%----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_0, type, t: a).
thf(func_def_1, type, cA: ((a > $o) > $o)).
thf(func_def_5, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_6, type, vOR: ($o > $o > $o)).
thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_9, type, sP0: ((a > $o) > $o)).
thf(func_def_10, type, sP1: $o).
thf(func_def_11, type, sK2: (a > $o)).
thf(func_def_12, type, sK3: ((a > $o) > a > $o)).
thf(func_def_13, type, sK4: ((a > $o) > a)).
thf(func_def_14, type, sK5: ((a > $o) > (a > $o) > $o)).
thf(func_def_15, type, sK6: (a > $o)).
thf(func_def_16, type, vNOT: ($o > $o)).
thf(f1,conjecture,(
  ! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => ? [X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) & ! [X3 : (a > $o)] : (((cA @ X3) & ! [X2 : a] : ((X1 @ X2) => (X3 @ X2))) => ((cA @ X3) & (X3 @ t))) & ! [X4 : ((a > $o) > $o)] : ((! [X2 : (a > $o)] : ((X4 @ X2) => ! [X5 : a] : ((X1 @ X5) => (X4 @ (^[X6 : a] : ((X2 @ X6) | (X5 = X6)))))) & (X4 @ (^[X3 : a] : ($false)))) => (X4 @ X1)))) & ! [X0 : (a > $o)] : (((cA @ X0) & (X0 @ t)) => (cA @ X0))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMLEMMA5_pme)).
thf(f2,negated_conjecture,(
  ~(! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => ? [X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) & ! [X3 : (a > $o)] : (((cA @ X3) & ! [X2 : a] : ((X1 @ X2) => (X3 @ X2))) => ((cA @ X3) & (X3 @ t))) & ! [X4 : ((a > $o) > $o)] : ((! [X2 : (a > $o)] : ((X4 @ X2) => ! [X5 : a] : ((X1 @ X5) => (X4 @ (^[X6 : a] : ((X2 @ X6) | (X5 = X6)))))) & (X4 @ (^[X3 : a] : ($false)))) => (X4 @ X1)))) & ! [X0 : (a > $o)] : (((cA @ X0) & (X0 @ t)) => (cA @ X0)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => ? [X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) & ! [X3 : (a > $o)] : (((cA @ X3) & ! [X4 : a] : ((X1 @ X4) => (X3 @ X4))) => ((cA @ X3) & (X3 @ t))) & ! [X5 : ((a > $o) > $o)] : ((! [X6 : (a > $o)] : ((X5 @ X6) => ! [X7 : a] : ((X1 @ X7) => (X5 @ (^[X8 : a] : ((X6 @ X8) | (X7 = X8)))))) & (X5 @ (^[X9 : a] : ($false)))) => (X5 @ X1)))) & ! [X10 : (a > $o)] : (((cA @ X10) & (X10 @ t)) => (cA @ X10)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~(! [X0 : (a > $o)] : (((((cA @ X0)) = $true) & (((X0 @ t)) = $true)) => ? [X1 : (a > $o)] : (! [X5 : ((a > $o) > $o)] : ((($true = ((X5 @ (^[Y0 : a]: ($false))))) & ! [X6 : (a > $o)] : (($true = ((X5 @ X6))) => ! [X7 : a] : (($true = ((X1 @ X7))) => ($true = ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0))))))))) => (((X5 @ X1)) = $true)) & ! [X3 : (a > $o)] : (((((cA @ X3)) = $true) & ! [X4 : a] : (($true = ((X1 @ X4))) => (((X3 @ X4)) = $true))) => ((((cA @ X3)) = $true) & (((X3 @ t)) = $true))) & ! [X2 : a] : ((((X1 @ X2)) = $true) => (((X0 @ X2)) = $true)))) & ! [X10 : (a > $o)] : ((($true = ((cA @ X10))) & ($true = ((X10 @ t)))) => ($true = ((cA @ X10)))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ~(! [X8 : (a > $o)] : ((($true = ((cA @ X8))) & (((X8 @ t)) = $true)) => ($true = ((cA @ X8)))) & ! [X0 : (a > $o)] : (((((cA @ X0)) = $true) & (((X0 @ t)) = $true)) => ? [X1 : (a > $o)] : (! [X5 : ((a > $o) > $o)] : ((($true = ((X5 @ (^[Y0 : a]: ($false))))) & ! [X6 : (a > $o)] : (($true = ((X5 @ X6))) => ! [X7 : a] : (($true = ((X1 @ X7))) => ($true = ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0))))))))) => (((X5 @ X1)) = $true)) & ! [X3 : (a > $o)] : (((((cA @ X3)) = $true) & ! [X4 : a] : (($true = ((X1 @ X4))) => (((X3 @ X4)) = $true))) => ((((cA @ X3)) = $true) & (((X3 @ t)) = $true))) & ! [X2 : a] : ((((X1 @ X2)) = $true) => (((X0 @ X2)) = $true)))))),
  inference(rectify,[],[f4])).
thf(f6,plain,(
  ? [X8 : (a > $o)] : (($true != ((cA @ X8))) & (($true = ((cA @ X8))) & (((X8 @ t)) = $true))) | ? [X0 : (a > $o)] : (! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & (($true = ((X5 @ (^[Y0 : a]: ($false))))) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true != ((X1 @ X7))) | ($true = ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0))))))) | ($true != ((X5 @ X6)))))) | ? [X3 : (a > $o)] : (((((cA @ X3)) != $true) | (((X3 @ t)) != $true)) & ((((cA @ X3)) = $true) & ! [X4 : a] : ((((X3 @ X4)) = $true) | ($true != ((X1 @ X4)))))) | ? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true))) & ((((cA @ X0)) = $true) & (((X0 @ t)) = $true)))),
  inference(ennf_transformation,[],[f5])).
thf(f7,plain,(
  ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X3 : (a > $o)] : (((((cA @ X3)) != $true) | (((X3 @ t)) != $true)) & (((cA @ X3)) = $true) & ! [X4 : a] : ((((X3 @ X4)) = $true) | ($true != ((X1 @ X4))))) | ? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true)) | ? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & ($true = ((X5 @ (^[Y0 : a]: ($false))))) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true != ((X1 @ X7))) | ($true = ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0))))))) | ($true != ((X5 @ X6)))))) & (((cA @ X0)) = $true)) | ? [X8 : (a > $o)] : (($true = ((cA @ X8))) & ($true != ((cA @ X8))) & (((X8 @ t)) = $true))),
  inference(flattening,[],[f6])).
thf(f8,definition,(
  ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & ($true = ((X5 @ (^[Y0 : a]: ($false))))) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true != ((X1 @ X7))) | ($true = ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0))))))) | ($true != ((X5 @ X6))))) | ~ ($true = ((sP0 @ X1))))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f9,definition,(
  ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X3 : (a > $o)] : (((((cA @ X3)) != $true) | (((X3 @ t)) != $true)) & (((cA @ X3)) = $true) & ! [X4 : a] : ((((X3 @ X4)) = $true) | ($true != ((X1 @ X4))))) | ? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true)) | ($true = ((sP0 @ X1)))) & (((cA @ X0)) = $true)) | ~ ($true = sP1)),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f10,plain,(
  ($true = sP1) | ? [X8 : (a > $o)] : (($true = ((cA @ X8))) & ($true != ((cA @ X8))) & (((X8 @ t)) = $true))),
  inference(definition_folding,[],[f7,f9,f8])).
thf(f11,plain,(
  ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X3 : (a > $o)] : (((((cA @ X3)) != $true) | (((X3 @ t)) != $true)) & (((cA @ X3)) = $true) & ! [X4 : a] : ((((X3 @ X4)) = $true) | ($true != ((X1 @ X4))))) | ? [X2 : a] : ((((X1 @ X2)) = $true) & (((X0 @ X2)) != $true)) | ($true = ((sP0 @ X1)))) & (((cA @ X0)) = $true)) | ($true != sP1)),
  inference(nnf_transformation,[],[f9])).
thf(f12,plain,(
  ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X2 : (a > $o)] : ((($true != ((cA @ X2))) | (((X2 @ t)) != $true)) & ($true = ((cA @ X2))) & ! [X3 : a] : (($true = ((X2 @ X3))) | (((X1 @ X3)) != $true))) | ? [X4 : a] : (($true = ((X1 @ X4))) & ($true != ((X0 @ X4)))) | ($true = ((sP0 @ X1)))) & (((cA @ X0)) = $true)) | ($true != sP1)),
  inference(rectify,[],[f11])).
thf(f13,plain,(
  (($true = ((sK2 @ t))) & ! [X1 : (a > $o)] : (((($true != ((cA @ (sK3 @ X1)))) | ($true != ((sK3 @ X1 @ t)))) & ($true = ((cA @ (sK3 @ X1)))) & ! [X3 : a] : (($true = ((sK3 @ X1 @ X3))) | (((X1 @ X3)) != $true))) | (($true = ((X1 @ (sK4 @ X1)))) & ($true != ((sK2 @ (sK4 @ X1))))) | ($true = ((sP0 @ X1)))) & ($true = ((cA @ sK2)))) | ($true != sP1)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK2,vAPP]),skolemize(X0,$thf(sK2)),skolemize(X4,$thf(sK4 @ X1)),skolemize(X4,$thf(sK4 @ X1))],[f12])).
thf(f14,plain,(
  ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & ($true = ((X5 @ (^[Y0 : a]: ($false))))) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true != ((X1 @ X7))) | ($true = ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0))))))) | ($true != ((X5 @ X6))))) | ($true != ((sP0 @ X1))))),
  inference(nnf_transformation,[],[f8])).
thf(f15,plain,(
  ! [X0 : (a > $o)] : (? [X1 : ((a > $o) > $o)] : (($true != ((X1 @ X0))) & ($true = ((X1 @ (^[Y0 : a]: ($false))))) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true != ((X0 @ X3))) | ($true = ((X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))))) | ($true != ((X1 @ X2))))) | ($true != ((sP0 @ X0))))),
  inference(rectify,[],[f14])).
thf(f16,plain,(
  ! [X0 : (a > $o)] : ((($true != ((sK5 @ X0 @ X0))) & ($true = ((sK5 @ X0 @ (^[Y0 : a]: ($false))))) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true != ((X0 @ X3))) | ($true = ((sK5 @ X0 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))))) | ($true != ((sK5 @ X0 @ X2))))) | ($true != ((sP0 @ X0))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,$thf(sK4 @ X1))],[f15])).
thf(f17,plain,(
  ($true = sP1) | ? [X0 : (a > $o)] : ((((cA @ X0)) = $true) & (((cA @ X0)) != $true) & (((X0 @ t)) = $true))),
  inference(rectify,[],[f10])).
thf(f18,plain,(
  ($true = sP1) | (($true = ((cA @ sK6))) & ($true != ((cA @ sK6))) & ($true = ((sK6 @ t))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,$thf(sK6))],[f17])).
thf(f20,plain,(
  ( ! [X3 : a,X1 : (a > $o)] : (($true != sP1) | ($true = ((sK3 @ X1 @ X3))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | (((X1 @ X3)) != $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f21,plain,(
  ( ! [X3 : a,X1 : (a > $o)] : ((((X1 @ X3)) != $true) | ($true = ((X1 @ (sK4 @ X1)))) | ($true != sP1) | ($true = ((sK3 @ X1 @ X3))) | ($true = ((sP0 @ X1)))) )),
  inference(cnf_transformation,[],[f13])).
thf(f22,plain,(
  ( ! [X1 : (a > $o)] : (($true != sP1) | ($true = ((cA @ (sK3 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != ((sK2 @ (sK4 @ X1))))) )),
  inference(cnf_transformation,[],[f13])).
thf(f23,plain,(
  ( ! [X1 : (a > $o)] : (($true = ((X1 @ (sK4 @ X1)))) | ($true != sP1) | ($true = ((cA @ (sK3 @ X1)))) | ($true = ((sP0 @ X1)))) )),
  inference(cnf_transformation,[],[f13])).
thf(f24,plain,(
  ( ! [X1 : (a > $o)] : (($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1) | ($true != ((cA @ (sK3 @ X1)))) | ($true != ((sK3 @ X1 @ t)))) )),
  inference(cnf_transformation,[],[f13])).
thf(f25,plain,(
  ( ! [X1 : (a > $o)] : (($true != ((cA @ (sK3 @ X1)))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != ((sK3 @ X1 @ t))) | ($true != sP1)) )),
  inference(cnf_transformation,[],[f13])).
thf(f26,plain,(
  ($true != sP1) | ($true = ((sK2 @ t)))),
  inference(cnf_transformation,[],[f13])).
thf(f27,plain,(
  ( ! [X2 : (a > $o),X3 : a,X0 : (a > $o)] : (($true = ((sK5 @ X0 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | ($true != ((sP0 @ X0))) | ($true != ((sK5 @ X0 @ X2))) | ($true != ((X0 @ X3)))) )),
  inference(cnf_transformation,[],[f16])).
thf(f28,plain,(
  ( ! [X0 : (a > $o)] : (($true = ((sK5 @ X0 @ (^[Y0 : a]: ($false))))) | ($true != ((sP0 @ X0)))) )),
  inference(cnf_transformation,[],[f16])).
thf(f29,plain,(
  ( ! [X0 : (a > $o)] : (($true != ((sK5 @ X0 @ X0))) | ($true != ((sP0 @ X0)))) )),
  inference(cnf_transformation,[],[f16])).
thf(f31,plain,(
  ($true = sP1) | ($true != ((cA @ sK6)))),
  inference(cnf_transformation,[],[f18])).
thf(f32,plain,(
  ($true = ((cA @ sK6))) | ($true = sP1)),
  inference(cnf_transformation,[],[f18])).
thf(f35,definition,(
  spl7_1 <=> ($true = sP1)),
  introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
thf(f39,definition,(
  spl7_2 <=> ($true = ((sK2 @ t)))),
  introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
thf(f41,plain,(
  ($true = ((sK2 @ t))) | ~spl7_2),
  inference(avatar_component_clause,[],[f39])).
thf(f42,plain,(
  ~spl7_1 | spl7_2),
  inference(avatar_split_clause,[],[f26,f39,f35])).
thf(f44,definition,(
  spl7_3 <=> ! [X1 : (a > $o)] : (($true != ((sK2 @ (sK4 @ X1)))) | ($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1)))) | ($true = ((sP0 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
thf(f45,plain,(
  ( ! [X1 : (a > $o)] : (($true != ((cA @ (sK3 @ X1)))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != ((sK3 @ X1 @ t)))) ) | ~spl7_3),
  inference(avatar_component_clause,[],[f44])).
thf(f46,plain,(
  spl7_3 | ~spl7_1),
  inference(avatar_split_clause,[],[f24,f35,f44])).
thf(f48,definition,(
  spl7_4 <=> ($true = ((cA @ sK6)))),
  introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
thf(f51,plain,(
  spl7_1 | spl7_4),
  inference(avatar_split_clause,[],[f32,f48,f35])).
thf(f58,definition,(
  spl7_6 <=> ! [X1 : (a > $o)] : (($true != ((cA @ (sK3 @ X1)))) | ($true != ((sK3 @ X1 @ t))) | ($true = ((sP0 @ X1))) | ($true = ((X1 @ (sK4 @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
thf(f59,plain,(
  ( ! [X1 : (a > $o)] : (($true = ((X1 @ (sK4 @ X1)))) | ($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_6),
  inference(avatar_component_clause,[],[f58])).
thf(f60,plain,(
  ~spl7_1 | spl7_6),
  inference(avatar_split_clause,[],[f25,f58,f35])).
thf(f62,definition,(
  spl7_7 <=> ! [X1 : (a > $o),X3 : a] : (($true = ((sK3 @ X1 @ X3))) | (((X1 @ X3)) != $true) | ($true = ((sP0 @ X1))) | ($true != ((sK2 @ (sK4 @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
thf(f63,plain,(
  ( ! [X3 : a,X1 : (a > $o)] : (($true = ((sK3 @ X1 @ X3))) | ($true != ((sK2 @ (sK4 @ X1)))) | (((X1 @ X3)) != $true) | ($true = ((sP0 @ X1)))) ) | ~spl7_7),
  inference(avatar_component_clause,[],[f62])).
thf(f64,plain,(
  spl7_7 | ~spl7_1),
  inference(avatar_split_clause,[],[f20,f35,f62])).
thf(f66,definition,(
  spl7_8 <=> ! [X1 : (a > $o)] : (($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true = ((cA @ (sK3 @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
thf(f67,plain,(
  ( ! [X1 : (a > $o)] : (($true = ((cA @ (sK3 @ X1)))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_8),
  inference(avatar_component_clause,[],[f66])).
thf(f68,plain,(
  ~spl7_1 | spl7_8),
  inference(avatar_split_clause,[],[f23,f66,f35])).
thf(f74,plain,(
  ~spl7_4 | spl7_1),
  inference(avatar_split_clause,[],[f31,f35,f48])).
thf(f76,definition,(
  spl7_10 <=> ! [X1 : (a > $o)] : (($true = ((cA @ (sK3 @ X1)))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition])).
thf(f77,plain,(
  ( ! [X1 : (a > $o)] : (($true = ((cA @ (sK3 @ X1)))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_10),
  inference(avatar_component_clause,[],[f76])).
thf(f78,plain,(
  ~spl7_1 | spl7_10),
  inference(avatar_split_clause,[],[f22,f76,f35])).
thf(f80,definition,(
  spl7_11 <=> ! [X1 : (a > $o),X3 : a] : ((((X1 @ X3)) != $true) | ($true = ((sP0 @ X1))) | ($true = ((sK3 @ X1 @ X3))) | ($true = ((X1 @ (sK4 @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition])).
thf(f81,plain,(
  ( ! [X3 : a,X1 : (a > $o)] : (($true = ((sK3 @ X1 @ X3))) | (((X1 @ X3)) != $true) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_11),
  inference(avatar_component_clause,[],[f80])).
thf(f82,plain,(
  ~spl7_1 | spl7_11),
  inference(avatar_split_clause,[],[f21,f80,f35])).
thf(f84,plain,(
  ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true = ((sP0 @ X1))) | ($true != ((sK2 @ (sK4 @ X1))))) ) | (~spl7_3 | ~spl7_10)),
  inference(forward_subsumption_resolution,[],[f45,f77])).
thf(f93,plain,(
  ( ! [X0 : (a > $o)] : (($true != $true) | (((X0 @ t)) != $true) | (((sK2 @ (sK4 @ X0))) != $true) | (((sK2 @ (sK4 @ X0))) != $true) | ($true = ((sP0 @ X0))) | ($true = ((sP0 @ X0)))) ) | (~spl7_3 | ~spl7_7 | ~spl7_10)),
  inference(superposition,[],[f84,f63])).
thf(f94,plain,(
  ( ! [X0 : (a > $o)] : ((((sK2 @ (sK4 @ X0))) != $true) | (((X0 @ t)) != $true) | ($true = ((sP0 @ X0))) | ($true != $true)) ) | (~spl7_3 | ~spl7_7 | ~spl7_10)),
  inference(duplicate_literal_removal,[],[f93])).
thf(f95,plain,(
  ( ! [X0 : (a > $o)] : ((((sK2 @ (sK4 @ X0))) != $true) | (((X0 @ t)) != $true) | ($true = ((sP0 @ X0)))) ) | (~spl7_3 | ~spl7_7 | ~spl7_10)),
  inference(trivial_inequality_removal,[],[f94])).
thf(f96,plain,(
  ( ! [X0 : a] : ((((sK3 @ (= @ X0) @ X0)) = $true) | (((sK4 @ (= @ X0))) = X0) | ($true = ((sP0 @ (= @ X0))))) ) | ~spl7_11),
  inference(leibniz_equality_elimination,[],[f81])).
thf(f108,definition,(
  spl7_14 <=> (t = ((sK4 @ (= @ t))))),
  introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition])).
thf(f110,plain,(
  (t = ((sK4 @ (= @ t)))) | ~spl7_14),
  inference(avatar_component_clause,[],[f108])).
thf(f112,definition,(
  spl7_15 <=> ($true = ((sP0 @ (= @ t))))),
  introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition])).
thf(f114,plain,(
  ($true = ((sP0 @ (= @ t)))) | ~spl7_15),
  inference(avatar_component_clause,[],[f112])).
thf(f116,plain,(
  ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | (~spl7_6 | ~spl7_8)),
  inference(forward_subsumption_resolution,[],[f59,f67])).
thf(f119,plain,(
  ($true = ((t = (sK4 @ (= @ t))))) | ($true != $true) | ($true = ((sP0 @ (= @ t)))) | (t = ((sK4 @ (= @ t)))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_6 | ~spl7_8 | ~spl7_11)),
  inference(superposition,[],[f116,f96])).
thf(f122,plain,(
  ($true = ((sP0 @ (= @ t)))) | (t = ((sK4 @ (= @ t)))) | ($true = ((sP0 @ (= @ t)))) | (t = ((sK4 @ (= @ t)))) | ($true != $true) | (~spl7_6 | ~spl7_8 | ~spl7_11)),
  inference(equality_proxy_clausification,[],[f119])).
thf(f123,plain,(
  ($true = ((sP0 @ (= @ t)))) | ($true != $true) | (t = ((sK4 @ (= @ t)))) | (~spl7_6 | ~spl7_8 | ~spl7_11)),
  inference(duplicate_literal_removal,[],[f122])).
thf(f124,plain,(
  (t = ((sK4 @ (= @ t)))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_6 | ~spl7_8 | ~spl7_11)),
  inference(trivial_inequality_removal,[],[f123])).
thf(f127,plain,(
  spl7_15 | spl7_14 | ~spl7_6 | ~spl7_8 | ~spl7_11),
  inference(avatar_split_clause,[],[f124,f80,f66,f58,f108,f112])).
thf(f129,plain,(
  ($true = ((sP0 @ (= @ t)))) | ($true != ((sK2 @ t))) | ($true != ((t = t))) | (~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14)),
  inference(superposition,[],[f95,f110])).
thf(f130,plain,(
  ($true != ((sK2 @ t))) | (t != t) | ($true = ((sP0 @ (= @ t)))) | (~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14)),
  inference(equality_proxy_clausification,[],[f129])).
thf(f131,plain,(
  ($true != ((sK2 @ t))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14)),
  inference(trivial_inequality_removal,[],[f130])).
thf(f132,plain,(
  ($true = ((sP0 @ (= @ t)))) | (~spl7_2 | ~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14)),
  inference(forward_subsumption_resolution,[],[f131,f41])).
thf(f133,plain,(
  spl7_15 | ~spl7_2 | ~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14),
  inference(avatar_split_clause,[],[f132,f108,f76,f62,f44,f39,f112])).
thf(f135,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) | ($true != $true) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true != (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)))) )),
  inference(superposition,[],[f29,f27])).
thf(f136,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($true != $true) | ($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) )),
  inference(duplicate_literal_removal,[],[f135])).
thf(f137,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true != (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)))) )),
  inference(trivial_inequality_removal,[],[f136])).
thf(f138,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true != (((X0 = X0) | (X1 @ X0))))) )),
  inference(beta-eta_normalization,[],[f137])).
thf(f140,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : ((((X0 = X0)) = $false) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)))) )),
  inference(or_proxy_clausification,[],[f138])).
thf(f141,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) | (X0 != X0) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) )),
  inference(equality_proxy_clausification,[],[f140])).
thf(f142,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != ((sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) )),
  inference(trivial_inequality_removal,[],[f141])).
thf(f164,plain,(
  ( ! [X0 : a] : (($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | ($true != $true) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) )),
  inference(superposition,[],[f142,f28])).
thf(f166,plain,(
  ( ! [X0 : a] : (($true != $true) | ($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) )),
  inference(duplicate_literal_removal,[],[f164])).
thf(f167,plain,(
  ( ! [X0 : a] : (($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) )),
  inference(trivial_inequality_removal,[],[f166])).
thf(f168,plain,(
  ( ! [X0 : a] : (($true != ((sP0 @ (^[Y0 : a]: ((X0 = Y0) | $false)))))) )),
  inference(beta-eta_normalization,[],[f167])).
thf(f169,plain,(
  ( ! [X0 : a] : (($true != ((sP0 @ (^[Y0 : a]: (X0 = Y0)))))) )),
  inference(boolean_simplification,[],[f168])).
thf(f170,plain,(
  ( ! [X0 : a] : (($true != ((sP0 @ (= @ X0))))) )),
  inference(beta-eta_normalization,[],[f169])).
thf(f257,plain,(
  ($true != $true) | ~spl7_15),
  inference(superposition,[],[f170,f114])).
thf(f258,plain,(
  $false | ~spl7_15),
  inference(trivial_inequality_removal,[],[f257])).
thf(f259,plain,(
  ~spl7_15),
  inference(avatar_contradiction_clause,[],[f258])).
cnf(s1, plain, ~spl7_1 | spl7_2, inference(sat_conversion,[],[f42])).
cnf(s2, plain, ~spl7_1 | spl7_3, inference(sat_conversion,[],[f46])).
cnf(s3, plain, spl7_1 | spl7_4, inference(sat_conversion,[],[f51])).
cnf(s5, plain, ~spl7_1 | spl7_6, inference(sat_conversion,[],[f60])).
cnf(s6, plain, ~spl7_1 | spl7_7, inference(sat_conversion,[],[f64])).
cnf(s7, plain, ~spl7_1 | spl7_8, inference(sat_conversion,[],[f68])).
cnf(s9, plain, spl7_1 | ~spl7_4, inference(sat_conversion,[],[f74])).
cnf(s10, plain, ~spl7_1 | spl7_10, inference(sat_conversion,[],[f78])).
cnf(s11, plain, ~spl7_1 | spl7_11, inference(sat_conversion,[],[f82])).
cnf(s14, plain, ~spl7_6 | ~spl7_8 | ~spl7_11 | spl7_14 | spl7_15, inference(sat_conversion,[],[f127])).
cnf(s16, plain, ~spl7_2 | ~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14 | spl7_15, inference(sat_conversion,[],[f133])).
cnf(s20, plain, ~spl7_15, inference(sat_conversion,[],[f259])).
cnf(s21, plain, ~spl7_2 | ~spl7_3 | ~spl7_7 | ~spl7_10 | ~spl7_14, inference(rat,[],[s16,s20])).
cnf(s22, plain, ~spl7_6 | ~spl7_8 | ~spl7_11 | spl7_14, inference(rat,[],[s14,s20])).
cnf(s24, plain, spl7_1, inference(rat,[],[s3,s9])).
cnf(s25, plain, spl7_11, inference(rat,[],[s11,s24])).
cnf(s26, plain, spl7_10, inference(rat,[],[s10,s24])).
cnf(s28, plain, spl7_8, inference(rat,[],[s7,s24])).
cnf(s29, plain, spl7_7, inference(rat,[],[s6,s24])).
cnf(s30, plain, spl7_6, inference(rat,[],[s5,s24])).
cnf(s31, plain, spl7_3, inference(rat,[],[s2,s24])).
cnf(s32, plain, spl7_2, inference(rat,[],[s1,s24])).
cnf(s33, plain, spl7_14, inference(rat,[],[s22,s28,s25,s30])).
cnf(s34, plain, $false, inference(rat,[],[s21,s33,s26,s29,s31,s32])).
thf(f260,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s34])).
% SZS output end Proof for theBenchmark