%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, cHALF: ($i > $i > $o)).
thf(func_def_1, type, cDOUBLE: ($i > $i > $o)).
thf(func_def_2, type, cS: ($i > $i)).
thf(func_def_7, type, sK0: (($i > $i > $o) > $i)).
thf(func_def_8, type, sK1: (($i > $i > $o) > $i)).
thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_14, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_15, type, sK4: (($i > $i > $o) > ($i > $i > $i) > $i)).
thf(func_def_16, type, sK5: (($i > $i > $i) > ($i > $i > $i) > $i)).
thf(f1,conjecture,(
  (! [X3 : $i,X2 : $i] : ((cHALF @ X2 @ X3) => (cHALF @ (cS @ (cS @ X2)) @ (cS @ X3))) & (cHALF @ c0 @ c0) & (cHALF @ (cS @ c0) @ c0) & ! [X0 : $i,X4 : ($i > $i > $o),X1 : $i] : ((! [X2 : $i,X3 : $i] : ((X4 @ X2 @ X3) => (X4 @ (cS @ X2) @ (cS @ (cS @ X3)))) & (cDOUBLE @ X0 @ X1) & (X4 @ c0 @ c0)) => (X4 @ X0 @ X1))) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM301)).
thf(f2,negated_conjecture,(
  ~((! [X3 : $i,X2 : $i] : ((cHALF @ X2 @ X3) => (cHALF @ (cS @ (cS @ X2)) @ (cS @ X3))) & (cHALF @ c0 @ c0) & (cHALF @ (cS @ c0) @ c0) & ! [X0 : $i,X4 : ($i > $i > $o),X1 : $i] : ((! [X2 : $i,X3 : $i] : ((X4 @ X2 @ X3) => (X4 @ (cS @ X2) @ (cS @ (cS @ X3)))) & (cDOUBLE @ X0 @ X1) & (X4 @ c0 @ c0)) => (X4 @ X0 @ X1))) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~((! [X0 : $i,X1 : $i] : ((cHALF @ X1 @ X0) => (cHALF @ (cS @ (cS @ X1)) @ (cS @ X0))) & (cHALF @ c0 @ c0) & (cHALF @ (cS @ c0) @ c0) & ! [X2 : $i,X3 : ($i > $i > $o),X4 : $i] : ((! [X5 : $i,X6 : $i] : ((X3 @ X5 @ X6) => (X3 @ (cS @ X5) @ (cS @ (cS @ X6)))) & (cDOUBLE @ X2 @ X4) & (X3 @ c0 @ c0)) => (X3 @ X2 @ X4))) => ! [X7 : $i,X8 : $i] : ((cDOUBLE @ X7 @ X8) => (cHALF @ X8 @ X7)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~((! [X2 : $i,X3 : ($i > $i > $o),X4 : $i] : ((($true = ((X3 @ c0 @ c0))) & ! [X5 : $i,X6 : $i] : ((((X3 @ X5 @ X6)) = $true) => ($true = ((X3 @ (cS @ X5) @ (cS @ (cS @ X6)))))) & ($true = ((cDOUBLE @ X2 @ X4)))) => (((X3 @ X2 @ X4)) = $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X1 : $i,X0 : $i] : ((((cHALF @ X1 @ X0)) = $true) => ($true = ((cHALF @ (cS @ (cS @ X1)) @ (cS @ X0)))))) => ! [X8 : $i,X7 : $i] : (($true = ((cDOUBLE @ X7 @ X8))) => ($true = ((cHALF @ X8 @ X7)))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X7 : $i,X8 : $i] : (($true != ((cHALF @ X8 @ X7))) & ($true = ((cDOUBLE @ X7 @ X8)))) & (! [X2 : $i,X3 : ($i > $i > $o),X4 : $i] : ((((X3 @ X2 @ X4)) = $true) | (($true != ((X3 @ c0 @ c0))) | ? [X5 : $i,X6 : $i] : ((((X3 @ X5 @ X6)) = $true) & ($true != ((X3 @ (cS @ X5) @ (cS @ (cS @ X6)))))) | ($true != ((cDOUBLE @ X2 @ X4))))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X1 : $i,X0 : $i] : ((((cHALF @ X1 @ X0)) != $true) | ($true = ((cHALF @ (cS @ (cS @ X1)) @ (cS @ X0))))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  (((cHALF @ c0 @ c0)) = $true) & (((cHALF @ (cS @ c0) @ c0)) = $true) & ! [X3 : ($i > $i > $o),X4 : $i,X2 : $i] : ((((X3 @ X2 @ X4)) = $true) | ? [X5 : $i,X6 : $i] : ((((X3 @ X5 @ X6)) = $true) & ($true != ((X3 @ (cS @ X5) @ (cS @ (cS @ X6)))))) | ($true != ((cDOUBLE @ X2 @ X4))) | ($true != ((X3 @ c0 @ c0)))) & ! [X1 : $i,X0 : $i] : ((((cHALF @ X1 @ X0)) != $true) | ($true = ((cHALF @ (cS @ (cS @ X1)) @ (cS @ X0))))) & ? [X7 : $i,X8 : $i] : (($true != ((cHALF @ X8 @ X7))) & ($true = ((cDOUBLE @ X7 @ X8))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  (((cHALF @ c0 @ c0)) = $true) & (((cHALF @ (cS @ c0) @ c0)) = $true) & ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i] : (($true = ((X0 @ X2 @ X1))) | ? [X3 : $i,X4 : $i] : (($true = ((X0 @ X3 @ X4))) & (((X0 @ (cS @ X3) @ (cS @ (cS @ X4)))) != $true)) | ($true != ((cDOUBLE @ X2 @ X1))) | ($true != ((X0 @ c0 @ c0)))) & ! [X5 : $i,X6 : $i] : (($true != ((cHALF @ X5 @ X6))) | (((cHALF @ (cS @ (cS @ X5)) @ (cS @ X6))) = $true)) & ? [X7 : $i,X8 : $i] : (($true != ((cHALF @ X8 @ X7))) & ($true = ((cDOUBLE @ X7 @ X8))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  (((cHALF @ c0 @ c0)) = $true) & (((cHALF @ (cS @ c0) @ c0)) = $true) & ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i] : (($true = ((X0 @ X2 @ X1))) | (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) & ($true != ((X0 @ (cS @ (sK0 @ X0)) @ (cS @ (cS @ (sK1 @ X0))))))) | ($true != ((cDOUBLE @ X2 @ X1))) | ($true != ((X0 @ c0 @ c0)))) & ! [X5 : $i,X6 : $i] : (($true != ((cHALF @ X5 @ X6))) | (((cHALF @ (cS @ (cS @ X5)) @ (cS @ X6))) = $true)) & (($true != ((cHALF @ sK3 @ sK2))) & ($true = ((cDOUBLE @ sK2 @ sK3))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK2,sK3]),skolemize(X4,$thf(sK1 @ X0)),skolemize(X4,$thf(sK1 @ X0)),skolemize(X7,$thf(sK2)),skolemize(X8,$thf(sK3))],[f7])).
thf(f9,plain,(
  ($true = ((cDOUBLE @ sK2 @ sK3)))),
  inference(cnf_transformation,[],[f8])).
thf(f10,plain,(
  ($true != ((cHALF @ sK3 @ sK2)))),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X6 : $i,X5 : $i] : ((((cHALF @ (cS @ (cS @ X5)) @ (cS @ X6))) = $true) | ($true != ((cHALF @ X5 @ X6)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f12,plain,(
  ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : (($true != ((X0 @ (cS @ (sK0 @ X0)) @ (cS @ (cS @ (sK1 @ X0)))))) | ($true != ((X0 @ c0 @ c0))) | ($true != ((cDOUBLE @ X2 @ X1))) | ($true = ((X0 @ X2 @ X1)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f13,plain,(
  ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true != ((X0 @ c0 @ c0))) | ($true != ((cDOUBLE @ X2 @ X1))) | ($true = ((X0 @ X2 @ X1)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f15,plain,(
  (((cHALF @ c0 @ c0)) = $true)),
  inference(cnf_transformation,[],[f8])).
thf(f30,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $i),X1 : $i,X4 : $i] : ((((X0 @ (cS @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))))))) != ((cS @ (cS @ X1)))) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) | ($true != $true) | (((cHALF @ X1 @ X2)) != $true) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X3 @ X4))) | ($true != ((cDOUBLE @ X3 @ X4))) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) != X2)) )),
  inference(constrained_superposition,[],[f12,f11])).
thf(f48,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $i),X1 : $i,X4 : $i] : (($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) != X2) | (((X0 @ (cS @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))))))) != ((cS @ (cS @ X1)))) | (((cHALF @ X1 @ X2)) != $true) | ($true != ((cDOUBLE @ X3 @ X4))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X3 @ X4)))) )),
  inference(trivial_inequality_removal,[],[f30])).
thf(f49,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $i),X1 : $i,X4 : $i] : ((((X0 @ (cS @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))))))) != ((cS @ (cS @ X1)))) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) != X2) | (((cHALF @ (X0 @ X3 @ X4) @ X3)) = $true) | (((cHALF @ X1 @ X2)) != $true) | ($true != ((cDOUBLE @ X3 @ X4))) | ($true != ((cHALF @ (X0 @ c0 @ c0) @ c0)))) )),
  inference(beta-eta_normalization,[],[f48])).
thf(f126,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X0 : $i,X1 : $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X3) | (((cHALF @ (sK1 @ X3) @ X0)) != $true) | ($true != ((cDOUBLE @ X1 @ X2))) | ($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X1 @ X2) @ X1))) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))) != X0) | ($true != ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ c0 @ c0) @ c0)))) )),
  inference(equality_resolution,[],[f49])).
thf(f130,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X0 : $i,X1 : $i] : ((((cHALF @ (sK1 @ X3) @ X0)) != $true) | ($true != ((cDOUBLE @ X1 @ X2))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X3) | (((cHALF @ X2 @ X1)) = $true) | (((cHALF @ c0 @ c0)) != $true) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) != X0)) )),
  inference(beta-eta_normalization,[],[f126])).
thf(f134,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X0 : $i,X1 : $i] : ((((cHALF @ (sK1 @ X3) @ X0)) != $true) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) != X0) | ($true != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X3) | (((cHALF @ X2 @ X1)) = $true) | ($true != ((cDOUBLE @ X1 @ X2)))) )),
  inference(forward_demodulation,[],[f130,f15])).
thf(f135,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X0 : $i,X1 : $i] : ((((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) != X0) | (((cHALF @ (sK1 @ X3) @ X0)) != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X3) | (((cHALF @ X2 @ X1)) = $true) | ($true != ((cDOUBLE @ X1 @ X2)))) )),
  inference(trivial_inequality_removal,[],[f134])).
thf(f176,plain,(
  ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : ((((cHALF @ (sK1 @ X0) @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) != $true) | (((cHALF @ X1 @ X2)) = $true) | ($true != ((cDOUBLE @ X2 @ X1))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X0)) )),
  inference(equality_resolution,[],[f135])).
thf(f177,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $i),X4 : $i,X5 : $i] : (($true != $true) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) | (((sK1 @ X0)) != ((X1 @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ Y0)))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X1) | (((cDOUBLE @ X4 @ X5)) != $true) | (((cHALF @ X2 @ X3)) = $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X0) | ($true != ((cDOUBLE @ X3 @ X2))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X4 @ X5)) = $true)) )),
  inference(constrained_superposition,[],[f176,f13])).
thf(f182,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $i),X4 : $i,X5 : $i] : ((((cHALF @ X2 @ X3)) = $true) | (((cDOUBLE @ X4 @ X5)) != $true) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) | ($true != ((cDOUBLE @ X3 @ X2))) | (((sK1 @ X0)) != ((X1 @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ Y0)))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X1) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X4 @ X5)) = $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X0)) )),
  inference(trivial_inequality_removal,[],[f177])).
thf(f183,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $i),X4 : $i,X5 : $i] : ((((sK1 @ X0)) != ((X1 @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X1 @ Y0 @ Y1) @ Y0)))))))) | (((cHALF @ X2 @ X3)) = $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X1) | ($true != ((cHALF @ (X1 @ c0 @ c0) @ c0))) | ($true != ((cDOUBLE @ X3 @ X2))) | (((cDOUBLE @ X4 @ X5)) != $true) | ($true = ((cHALF @ (X1 @ X4 @ X5) @ X4))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))) != X0)) )),
  inference(beta-eta_normalization,[],[f182])).
thf(f204,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : ($i > $i > $i),X5 : ($i > $i > $i)] : (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X4 @ Y0 @ Y1) @ (X5 @ Y0 @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X4) | ($true != ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ c0 @ c0) @ c0))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) != X5) | ($true = ((cHALF @ X0 @ X1))) | ($true != ((cDOUBLE @ X2 @ X3))) | (((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X2 @ X3) @ X2)) = $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (Y1))))) | ($true != ((cDOUBLE @ X1 @ X0)))) )),
  inference(equality_resolution,[],[f183])).
thf(f206,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : ($i > $i > $i),X5 : ($i > $i > $i)] : ((((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X2 @ X3) @ X2)) = $true) | ($true = ((cHALF @ X0 @ X1))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X4) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) != X5) | ($true != ((cDOUBLE @ X2 @ X3))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X4 @ Y0 @ Y1) @ (X5 @ Y0 @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) | ($true != ((cDOUBLE @ X1 @ X0))) | ($true != ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ c0 @ c0) @ c0)))) )),
  inference(trivial_inequality_removal,[],[f204])).
thf(f207,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : ($i > $i > $i),X5 : ($i > $i > $i)] : ((((cHALF @ c0 @ c0)) != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) != X5) | (((cHALF @ X3 @ X2)) = $true) | ($true = ((cHALF @ X0 @ X1))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X4 @ Y0 @ Y1) @ (X5 @ Y0 @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) | ($true != ((cDOUBLE @ X2 @ X3))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X4) | ($true != ((cDOUBLE @ X1 @ X0)))) )),
  inference(beta-eta_normalization,[],[f206])).
thf(f209,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : ($i > $i > $i),X5 : ($i > $i > $i)] : (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) != X5) | ($true != ((cDOUBLE @ X1 @ X0))) | ($true = ((cHALF @ X0 @ X1))) | (((cHALF @ X3 @ X2)) = $true) | ($true != ((cDOUBLE @ X2 @ X3))) | ($true != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X4 @ Y0 @ Y1) @ (X5 @ Y0 @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X4)) )),
  inference(forward_demodulation,[],[f207,f15])).
thf(f210,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : ($i > $i > $i),X5 : ($i > $i > $i)] : (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X4 @ Y0 @ Y1) @ (X5 @ Y0 @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) | (((cHALF @ X3 @ X2)) = $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != X4) | ($true != ((cDOUBLE @ X2 @ X3))) | ($true = ((cHALF @ X0 @ X1))) | ($true != ((cDOUBLE @ X1 @ X0))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) != X5)) )),
  inference(trivial_inequality_removal,[],[f209])).
thf(f215,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (Y0))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (Y1))))) | ($true = ((cHALF @ X0 @ X1))) | (((cHALF @ X2 @ X3)) = $true) | ($true != ((cDOUBLE @ X3 @ X2))) | ($true != ((cDOUBLE @ X1 @ X0)))) )),
  inference(equality_resolution,[],[f210])).
thf(f216,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((cHALF @ X0 @ X1))) | ($true != ((cDOUBLE @ X3 @ X2))) | (((cHALF @ X2 @ X3)) = $true) | ($true != ((cDOUBLE @ X1 @ X0)))) )),
  inference(trivial_inequality_removal,[],[f215])).
thf(f229,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((cDOUBLE @ X1 @ X0))) | ($true = ((cHALF @ X0 @ X1))) | ($true != ((cDOUBLE @ X1 @ X0))) | ($true != $true)) )),
  inference(equality_factoring,[],[f216])).
thf(f242,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((cDOUBLE @ X1 @ X0))) | ($true = ((cHALF @ X0 @ X1))) | ($true != $true)) )),
  inference(duplicate_literal_removal,[],[f229])).
thf(f243,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ X0 @ X1))) | ($true != ((cDOUBLE @ X1 @ X0)))) )),
  inference(trivial_inequality_removal,[],[f242])).
thf(f256,plain,(
  ($true != ((cDOUBLE @ sK2 @ sK3))) | ($true != $true)),
  inference(constrained_superposition,[],[f10,f243])).
thf(f269,plain,(
  ($true != ((cDOUBLE @ sK2 @ sK3)))),
  inference(trivial_inequality_removal,[],[f256])).
thf(f273,plain,(
  ($true != $true)),
  inference(forward_demodulation,[],[f269,f9])).
thf(f274,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f273])).
% SZS output end Proof for theBenchmark