%----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 > $i)).
thf(func_def_1, type, cS: ($i > $o)).
thf(func_def_3, type, sK0: (($i > $o) > $i)).
thf(func_def_6, type, vNOT: ($o > $o)).
thf(func_def_7, type, inv_f_1: ($i > $i)).
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 : $i,X1 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X0 : $i] : ((X2 @ (f @ X0)) <=> (cS @ X0))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSV5_pme)).
thf(f2,negated_conjecture,(
  ~(! [X0 : $i,X1 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X0 : $i] : ((X2 @ (f @ X0)) <=> (cS @ X0)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(! [X0 : $i,X1 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X3 : $i] : ((X2 @ (f @ X3)) <=> (cS @ X3)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~(! [X1 : $i,X0 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X3 : $i] : (((cS @ X3)) = ((X2 @ (f @ X3)))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ! [X2 : ($i > $o)] : ? [X3 : $i] : (((cS @ X3)) != ((X2 @ (f @ X3)))) & ! [X1 : $i,X0 : $i] : ((X0 = X1) | (((f @ X0)) != ((f @ X1))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ! [X0 : ($i > $o)] : ? [X1 : $i] : (((X0 @ (f @ X1))) != ((cS @ X1))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X3)) != ((f @ X2))))),
  inference(rectify,[],[f5])).
thf(f7,plain,(
  ! [X0 : ($i > $o)] : (((X0 @ (f @ (sK0 @ X0)))) != ((cS @ (sK0 @ X0)))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X3)) != ((f @ X2))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f6])).
thf(f8,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((f @ X3)) != ((f @ X2))) | (X2 = X3)) )),
  inference(cnf_transformation,[],[f7])).
thf(f9,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ (f @ (sK0 @ X0)))) != ((cS @ (sK0 @ X0))))) )),
  inference(cnf_transformation,[],[f7])).
thf(f12,plain,(
  ( ! [X3 : $i] : ((((inv_f_1 @ (f @ X3))) = X3)) )),
  inference(injectivity,[],[f8])).
thf(f17,plain,(
  ( ! [X1 : ($i > $i)] : (((((^[Y0 : $i]: (cS @ (X1 @ Y0))) @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0))))))) != ((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0)))))))) )),
  inference(imitation,[],[f9])).
thf(f18,plain,(
  ( ! [X1 : ($i > $i)] : ((((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0)))))) != ((cS @ (X1 @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0)))))))))) )),
  inference(beta-eta_normalization,[],[f17])).
thf(f22,plain,(
  (((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (inv_f_1 @ Y0)))))) != ((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (inv_f_1 @ Y0)))))))),
  inference(constrained_superposition,[],[f18,f12])).
thf(f23,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f22])).
% SZS output end Proof for theBenchmark