%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, a: $tType).
thf(type_def_6, type, b: $tType).
thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, r: (a > b > $o)).
thf(func_def_4, type, sK0: ((a > b) > a)).
thf(func_def_5, type, sK1: (a > b)).
thf(f1,axiom,(
  ! [X0 : a] : ? [X1 : b] : (r @ X0 @ X1)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rtotal)).
thf(f2,conjecture,(
  ? [X0 : (a > b)] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',skolem)).
thf(f3,negated_conjecture,(
  ~ ? [X0 : (a > b)] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ~ ? [X0 : (a > b)] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
  inference(rectify,[],[f3])).
thf(f5,plain,(
  ~ ? [X0 : (a > b)] : ! [X1 : a] : (((r @ X1 @ (X0 @ X1))) = $true)),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ! [X0 : a] : ? [X1 : b] : (r @ X0 @ X1)),
  inference(rectify,[],[f1])).
thf(f7,plain,(
  ! [X0 : a] : ? [X1 : b] : (((r @ X0 @ X1)) = $true)),
  inference(fool_elimination,[],[f6])).
thf(f8,plain,(
  ! [X0 : (a > b)] : ? [X1 : a] : (((r @ X1 @ (X0 @ X1))) != $true)),
  inference(ennf_transformation,[],[f5])).
thf(f9,plain,(
  ! [X0 : (a > b)] : ($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f8])).
thf(f10,plain,(
  ! [X0 : a] : ($true = ((r @ X0 @ (sK1 @ X0))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f7])).
thf(f11,plain,(
  ( ! [X0 : (a > b)] : (($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))))) )),
  inference(cnf_transformation,[],[f9])).
thf(f12,plain,(
  ( ! [X0 : a] : (($true = ((r @ X0 @ (sK1 @ X0))))) )),
  inference(cnf_transformation,[],[f10])).
thf(f14,plain,(
  ($true != $true)),
  inference(superposition,[],[f11,f12])).
thf(f15,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f14])).
% SZS output end Proof for theBenchmark