%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, f: ($i > $i)).
thf(func_def_2, type, sK0: (($i > $i) > $i)).
thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_5, type, inv_f_1: ($i > $i)).
thf(f1,axiom,(
  ! [X0 : $i,X1 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finj)).
thf(f2,conjecture,(
  ? [X0 : ($i > $i)] : ! [X1 : $i] : (((X0 @ (f @ X1))) = X1)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invexists)).
thf(f3,negated_conjecture,(
  ~ ? [X0 : ($i > $i)] : ! [X1 : $i] : (((X0 @ (f @ X1))) = X1)),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ! [X0 : $i,X1 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1))),
  inference(fool_elimination,[],[f1])).
thf(f5,plain,(
  ~ ? [X0 : ($i > $i)] : ! [X1 : $i] : (((X0 @ (f @ X1))) = X1)),
  inference(fool_elimination,[],[f3])).
thf(f6,plain,(
  ! [X1 : $i,X0 : $i] : ((((f @ X0)) != ((f @ X1))) | (X0 = X1))),
  inference(ennf_transformation,[],[f4])).
thf(f7,plain,(
  ! [X0 : ($i > $i)] : ? [X1 : $i] : (((X0 @ (f @ X1))) != X1)),
  inference(ennf_transformation,[],[f5])).
thf(f8,plain,(
  ! [X0 : ($i > $i)] : (((sK0 @ X0)) != ((X0 @ (f @ (sK0 @ X0)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f7])).
thf(f9,plain,(
  ! [X0 : $i,X1 : $i] : ((((f @ X0)) != ((f @ X1))) | (X0 = X1))),
  inference(rectify,[],[f6])).
thf(f10,plain,(
  ( ! [X0 : ($i > $i)] : ((((sK0 @ X0)) != ((X0 @ (f @ (sK0 @ X0)))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((f @ X0)) != ((f @ X1))) | (X0 = X1)) )),
  inference(cnf_transformation,[],[f9])).
thf(f14,plain,(
  ( ! [X0 : $i] : ((((inv_f_1 @ (f @ X0))) = X0)) )),
  inference(injectivity,[],[f11])).
thf(f16,plain,(
  (((sK0 @ inv_f_1)) != ((sK0 @ inv_f_1)))),
  inference(constrained_superposition,[],[f10,f14])).
thf(f17,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f16])).
% SZS output end Proof for theBenchmark