%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
thf(func_def_7, type, sK4: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
thf(func_def_8, type, sK5: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
thf(func_def_9, type, sK6: ((($i > $o) > ($i > $o) > $o) > $i)).
thf(func_def_10, type, vNOT: ($o > $o)).
thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)) & ! [X4 : ($i > $o)] : (X0 @ X4 @ X4))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM122_pme)).
thf(f2,negated_conjecture,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)) & ! [X4 : ($i > $o)] : (X0 @ X4 @ X4))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X6 @ X4) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X4)) & ! [X7 : ($i > $o)] : (X0 @ X7 @ X7))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X6 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X6 @ X4)) = $true) & (((X0 @ X5 @ X6)) = $true)) => ($true = ((X0 @ X5 @ X4)))) & ! [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) = $true) & ! [X2 : ($i > $o),X1 : ($i > $o)] : ((((X0 @ X1 @ X2)) = $true) => ! [X3 : $i] : ((((X1 @ X3)) = $true) => (((X2 @ X3)) = $true))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((X0 @ X5 @ X4))) & ((((X0 @ X6 @ X4)) = $true) & (((X0 @ X5 @ X6)) = $true))) | ? [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) != $true) | ? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : ((((X1 @ X3)) = $true) & (((X2 @ X3)) != $true)) & (((X0 @ X1 @ X2)) = $true)))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X5 @ X6)) = $true) & ($true != ((X0 @ X5 @ X4))) & (((X0 @ X6 @ X4)) = $true)) | ? [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) != $true) | ? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : ((((X1 @ X3)) = $true) & (((X2 @ X3)) != $true)) & (((X0 @ X1 @ X2)) = $true)))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (($true = ((X0 @ X2 @ X3))) & (((X0 @ X2 @ X1)) != $true) & (((X0 @ X3 @ X1)) = $true)) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true) | ? [X5 : ($i > $o),X6 : ($i > $o)] : (? [X7 : $i] : ((((X5 @ X7)) = $true) & (((X6 @ X7)) != $true)) & (((X0 @ X5 @ X6)) = $true)))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) & (((X0 @ (sK1 @ X0) @ (sK0 @ X0))) != $true) & ($true = ((X0 @ (sK2 @ X0) @ (sK0 @ X0))))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ((($true = ((sK4 @ X0 @ (sK6 @ X0)))) & ($true != ((sK5 @ X0 @ (sK6 @ X0))))) & (((X0 @ (sK4 @ X0) @ (sK5 @ X0))) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X7,$thf(sK6 @ X0)),skolemize(X7,$thf(sK6 @ X0)),skolemize(X7,$thf(sK6 @ X0)),skolemize(X7,$thf(sK6 @ X0)),skolemize(X7,$thf(sK6 @ X0)),skolemize(X7,$thf(sK6 @ X0)),skolemize(X7,$thf(sK6 @ X0))],[f7])).
thf(f9,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK2 @ X0) @ (sK0 @ X0)))) | (((X0 @ (sK4 @ X0) @ (sK5 @ X0))) = $true) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f10,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK2 @ X0) @ (sK0 @ X0)))) | ($true != ((sK5 @ X0 @ (sK6 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK2 @ X0) @ (sK0 @ X0)))) | ($true = ((sK4 @ X0 @ (sK6 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f12,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK5 @ X0))) = $true) | (((X0 @ (sK1 @ X0) @ (sK0 @ X0))) != $true) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f13,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true != ((sK5 @ X0 @ (sK6 @ X0)))) | (((X0 @ (sK1 @ X0) @ (sK0 @ X0))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f14,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((sK4 @ X0 @ (sK6 @ X0)))) | (((X0 @ (sK1 @ X0) @ (sK0 @ X0))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f15,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | (((X0 @ (sK4 @ X0) @ (sK5 @ X0))) = $true) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f16,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true != ((sK5 @ X0 @ (sK6 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f17,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | ($true = ((sK4 @ X0 @ (sK6 @ X0)))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f19,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f13])).
thf(f34,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true != ((sK5 @ = @ (sK6 @ =)))) | ((((sK1 @ =) = (sK0 @ =))) != $true)),
  inference(beta-eta_normalization,[],[f19])).
thf(f35,plain,(
  ($true != ((sK5 @ = @ (sK6 @ =)))) | (((sK3 @ =)) != ((sK3 @ =))) | ((((sK1 @ =) = (sK0 @ =))) != $true)),
  inference(equality_proxy_clausification,[],[f34])).
thf(f36,plain,(
  (((sK0 @ =)) != ((sK1 @ =))) | ($true != ((sK5 @ = @ (sK6 @ =)))) | (((sK3 @ =)) != ((sK3 @ =)))),
  inference(equality_proxy_clausification,[],[f35])).
thf(f37,plain,(
  (((sK0 @ =)) != ((sK1 @ =))) | ($true != ((sK5 @ = @ (sK6 @ =))))),
  inference(trivial_inequality_removal,[],[f36])).
thf(f51,definition,(
  spl7_2 <=> (((sK0 @ =)) = ((sK1 @ =)))),
  introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
thf(f55,definition,(
  spl7_3 <=> ($true = ((sK5 @ = @ (sK6 @ =))))),
  introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
thf(f58,plain,(
  ~spl7_2 | ~spl7_3),
  inference(avatar_split_clause,[],[f37,f55,f51])).
thf(f83,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f10])).
thf(f88,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true != ((sK5 @ = @ (sK6 @ =)))) | ((((sK2 @ =) = (sK0 @ =))) = $true)),
  inference(beta-eta_normalization,[],[f83])).
thf(f89,plain,(
  ((((sK2 @ =) = (sK0 @ =))) = $true) | ($true != ((sK5 @ = @ (sK6 @ =)))) | (((sK3 @ =)) != ((sK3 @ =)))),
  inference(equality_proxy_clausification,[],[f88])).
thf(f90,plain,(
  (((sK0 @ =)) = ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | ($true != ((sK5 @ = @ (sK6 @ =))))),
  inference(equality_proxy_clausification,[],[f89])).
thf(f91,plain,(
  ($true != ((sK5 @ = @ (sK6 @ =)))) | (((sK0 @ =)) = ((sK2 @ =)))),
  inference(trivial_inequality_removal,[],[f90])).
thf(f102,plain,(
  (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f11])).
thf(f109,plain,(
  (((sK4 @ = @ (sK6 @ =))) = $true) | ((((sK2 @ =) = (sK0 @ =))) = $true) | ($true != (((sK3 @ =) = (sK3 @ =))))),
  inference(beta-eta_normalization,[],[f102])).
thf(f110,plain,(
  (((sK0 @ =)) = ((sK2 @ =))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | (((sK4 @ = @ (sK6 @ =))) = $true)),
  inference(equality_proxy_clausification,[],[f109])).
thf(f111,plain,(
  (((sK0 @ =)) = ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | (((sK4 @ = @ (sK6 @ =))) = $true)),
  inference(equality_proxy_clausification,[],[f110])).
thf(f112,plain,(
  (((sK0 @ =)) = ((sK2 @ =))) | (((sK4 @ = @ (sK6 @ =))) = $true)),
  inference(trivial_inequality_removal,[],[f111])).
thf(f122,definition,(
  spl7_8 <=> (((sK4 @ = @ (sK6 @ =))) = $true)),
  introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
thf(f126,definition,(
  spl7_9 <=> (((sK0 @ =)) = ((sK2 @ =)))),
  introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition])).
thf(f129,plain,(
  spl7_8 | spl7_9),
  inference(avatar_split_clause,[],[f112,f126,f122])).
thf(f130,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true)),
  inference(primitive_instantiation,[],[f14])).
thf(f144,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | (((sK4 @ = @ (sK6 @ =))) = $true) | ((((sK1 @ =) = (sK0 @ =))) != $true)),
  inference(beta-eta_normalization,[],[f130])).
thf(f145,plain,(
  ((((sK1 @ =) = (sK0 @ =))) != $true) | (((sK4 @ = @ (sK6 @ =))) = $true) | (((sK3 @ =)) != ((sK3 @ =)))),
  inference(equality_proxy_clausification,[],[f144])).
thf(f146,plain,(
  (((sK4 @ = @ (sK6 @ =))) = $true) | (((sK0 @ =)) != ((sK1 @ =))) | (((sK3 @ =)) != ((sK3 @ =)))),
  inference(equality_proxy_clausification,[],[f145])).
thf(f147,plain,(
  (((sK0 @ =)) != ((sK1 @ =))) | (((sK4 @ = @ (sK6 @ =))) = $true)),
  inference(trivial_inequality_removal,[],[f146])).
thf(f161,plain,(
  (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f16])).
thf(f171,plain,(
  ($true != ((sK5 @ = @ (sK6 @ =)))) | ($true != (((sK3 @ =) = (sK3 @ =)))) | ((((sK1 @ =) = (sK2 @ =))) = $true)),
  inference(beta-eta_normalization,[],[f161])).
thf(f172,plain,(
  (((sK3 @ =)) != ((sK3 @ =))) | ((((sK1 @ =) = (sK2 @ =))) = $true) | ($true != ((sK5 @ = @ (sK6 @ =))))),
  inference(equality_proxy_clausification,[],[f171])).
thf(f173,plain,(
  (((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | ($true != ((sK5 @ = @ (sK6 @ =))))),
  inference(equality_proxy_clausification,[],[f172])).
thf(f174,plain,(
  ($true != ((sK5 @ = @ (sK6 @ =)))) | (((sK1 @ =)) = ((sK2 @ =)))),
  inference(trivial_inequality_removal,[],[f173])).
thf(f184,plain,(
  (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
  inference(primitive_instantiation,[],[f17])).
thf(f199,plain,(
  ((((sK1 @ =) = (sK2 @ =))) = $true) | (((sK4 @ = @ (sK6 @ =))) = $true) | ($true != (((sK3 @ =) = (sK3 @ =))))),
  inference(beta-eta_normalization,[],[f184])).
thf(f200,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | (((sK4 @ = @ (sK6 @ =))) = $true) | (((sK1 @ =)) = ((sK2 @ =)))),
  inference(equality_proxy_clausification,[],[f199])).
thf(f201,plain,(
  (((sK4 @ = @ (sK6 @ =))) = $true) | (((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =)))),
  inference(equality_proxy_clausification,[],[f200])).
thf(f202,plain,(
  (((sK4 @ = @ (sK6 @ =))) = $true) | (((sK1 @ =)) = ((sK2 @ =)))),
  inference(trivial_inequality_removal,[],[f201])).
thf(f207,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f9])).
thf(f218,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | ((((sK2 @ =) = (sK0 @ =))) = $true) | ((((sK4 @ =) = (sK5 @ =))) = $true)),
  inference(beta-eta_normalization,[],[f207])).
thf(f219,plain,(
  ((((sK4 @ =) = (sK5 @ =))) = $true) | (((sK3 @ =)) != ((sK3 @ =))) | ((((sK2 @ =) = (sK0 @ =))) = $true)),
  inference(equality_proxy_clausification,[],[f218])).
thf(f220,plain,(
  ((((sK2 @ =) = (sK0 @ =))) = $true) | (((sK3 @ =)) != ((sK3 @ =))) | (((sK4 @ =)) = ((sK5 @ =)))),
  inference(equality_proxy_clausification,[],[f219])).
thf(f221,plain,(
  (((sK3 @ =)) != ((sK3 @ =))) | (((sK0 @ =)) = ((sK2 @ =))) | (((sK4 @ =)) = ((sK5 @ =)))),
  inference(equality_proxy_clausification,[],[f220])).
thf(f222,plain,(
  (((sK4 @ =)) = ((sK5 @ =))) | (((sK0 @ =)) = ((sK2 @ =)))),
  inference(trivial_inequality_removal,[],[f221])).
thf(f233,definition,(
  spl7_11 <=> (((sK4 @ =)) = ((sK5 @ =)))),
  introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition])).
thf(f236,plain,(
  spl7_11 | spl7_9),
  inference(avatar_split_clause,[],[f222,f126,f233])).
thf(f237,plain,(
  ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f12])).
thf(f257,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | ((((sK4 @ =) = (sK5 @ =))) = $true) | ((((sK1 @ =) = (sK0 @ =))) != $true)),
  inference(beta-eta_normalization,[],[f237])).
thf(f258,plain,(
  ((((sK4 @ =) = (sK5 @ =))) = $true) | (((sK3 @ =)) != ((sK3 @ =))) | ((((sK1 @ =) = (sK0 @ =))) != $true)),
  inference(equality_proxy_clausification,[],[f257])).
thf(f259,plain,(
  (((sK3 @ =)) != ((sK3 @ =))) | ((((sK1 @ =) = (sK0 @ =))) != $true) | (((sK4 @ =)) = ((sK5 @ =)))),
  inference(equality_proxy_clausification,[],[f258])).
thf(f260,plain,(
  (((sK3 @ =)) != ((sK3 @ =))) | (((sK4 @ =)) = ((sK5 @ =))) | (((sK0 @ =)) != ((sK1 @ =)))),
  inference(equality_proxy_clausification,[],[f259])).
thf(f261,plain,(
  (((sK0 @ =)) != ((sK1 @ =))) | (((sK4 @ =)) = ((sK5 @ =)))),
  inference(trivial_inequality_removal,[],[f260])).
thf(f264,definition,(
  (((sK4 @ =)) != ((sK5 @ =))) | (((sK4 @ = @ (sK6 @ =))) != $true) | ($true = ((sK5 @ = @ (sK6 @ =))))),
  introduced(theory,[theory_tautology_sat_conflict])).
thf(f270,plain,(
  ~spl7_2 | spl7_8),
  inference(avatar_split_clause,[],[f147,f122,f51])).
thf(f272,definition,(
  spl7_12 <=> (((sK1 @ =)) = ((sK2 @ =)))),
  introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition])).
thf(f275,plain,(
  spl7_12 | spl7_8),
  inference(avatar_split_clause,[],[f202,f122,f272])).
thf(f276,plain,(
  spl7_11 | ~spl7_2),
  inference(avatar_split_clause,[],[f261,f51,f233])).
thf(f277,definition,(
  (((sK0 @ =)) != ((sK2 @ =))) | (((sK1 @ =)) != ((sK2 @ =))) | (((sK0 @ =)) = ((sK1 @ =)))),
  introduced(theory,[theory_tautology_sat_conflict])).
thf(f278,plain,(
  spl7_9 | ~spl7_3),
  inference(avatar_split_clause,[],[f91,f55,f126])).
thf(f279,plain,(
  ~spl7_3 | spl7_12),
  inference(avatar_split_clause,[],[f174,f272,f55])).
thf(f314,plain,(
  ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
  inference(primitive_instantiation,[],[f15])).
thf(f319,plain,(
  ($true != (((sK3 @ =) = (sK3 @ =)))) | ((((sK4 @ =) = (sK5 @ =))) = $true) | ((((sK1 @ =) = (sK2 @ =))) = $true)),
  inference(beta-eta_normalization,[],[f314])).
thf(f320,plain,(
  ((((sK1 @ =) = (sK2 @ =))) = $true) | (((sK3 @ =)) != ((sK3 @ =))) | ((((sK4 @ =) = (sK5 @ =))) = $true)),
  inference(equality_proxy_clausification,[],[f319])).
thf(f321,plain,(
  (((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | ((((sK4 @ =) = (sK5 @ =))) = $true)),
  inference(equality_proxy_clausification,[],[f320])).
thf(f322,plain,(
  (((sK1 @ =)) = ((sK2 @ =))) | (((sK3 @ =)) != ((sK3 @ =))) | (((sK4 @ =)) = ((sK5 @ =)))),
  inference(equality_proxy_clausification,[],[f321])).
thf(f323,plain,(
  (((sK1 @ =)) = ((sK2 @ =))) | (((sK4 @ =)) = ((sK5 @ =)))),
  inference(trivial_inequality_removal,[],[f322])).
thf(f339,plain,(
  spl7_11 | spl7_12),
  inference(avatar_split_clause,[],[f323,f272,f233])).
cnf(s3, plain, ~spl7_2 | ~spl7_3, inference(sat_conversion,[],[f58])).
cnf(s6, plain, spl7_8 | spl7_9, inference(sat_conversion,[],[f129])).
cnf(s9, plain, spl7_9 | spl7_11, inference(sat_conversion,[],[f236])).
cnf(s11, plain, spl7_3 | ~spl7_8 | ~spl7_11, inference(sat_conversion,[],[f264])).
cnf(s15, plain, ~spl7_2 | spl7_8, inference(sat_conversion,[],[f270])).
cnf(s16, plain, spl7_8 | spl7_12, inference(sat_conversion,[],[f275])).
cnf(s17, plain, ~spl7_2 | spl7_11, inference(sat_conversion,[],[f276])).
cnf(s18, plain, spl7_2 | ~spl7_9 | ~spl7_12, inference(sat_conversion,[],[f277])).
cnf(s19, plain, ~spl7_3 | spl7_9, inference(sat_conversion,[],[f278])).
cnf(s20, plain, ~spl7_3 | spl7_12, inference(sat_conversion,[],[f279])).
cnf(s23, plain, spl7_11 | spl7_12, inference(sat_conversion,[],[f339])).
cnf(s24, plain, spl7_8 | spl7_2, inference(rat,[],[s18,s6,s16])).
cnf(s25, plain, spl7_11 | spl7_2, inference(rat,[],[s18,s9,s23])).
cnf(s26, plain, spl7_2, inference(rat,[],[s18,s19,s20,s11,s25,s24])).
cnf(s27, plain, spl7_11, inference(rat,[],[s17,s26])).
cnf(s28, plain, spl7_8, inference(rat,[],[s15,s26])).
cnf(s29, plain, ~spl7_3, inference(rat,[],[s3,s26])).
cnf(s30, plain, $false, inference(rat,[],[s11,s28,s29,s27])).
thf(f340,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s30])).
% SZS output end Proof for theBenchmark