%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_1, type, succ: ($i > $i)).
thf(func_def_6, type, sK1: (($i > $o) > $i)).
thf(func_def_7, type, vNOT: ($o > $o)).
thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,axiom,(
  ! [X1 : $i,X0 : $i] : ((((succ @ X0)) = ((succ @ X1))) => (X0 = X1))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective)).
thf(f2,axiom,(
  ! [X0 : ($i > $o)] : ((! [X2 : $i] : ((X0 @ X2) => (X0 @ (succ @ X2))) & (X0 @ one)) => ! [X1 : $i] : (X0 @ X1))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction)).
thf(f3,axiom,(
  ! [X0 : $i] : (((succ @ X0)) != one)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_is_first)).
thf(f4,conjecture,(
  ! [X0 : $i] : (((succ @ X0)) != X0)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz2)).
thf(f5,negated_conjecture,(
  ~ ! [X0 : $i] : (((succ @ X0)) != X0)),
  inference(negated_conjecture,[status(cth)],[f4])).
thf(f6,plain,(
  ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
  inference(rectify,[],[f2])).
thf(f7,plain,(
  ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (succ @ X1))) = $true)) & (((X0 @ one)) = $true)) => ! [X2 : $i] : (((X0 @ X2)) = $true))),
  inference(fool_elimination,[],[f6])).
thf(f8,plain,(
  ! [X1 : $i,X0 : $i] : ((((succ @ X0)) = ((succ @ X1))) => (X0 = X1))),
  inference(rectify,[],[f1])).
thf(f9,plain,(
  ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (succ @ X1))) != $true)) | (((X0 @ one)) != $true)))),
  inference(ennf_transformation,[],[f7])).
thf(f10,plain,(
  ! [X0 : ($i > $o)] : ((((X0 @ one)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (succ @ X1))) != $true)) | ! [X2 : $i] : (((X0 @ X2)) = $true))),
  inference(flattening,[],[f9])).
thf(f11,plain,(
  ! [X0 : $i,X1 : $i] : ((((succ @ X0)) != ((succ @ X1))) | (X0 = X1))),
  inference(ennf_transformation,[],[f8])).
thf(f12,plain,(
  ? [X0 : $i] : (((succ @ X0)) = X0)),
  inference(ennf_transformation,[],[f5])).
thf(f13,plain,(
  (sK0 = ((succ @ sK0)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,$thf(sK0))],[f12])).
thf(f14,plain,(
  ! [X0 : ($i > $o)] : ((((X0 @ one)) != $true) | ((((X0 @ (sK1 @ X0))) = $true) & (((X0 @ (succ @ (sK1 @ X0)))) != $true)) | ! [X2 : $i] : (((X0 @ X2)) = $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK1 @ X0))],[f10])).
thf(f15,plain,(
  (sK0 = ((succ @ sK0)))),
  inference(cnf_transformation,[],[f13])).
thf(f16,plain,(
  ( ! [X0 : $i] : ((((succ @ X0)) != one)) )),
  inference(cnf_transformation,[],[f3])).
thf(f17,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((succ @ X0)) != ((succ @ X1))) | (X0 = X1)) )),
  inference(cnf_transformation,[],[f11])).
thf(f18,plain,(
  ( ! [X2 : $i,X0 : ($i > $o)] : ((((X0 @ (succ @ (sK1 @ X0)))) != $true) | (((X0 @ X2)) = $true) | (((X0 @ one)) != $true)) )),
  inference(cnf_transformation,[],[f14])).
thf(f19,plain,(
  ( ! [X2 : $i,X0 : ($i > $o)] : ((((X0 @ one)) != $true) | (((X0 @ X2)) = $true) | (((X0 @ (sK1 @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f14])).
thf(f22,plain,(
  ( ! [X0 : $i] : ((((succ @ X0)) != sK0) | (sK0 = X0)) )),
  inference(constrained_superposition,[],[f17,f15])).
thf(f25,plain,(
  (one != sK0)),
  inference(constrained_superposition,[],[f16,f15])).
thf(f27,plain,(
  ( ! [X0 : $i] : (((((^[Y0 : $i]: (~ (Y0 = X0))) @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = $true) | (one = X0)) )),
  inference(leibniz_equality_elimination,[],[f19])).
thf(f36,plain,(
  ( ! [X0 : $i] : ((((~ ((sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))) = X0))) = $true) | (one = X0)) )),
  inference(beta-eta_normalization,[],[f27])).
thf(f37,plain,(
  ( ! [X0 : $i] : (((((sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))) = X0)) = $false) | (one = X0)) )),
  inference(not_proxy_clausification,[],[f36])).
thf(f38,plain,(
  ( ! [X0 : $i] : ((((sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))))) != X0) | (one = X0)) )),
  inference(equality_proxy_clausification,[],[f37])).
thf(f54,plain,(
  ( ! [X0 : $i] : (($true != (((^[Y0 : $i]: (~ (Y0 = X0))) @ one))) | (((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
  inference(leibniz_equality_elimination,[],[f18])).
thf(f62,plain,(
  ( ! [X0 : $i] : ((((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (((~ (one = X0))) != $true)) )),
  inference(beta-eta_normalization,[],[f54])).
thf(f63,plain,(
  ( ! [X0 : $i] : ((((one = X0)) = $true) | (((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
  inference(not_proxy_clausification,[],[f62])).
thf(f64,plain,(
  ( ! [X0 : $i] : ((((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (one = X0)) )),
  inference(equality_proxy_clausification,[],[f63])).
thf(f79,plain,(
  ( ! [X0 : $i] : ((sK0 != X0) | (((sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))))) = sK0) | (one = X0)) )),
  inference(constrained_superposition,[],[f22,f64])).
thf(f91,plain,(
  (one = sK0) | (sK0 = ((sK1 @ (^[Y0 : $i]: (~ (Y0 = sK0)))))) | (sK0 != sK0)),
  inference(imitation,[],[f79])).
thf(f93,plain,(
  (sK0 = ((sK1 @ (^[Y0 : $i]: (~ (Y0 = sK0)))))) | (one = sK0)),
  inference(trivial_inequality_removal,[],[f91])).
thf(f94,plain,(
  (one = sK0)),
  inference(forward_subsumption_resolution,[],[f93,f38])).
thf(f96,plain,(
  $false),
  inference(forward_subsumption_resolution,[],[f94,f25])).
% SZS output end Proof for theBenchmark