13))) | ($true = $false) | (~spl12_7 | ~spl12_9)),
  inference(constrained_superposition,[],[f147,f138])).
thf(f164,plain,(
  (((sK0 @ (sK15 @ sK16))) = $false) | ($false = ((sK16 @ (sK15 @ sK16) @ sK13))) | (~spl12_7 | ~spl12_9)),
  inference(trivial_inequality_removal,[],[f163])).
thf(f167,plain,(
  ($true = $false) | ($false = ((sK16 @ (sK15 @ sK16) @ sK13))) | (~spl12_6 | ~spl12_7 | ~spl12_9)),
  inference(forward_demodulation,[],[f164,f134])).
thf(f168,plain,(
  ($false = ((sK16 @ (sK15 @ sK16) @ sK13))) | (~spl12_6 | ~spl12_7 | ~spl12_9)),
  inference(trivial_inequality_removal,[],[f167])).
thf(f173,plain,(
  ($true = $false) | (((sK0 @ (sK15 @ sK16))) = $false) | (~spl12_6 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
  inference(constrained_superposition,[],[f154,f168])).
thf(f176,plain,(
  (((sK0 @ (sK15 @ sK16))) = $false) | (~spl12_6 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
  inference(trivial_inequality_removal,[],[f173])).
thf(f180,plain,(
  ($true = $false) | (~spl12_6 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
  inference(forward_demodulation,[],[f176,f134])).
thf(f181,plain,(
  $false | (~spl12_6 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
  inference(trivial_inequality_removal,[],[f180])).
thf(f182,plain,(
  ~spl12_6 | ~spl12_7 | ~spl12_9 | ~spl12_11),
  inference(avatar_contradiction_clause,[],[f181])).
thf(f184,plain,(
  ($true = $false) | ($false = ((sK17 @ (sK15 @ sK17) @ sK13))) | (((sK0 @ (sK15 @ sK17))) = $false) | (~spl12_7 | ~spl12_12)),
  inference(constrained_superposition,[],[f138,f158])).
thf(f185,plain,(
  ($false = ((sK17 @ (sK15 @ sK17) @ sK13))) | (((sK0 @ (sK15 @ sK17))) = $false) | (~spl12_7 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f184])).
thf(f187,plain,(
  ($true = $false) | ($false = ((sK17 @ (sK15 @ sK17) @ sK13))) | (~spl12_6 | ~spl12_7 | ~spl12_12)),
  inference(forward_demodulation,[],[f185,f134])).
thf(f188,plain,(
  ($false = ((sK17 @ (sK15 @ sK17) @ sK13))) | (~spl12_6 | ~spl12_7 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f187])).
thf(f191,plain,(
  ($true = $false) | (((sK0 @ (sK15 @ sK17))) = $false) | (~spl12_6 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
  inference(constrained_superposition,[],[f188,f150])).
thf(f195,plain,(
  (((sK0 @ (sK15 @ sK17))) = $false) | (~spl12_6 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f191])).
thf(f200,plain,(
  ($true = $false) | (~spl12_6 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
  inference(forward_demodulation,[],[f195,f134])).
thf(f201,plain,(
  $false | (~spl12_6 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f200])).
thf(f202,plain,(
  ~spl12_6 | ~spl12_7 | ~spl12_10 | ~spl12_12),
  inference(avatar_contradiction_clause,[],[f201])).
thf(f204,plain,(
  (((sK17 @ sK14 @ sK13)) = $false) | ($true = $false) | (((sK0 @ sK14)) = $false) | (~spl12_8 | ~spl12_12)),
  inference(constrained_superposition,[],[f142,f158])).
thf(f206,plain,(
  (((sK0 @ sK14)) = $false) | (((sK16 @ sK14 @ sK13)) = $false) | ($true = $false) | (~spl12_8 | ~spl12_9)),
  inference(constrained_superposition,[],[f147,f142])).
thf(f209,plain,(
  (((sK0 @ sK14)) = $false) | (((sK17 @ sK14 @ sK13)) = $false) | (~spl12_8 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f204])).
thf(f210,plain,(
  (((sK0 @ sK14)) = $false) | (((sK16 @ sK14 @ sK13)) = $false) | (~spl12_8 | ~spl12_9)),
  inference(trivial_inequality_removal,[],[f206])).
thf(f213,plain,(
  ($true = $false) | (((sK17 @ sK14 @ sK13)) = $false) | (~spl12_5 | ~spl12_8 | ~spl12_12)),
  inference(forward_demodulation,[],[f209,f131])).
thf(f214,plain,(
  (((sK17 @ sK14 @ sK13)) = $false) | (~spl12_5 | ~spl12_8 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f213])).
thf(f215,plain,(
  (((sK16 @ sK14 @ sK13)) = $false) | ($true = $false) | (~spl12_5 | ~spl12_8 | ~spl12_9)),
  inference(forward_demodulation,[],[f210,f131])).
thf(f216,plain,(
  (((sK16 @ sK14 @ sK13)) = $false) | (~spl12_5 | ~spl12_8 | ~spl12_9)),
  inference(trivial_inequality_removal,[],[f215])).
thf(f223,plain,(
  (((sK0 @ sK14)) = $false) | ($true = $false) | (~spl12_5 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
  inference(constrained_superposition,[],[f150,f214])).
thf(f226,plain,(
  (((sK0 @ sK14)) = $false) | (~spl12_5 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f223])).
thf(f230,plain,(
  ($true = $false) | (~spl12_5 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
  inference(forward_demodulation,[],[f226,f131])).
thf(f231,plain,(
  $false | (~spl12_5 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
  inference(trivial_inequality_removal,[],[f230])).
thf(f232,plain,(
  ~spl12_5 | ~spl12_8 | ~spl12_10 | ~spl12_12),
  inference(avatar_contradiction_clause,[],[f231])).
thf(f236,plain,(
  (((sK0 @ sK14)) = $false) | ($true = $false) | (~spl12_5 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
  inference(constrained_superposition,[],[f216,f154])).
thf(f238,plain,(
  (((sK0 @ sK14)) = $false) | (~spl12_5 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
  inference(trivial_inequality_removal,[],[f236])).
thf(f242,plain,(
  ($true = $false) | (~spl12_5 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
  inference(forward_demodulation,[],[f238,f131])).
thf(f243,plain,(
  $false | (~spl12_5 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
  inference(trivial_inequality_removal,[],[f242])).
thf(f244,plain,(
  ~spl12_5 | ~spl12_8 | ~spl12_9 | ~spl12_11),
  inference(avatar_contradiction_clause,[],[f243])).
cnf(s5, plain, spl12_5 | spl12_6, inference(sat_conversion,[],[f135])).
cnf(s6, plain, spl12_5 | spl12_7, inference(sat_conversion,[],[f139])).
cnf(s7, plain, spl12_6 | spl12_8, inference(sat_conversion,[],[f143])).
cnf(s8, plain, spl12_7 | spl12_8, inference(sat_conversion,[],[f144])).
cnf(s9, plain, spl12_9 | spl12_10, inference(sat_conversion,[],[f151])).
cnf(s10, plain, spl12_10 | spl12_11, inference(sat_conversion,[],[f155])).
cnf(s11, plain, spl12_9 | spl12_12, inference(sat_conversion,[],[f159])).
cnf(s12, plain, spl12_11 | spl12_12, inference(sat_conversion,[],[f160])).
cnf(s14, plain, ~spl12_6 | ~spl12_7 | ~spl12_9 | ~spl12_11, inference(sat_conversion,[],[f182])).
cnf(s16, plain, ~spl12_6 | ~spl12_7 | ~spl12_10 | ~spl12_12, inference(sat_conversion,[],[f202])).
cnf(s18, plain, ~spl12_5 | ~spl12_8 | ~spl12_10 | ~spl12_12, inference(sat_conversion,[],[f232])).
cnf(s20, plain, ~spl12_5 | ~spl12_8 | ~spl12_9 | ~spl12_11, inference(sat_conversion,[],[f244])).
cnf(s23, plain, spl12_9 | spl12_5, inference(rat,[],[s16,s9,s11,s6,s5])).
cnf(s24, plain, ~spl12_9 | ~spl12_6 | ~spl12_7, inference(rat,[],[s16,s10,s12,s14])).
cnf(s25, plain, spl12_5, inference(rat,[],[s24,s23,s5,s6])).
cnf(s26, plain, ~spl12_7 | ~spl12_6, inference(rat,[],[s16,s9,s11,s24])).
cnf(s27, plain, spl12_9 | ~spl12_8, inference(rat,[],[s18,s9,s11,s25])).
cnf(s28, plain, ~spl12_9 | ~spl12_8, inference(rat,[],[s18,s10,s12,s20,s25])).
cnf(s29, plain, ~spl12_8, inference(rat,[],[s28,s27])).
cnf(s30, plain, spl12_7, inference(rat,[],[s8,s29])).
cnf(s31, plain, spl12_6, inference(rat,[],[s7,s29])).
cnf(s32, plain, $false, inference(rat,[],[s26,s31,s30])).
thf(f245,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s32])).
% SZS output end Proof for theBenchmark