%----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, sK0: (a > a > $o)).
thf(func_def_4, type, sK1: ((a > $o) > a)).
thf(func_def_5, type, sK2: (a > a)).
thf(func_def_6, type, sK3: (a > (a > $o) > a)).
thf(func_def_7, type, vNOT: ($o > $o)).
thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X6 : (a > $o)] : (! [X9 : a] : ((X6 @ X9) => (X0 @ X9 @ (X1 @ X6))) & ! [X7 : a] : (! [X8 : a] : ((X6 @ X8) => (X0 @ X8 @ X7)) => (X0 @ (X1 @ X6) @ X7))) & ! [X9 : a,X5 : a,X4 : a] : (((X0 @ X4 @ X5) & (X0 @ X5 @ X9)) => (X0 @ X4 @ X9))) => ! [X2 : (a > a)] : (! [X5 : a,X4 : a] : ((X0 @ X4 @ X5) => (X0 @ (X2 @ X4) @ (X2 @ X5))) => ? [X3 : a] : (X0 @ X3 @ (X2 @ X3))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM402_pme)).
thf(f2,negated_conjecture,(
  ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X6 : (a > $o)] : (! [X9 : a] : ((X6 @ X9) => (X0 @ X9 @ (X1 @ X6))) & ! [X7 : a] : (! [X8 : a] : ((X6 @ X8) => (X0 @ X8 @ X7)) => (X0 @ (X1 @ X6) @ X7))) & ! [X9 : a,X5 : a,X4 : a] : (((X0 @ X4 @ X5) & (X0 @ X5 @ X9)) => (X0 @ X4 @ X9))) => ! [X2 : (a > a)] : (! [X5 : a,X4 : a] : ((X0 @ X4 @ X5) => (X0 @ (X2 @ X4) @ (X2 @ X5))) => ? [X3 : a] : (X0 @ X3 @ (X2 @ X3))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X3 : a] : ((X2 @ X3) => (X0 @ X3 @ (X1 @ X2))) & ! [X4 : a] : (! [X5 : a] : ((X2 @ X5) => (X0 @ X5 @ X4)) => (X0 @ (X1 @ X2) @ X4))) & ! [X6 : a,X7 : a,X8 : a] : (((X0 @ X8 @ X7) & (X0 @ X7 @ X6)) => (X0 @ X8 @ X6))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : ((X0 @ X11 @ X10) => (X0 @ (X9 @ X11) @ (X9 @ X10))) => ? [X12 : a] : (X0 @ X12 @ (X9 @ X12))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X3 : a] : ((((X2 @ X3)) = $true) => ($true = ((X0 @ X3 @ (X1 @ X2))))) & ! [X4 : a] : (! [X5 : a] : (($true = ((X2 @ X5))) => ($true = ((X0 @ X5 @ X4)))) => ($true = ((X0 @ (X1 @ X2) @ X4))))) & ! [X6 : a,X7 : a,X8 : a] : ((($true = ((X0 @ X7 @ X6))) & (((X0 @ X8 @ X7)) = $true)) => ($true = ((X0 @ X8 @ X6))))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : (($true = ((X0 @ X11 @ X10))) => ($true = ((X0 @ (X9 @ X11) @ (X9 @ X10))))) => ? [X12 : a] : (((X0 @ X12 @ (X9 @ X12))) = $true)))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X9 : (a > a)] : (! [X11 : a,X10 : a] : (($true != ((X0 @ X11 @ X10))) | ($true = ((X0 @ (X9 @ X11) @ (X9 @ X10))))) & ! [X12 : a] : (((X0 @ X12 @ (X9 @ X12))) != $true)) & (! [X2 : (a > $o)] : (! [X3 : a] : ((((X2 @ X3)) != $true) | ($true = ((X0 @ X3 @ (X1 @ X2))))) & ! [X4 : a] : (($true = ((X0 @ (X1 @ X2) @ X4))) | ? [X5 : a] : (($true != ((X0 @ X5 @ X4))) & ($true = ((X2 @ X5)))))) & ! [X6 : a,X7 : a,X8 : a] : (($true = ((X0 @ X8 @ X6))) | (($true != ((X0 @ X7 @ X6))) | (((X0 @ X8 @ X7)) != $true)))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X9 : (a > a)] : (! [X11 : a,X10 : a] : (($true != ((X0 @ X11 @ X10))) | ($true = ((X0 @ (X9 @ X11) @ (X9 @ X10))))) & ! [X12 : a] : (((X0 @ X12 @ (X9 @ X12))) != $true)) & ! [X8 : a,X6 : a,X7 : a] : (($true != ((X0 @ X7 @ X6))) | ($true = ((X0 @ X8 @ X6))) | (((X0 @ X8 @ X7)) != $true)) & ! [X2 : (a > $o)] : (! [X3 : a] : ((((X2 @ X3)) != $true) | ($true = ((X0 @ X3 @ (X1 @ X2))))) & ! [X4 : a] : (($true = ((X0 @ (X1 @ X2) @ X4))) | ? [X5 : a] : (($true != ((X0 @ X5 @ X4))) & ($true = ((X2 @ X5)))))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X2 : (a > a)] : (! [X3 : a,X4 : a] : (($true != ((X0 @ X3 @ X4))) | ($true = ((X0 @ (X2 @ X3) @ (X2 @ X4))))) & ! [X5 : a] : ($true != ((X0 @ X5 @ (X2 @ X5))))) & ! [X6 : a,X7 : a,X8 : a] : ((((X0 @ X8 @ X7)) != $true) | ($true = ((X0 @ X6 @ X7))) | (((X0 @ X6 @ X8)) != $true)) & ! [X9 : (a > $o)] : (! [X10 : a] : ((((X9 @ X10)) != $true) | (((X0 @ X10 @ (X1 @ X9))) = $true)) & ! [X11 : a] : ((((X0 @ (X1 @ X9) @ X11)) = $true) | ? [X12 : a] : (($true != ((X0 @ X12 @ X11))) & (((X9 @ X12)) = $true)))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  (! [X3 : a,X4 : a] : (($true != ((sK0 @ X3 @ X4))) | ($true = ((sK0 @ (sK2 @ X3) @ (sK2 @ X4))))) & ! [X5 : a] : ($true != ((sK0 @ X5 @ (sK2 @ X5))))) & ! [X6 : a,X7 : a,X8 : a] : (($true != ((sK0 @ X8 @ X7))) | ($true = ((sK0 @ X6 @ X7))) | ($true != ((sK0 @ X6 @ X8)))) & ! [X9 : (a > $o)] : (! [X10 : a] : ((((X9 @ X10)) != $true) | ($true = ((sK0 @ X10 @ (sK1 @ X9))))) & ! [X11 : a] : ((((sK0 @ (sK1 @ X9) @ X11)) = $true) | (($true != ((sK0 @ (sK3 @ X11 @ X9) @ X11))) & (((X9 @ (sK3 @ X11 @ X9))) = $true))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2)),skolemize(X12,$thf(sK3 @ X11 @ X9))],[f7])).
thf(f9,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((X9 @ (sK3 @ X11 @ X9))) = $true) | (((sK0 @ (sK1 @ X9) @ X11)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f13,plain,(
  ( ! [X5 : a] : (($true != ((sK0 @ X5 @ (sK2 @ X5))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f72,plain,(
  ( ! [X11 : a] : (($true = ((sK0 @ (sK1 @ (^[Y0 : a]: ($false))) @ X11))) | ($true = (((^[Y0 : a]: ($false)) @ (sK3 @ X11 @ (^[Y0 : a]: ($false))))))) )),
  inference(primitive_instantiation,[],[f9])).
thf(f94,plain,(
  ( ! [X11 : a] : (($true = ((sK0 @ (sK1 @ (^[Y0 : a]: ($false))) @ X11))) | ($true = $false)) )),
  inference(beta-eta_normalization,[],[f72])).
thf(f95,plain,(
  ( ! [X11 : a] : (($true = ((sK0 @ (sK1 @ (^[Y0 : a]: ($false))) @ X11)))) )),
  inference(trivial_inequality_removal,[],[f94])).
thf(f105,plain,(
  ($true != $true)),
  inference(constrained_superposition,[],[f13,f95])).
thf(f110,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f105])).
% SZS output end Proof for theBenchmark