%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_1, type, cP: ($i > $o)).
thf(func_def_4, type, cQ: ($i > $o)).
thf(func_def_6, type, cR: ($i > $o)).
thf(func_def_10, type, sK0: ($i > $i)).
thf(f1,conjecture,(
  ~((~(cP @ a) | ~(cP @ b)) & ! [X2 : $i] : ((cQ @ X2) & ((cP @ X2) | (cR @ X2))) & ! [X0 : $i] : ? [X1 : $i] : (~(cQ @ X0) | (cP @ X0) | ~(cQ @ c) | ~(cQ @ d) | ~(cQ @ X1)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM119)).
thf(f2,negated_conjecture,(
  ~ ~((~(cP @ a) | ~(cP @ b)) & ! [X2 : $i] : ((cQ @ X2) & ((cP @ X2) | (cR @ X2))) & ! [X0 : $i] : ? [X1 : $i] : (~(cQ @ X0) | (cP @ X0) | ~(cQ @ c) | ~(cQ @ d) | ~(cQ @ X1)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ~((~(cP @ a) | ~(cP @ b)) & ! [X0 : $i] : ((cQ @ X0) & ((cP @ X0) | (cR @ X0))) & ! [X1 : $i] : ? [X2 : $i] : (~(cQ @ X1) | (cP @ X1) | ~(cQ @ c) | ~(cQ @ d) | ~(cQ @ X2)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ~((~ (((cP @ a)) = $true) | ~ (((cP @ b)) = $true)) & ! [X0 : $i] : ((((cQ @ X0)) = $true) & (($true = ((cR @ X0))) | (((cP @ X0)) = $true))) & ! [X1 : $i] : ? [X2 : $i] : (~ (((cQ @ X1)) = $true) | ($true = ((cP @ X1))) | ~ (((cQ @ c)) = $true) | ~ (((cQ @ d)) = $true) | ~ (((cQ @ X2)) = $true)))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ! [X1 : $i] : ? [X2 : $i] : (($true = ((cP @ X1))) | (((cQ @ c)) != $true) | (((cQ @ X2)) != $true) | (((cQ @ d)) != $true) | (((cQ @ X1)) != $true)) & ((((cP @ a)) != $true) | (((cP @ b)) != $true)) & ! [X0 : $i] : ((((cQ @ X0)) = $true) & (($true = ((cR @ X0))) | (((cP @ X0)) = $true)))),
  inference(flattening,[],[f4])).
thf(f6,plain,(
  ! [X0 : $i] : ? [X1 : $i] : ((((cP @ X0)) = $true) | (((cQ @ c)) != $true) | (((cQ @ X1)) != $true) | (((cQ @ d)) != $true) | (((cQ @ X0)) != $true)) & ((((cP @ a)) != $true) | (((cP @ b)) != $true)) & ! [X2 : $i] : ((((cQ @ X2)) = $true) & ((((cR @ X2)) = $true) | (((cP @ X2)) = $true)))),
  inference(rectify,[],[f5])).
thf(f7,plain,(
  ! [X0 : $i] : ((((cP @ X0)) = $true) | (((cQ @ c)) != $true) | ($true != ((cQ @ (sK0 @ X0)))) | (((cQ @ d)) != $true) | (((cQ @ X0)) != $true)) & ((((cP @ a)) != $true) | (((cP @ b)) != $true)) & ! [X2 : $i] : ((((cQ @ X2)) = $true) & ((((cR @ X2)) = $true) | (((cP @ X2)) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f6])).
thf(f9,plain,(
  ( ! [X2 : $i] : ((((cQ @ X2)) = $true)) )),
  inference(cnf_transformation,[],[f7])).
thf(f10,plain,(
  (((cP @ b)) != $true) | (((cP @ a)) != $true)),
  inference(cnf_transformation,[],[f7])).
thf(f11,plain,(
  ( ! [X0 : $i] : ((((cP @ X0)) = $true) | (((cQ @ c)) != $true) | ($true != ((cQ @ (sK0 @ X0)))) | (((cQ @ d)) != $true) | (((cQ @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f7])).
thf(f13,plain,(
  ( ! [X0 : $i] : ((((cP @ X0)) = $true) | (((cQ @ X0)) != $true) | (((cQ @ d)) != $true) | ($true != ((cQ @ (sK0 @ X0))))) )),
  inference(forward_subsumption_resolution,[],[f11,f9])).
thf(f14,plain,(
  ( ! [X0 : $i] : ((((cQ @ X0)) != $true) | (((cP @ X0)) = $true) | ($true != ((cQ @ (sK0 @ X0))))) )),
  inference(forward_subsumption_resolution,[],[f13,f9])).
thf(f15,plain,(
  ( ! [X0 : $i] : ((((cP @ X0)) = $true) | ($true != ((cQ @ (sK0 @ X0))))) )),
  inference(forward_subsumption_resolution,[],[f14,f9])).
thf(f16,plain,(
  ( ! [X0 : $i] : ((((cP @ X0)) = $true)) )),
  inference(forward_subsumption_resolution,[],[f15,f9])).
thf(f17,plain,(
  (((cP @ a)) != $true) | ($true != $true)),
  inference(superposition,[],[f10,f16])).
thf(f18,plain,(
  (((cP @ a)) != $true)),
  inference(trivial_inequality_removal,[],[f17])).
thf(f19,plain,(
  $false),
  inference(forward_subsumption_resolution,[],[f18,f16])).
% SZS output end Proof for theBenchmark