%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
thf(func_def_4, type, sK0: ((($i > $o) > $i) > $i > $o)).
thf(func_def_5, type, sK1: ((($i > $o) > $i) > $i)).
thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ? [X0 : (($i > $o) > $i)] : ! [X1 : ($i > $o)] : (? [X2 : $i] : ~(X1 @ X2) => ~(X1 @ (X0 @ X1)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choicecomp)).
thf(f2,negated_conjecture,(
  ~ ? [X0 : (($i > $o) > $i)] : ! [X1 : ($i > $o)] : (? [X2 : $i] : ~(X1 @ X2) => ~(X1 @ (X0 @ X1)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ? [X0 : (($i > $o) > $i)] : ! [X1 : ($i > $o)] : (? [X2 : $i] : ~(X1 @ X2) => ~(X1 @ (X0 @ X1)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ? [X0 : (($i > $o) > $i)] : ! [X1 : ($i > $o)] : (? [X2 : $i] : ~ (((X1 @ X2)) = $true) => ~ (((X1 @ (X0 @ X1))) = $true))),
  inference(fool_elimination,[],[f3])).
thf(f5,definition,(
  ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X0 > X1)] : ((X2 = X3) | (((X3 @ (diff @ X0 @ X1 @ X2 @ X3))) != ((X2 @ (diff @ X0 @ X1 @ X2 @ X3))))) )),
  introduced(theory,[functional_extensionality_axiom])).
thf(f6,plain,(
  ~ ? [X0 : (($i > $o) > $i)] : ! [X1 : ($i > $o)] : (? [X2 : $i] : (((X1 @ X2)) != $true) => (((X1 @ (X0 @ X1))) != $true))),
  inference(flattening,[],[f4])).
thf(f7,plain,(
  ! [X0 : (($i > $o) > $i)] : ? [X1 : ($i > $o)] : ((((X1 @ (X0 @ X1))) = $true) & ? [X2 : $i] : (((X1 @ X2)) != $true))),
  inference(ennf_transformation,[],[f6])).
thf(f8,plain,(
  ! [X0 : (($i > $o) > $i)] : ((((sK0 @ X0 @ (X0 @ (sK0 @ X0)))) = $true) & (((sK0 @ X0 @ (sK1 @ X0))) != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK1 @ X0)),skolemize(X2,$thf(sK1 @ X0))],[f7])).
thf(f9,plain,(
  ( ! [X0 : (($i > $o) > $i)] : ((((sK0 @ X0 @ (sK1 @ X0))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f10,plain,(
  ( ! [X0 : (($i > $o) > $i)] : ((((sK0 @ X0 @ (X0 @ (sK0 @ X0)))) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f13,plain,(
  ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X0 > X1),X4 : X0] : ((((X2 @ X4)) = ((X3 @ X4))) | (((X3 @ (diff @ X0 @ X1 @ X2 @ X3))) != ((X2 @ (diff @ X0 @ X1 @ X2 @ X3))))) )),
  inference(argument_congruence,[],[f5])).
thf(f28,plain,(
  ( ! [X0 : ($i > $o),X1 : (($i > $o) > $i)] : ((((X0 @ (sK1 @ X1))) != $true) | (((sK0 @ X1 @ (diff @ $i @ $o @ X0 @ (sK0 @ X1)))) != ((X0 @ (diff @ $i @ $o @ X0 @ (sK0 @ X1)))))) )),
  inference(superposition,[],[f9,f13])).
thf(f40,plain,(
  ( ! [X0 : ($i > $o),X1 : (($i > $o) > $i)] : ((((X0 @ (sK1 @ X1))) != $true) | ($false = ((X0 @ (diff @ $i @ $o @ X0 @ (sK0 @ X1))))) | (((sK0 @ X1 @ (diff @ $i @ $o @ X0 @ (sK0 @ X1)))) = $false)) )),
  inference(xor_proxy_clausification,[],[f28])).
thf(f123,plain,(
  ( ! [X1 : (($i > $o) > $i)] : ((((sK0 @ X1 @ (diff @ $i @ $o @ (^[Y0 : $i]: ($true)) @ (sK0 @ X1)))) = $false) | ((((^[Y0 : $i]: ($true)) @ (sK1 @ X1))) != $true) | ($false = (((^[Y0 : $i]: ($true)) @ (diff @ $i @ $o @ (^[Y0 : $i]: ($true)) @ (sK0 @ X1)))))) )),
  inference(imitation,[],[f40])).
thf(f134,plain,(
  ( ! [X1 : (($i > $o) > $i)] : (($true != $true) | ($false = $true) | (((sK0 @ X1 @ (diff @ $i @ $o @ (^[Y0 : $i]: ($true)) @ (sK0 @ X1)))) = $false)) )),
  inference(beta-eta_normalization,[],[f123])).
thf(f135,plain,(
  ( ! [X1 : (($i > $o) > $i)] : ((((sK0 @ X1 @ (diff @ $i @ $o @ (^[Y0 : $i]: ($true)) @ (sK0 @ X1)))) = $false)) )),
  inference(trivial_inequality_removal,[],[f134])).
thf(f142,plain,(
  ($false = $true)),
  inference(superposition,[],[f135,f10])).
thf(f152,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f142])).
% SZS output end Proof for theBenchmark