%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, a: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, sK0: (a > a > $o)).
thf(func_def_4, type, sK1: ((a > $o) > a)).
thf(func_def_5, type, vNOT: ($o > $o)).
thf(func_def_6, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_11, type, sK2: ((a > $o) > a)).
thf(f1,conjecture,(
  ~ ? [X0 : (a > a > $o)] : ! [X1 : (a > $o)] : ? [X2 : a] : ! [X3 : ((a > $o) > $o)] : ((X3 @ (X0 @ X2)) => (X3 @ X1))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCT29)).
thf(f2,negated_conjecture,(
  ~ ~ ? [X0 : (a > a > $o)] : ! [X1 : (a > $o)] : ? [X2 : a] : ! [X3 : ((a > $o) > $o)] : ((X3 @ (X0 @ X2)) => (X3 @ X1))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ~ ? [X0 : (a > a > $o)] : ! [X1 : (a > $o)] : ? [X2 : a] : ! [X3 : ((a > $o) > $o)] : ((X3 @ (X0 @ X2)) => (X3 @ X1))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ~ ? [X0 : (a > a > $o)] : ! [X1 : (a > $o)] : ? [X2 : a] : ! [X3 : ((a > $o) > $o)] : ((((X3 @ (X0 @ X2))) = $true) => (((X3 @ X1)) = $true))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X0 : (a > a > $o)] : ! [X1 : (a > $o)] : ? [X2 : a] : ! [X3 : ((a > $o) > $o)] : ((((X3 @ (X0 @ X2))) = $true) => (((X3 @ X1)) = $true))),
  inference(flattening,[],[f4])).
thf(f6,plain,(
  ? [X0 : (a > a > $o)] : ! [X1 : (a > $o)] : ? [X2 : a] : ! [X3 : ((a > $o) > $o)] : ((((X3 @ X1)) = $true) | (((X3 @ (X0 @ X2))) != $true))),
  inference(ennf_transformation,[],[f5])).
thf(f7,plain,(
  ! [X1 : (a > $o)] : ! [X3 : ((a > $o) > $o)] : ((((X3 @ X1)) = $true) | (((X3 @ (sK0 @ (sK1 @ X1)))) != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X2,$thf(sK1 @ X1))],[f6])).
thf(f8,plain,(
  ( ! [X3 : ((a > $o) > $o),X1 : (a > $o)] : ((((X3 @ (sK0 @ (sK1 @ X1)))) != $true) | (((X3 @ X1)) = $true)) )),
  inference(cnf_transformation,[],[f7])).
thf(f11,plain,(
  ( ! [X0 : (a > $o)] : ((((sK0 @ (sK1 @ X0))) = X0)) )),
  inference(leibniz_equality_elimination,[],[f8])).
thf(f22,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((sK0 @ (sK1 @ X0) @ X1)) = ((X0 @ X1)))) )),
  inference(argument_congruence,[],[f11])).
thf(f26,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != ((~ (sK0 @ (sK1 @ X0) @ X1))))) )),
  inference(bool_equality_to_disequality,[],[f22])).
thf(f44,plain,(
  ( ! [X0 : (a > $o)] : (((^[Y0 : a]: (~ (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0)))) != X0)) )),
  inference(equality_resolution,[],[f26])).
thf(f47,plain,(
  ( ! [X0 : (a > $o)] : (((^[Y0 : a]: (~ (sK0 @ Y0 @ Y0))) != X0)) )),
  inference(beta-eta_normalization,[],[f44])).
thf(f78,plain,(
  $false),
  inference(equality_resolution,[],[f47])).
% SZS output end Proof for theBenchmark