%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_8, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_9, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_10, type, vNOT: ($o > $o)).
thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_17, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_18, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(f1,conjecture,(
  ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X5 : $i,X2 : ($i > $o)] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ! [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X1 @ X3 @ X4 @ X5) | (X0 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))) & ~ ! [X5 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120D_pme)).
thf(f2,negated_conjecture,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X5 : $i,X2 : ($i > $o)] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ! [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X1 @ X3 @ X4 @ X5) | (X0 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))) & ~ ! [X5 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i,X3 : ($i > $o)] : ((X0 @ X3 @ X3 @ X2) | (X1 @ X3 @ X3 @ X2)) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((! [X7 : $i] : ((X1 @ X4 @ X6 @ X7) | (X0 @ X4 @ X6 @ X7)) & ! [X8 : $i] : ((X1 @ X6 @ X5 @ X8) | (X0 @ X6 @ X5 @ X8))) => ! [X9 : $i] : ((X1 @ X4 @ X5 @ X9) | (X0 @ X4 @ X5 @ X9))) & ~ ! [X10 : $i] : ((X1 @ (^[X11 : $i] : ($true)) @ (^[X12 : $i] : ($false)) @ X10) | (X0 @ (^[X13 : $i] : ($true)) @ (^[X14 : $i] : ($false)) @ X10)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : ($i > $o),X2 : $i] : ((((X0 @ X3 @ X3 @ X2)) = $true) | (((X1 @ X3 @ X3 @ X2)) = $true)) & ! [X5 : ($i > $o),X6 : ($i > $o),X4 : ($i > $o)] : ((! [X8 : $i] : (($true = ((X0 @ X6 @ X5 @ X8))) | ($true = ((X1 @ X6 @ X5 @ X8)))) & ! [X7 : $i] : (($true = ((X1 @ X4 @ X6 @ X7))) | ($true = ((X0 @ X4 @ X6 @ X7))))) => ! [X9 : $i] : (($true = ((X0 @ X4 @ X5 @ X9))) | ($true = ((X1 @ X4 @ X5 @ X9))))) & ~ ! [X10 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X3 : ($i > $o),X2 : $i] : ((((X0 @ X3 @ X3 @ X2)) != $true) & (((X1 @ X3 @ X3 @ X2)) != $true)) | ? [X5 : ($i > $o),X6 : ($i > $o),X4 : ($i > $o)] : (? [X9 : $i] : (($true != ((X0 @ X4 @ X5 @ X9))) & ($true != ((X1 @ X4 @ X5 @ X9)))) & (! [X8 : $i] : (($true = ((X0 @ X6 @ X5 @ X8))) | ($true = ((X1 @ X6 @ X5 @ X8)))) & ! [X7 : $i] : (($true = ((X1 @ X4 @ X6 @ X7))) | ($true = ((X0 @ X4 @ X6 @ X7)))))) | ! [X10 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (? [X9 : $i] : (($true != ((X0 @ X4 @ X5 @ X9))) & ($true != ((X1 @ X4 @ X5 @ X9)))) & ! [X8 : $i] : (($true = ((X0 @ X6 @ X5 @ X8))) | ($true = ((X1 @ X6 @ X5 @ X8)))) & ! [X7 : $i] : (($true = ((X1 @ X4 @ X6 @ X7))) | ($true = ((X0 @ X4 @ X6 @ X7))))) | ! [X10 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) | ? [X3 : ($i > $o),X2 : $i] : ((((X0 @ X3 @ X3 @ X2)) != $true) & (((X1 @ X3 @ X3 @ X2)) != $true)))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X5 : $i] : ((((X1 @ X2 @ X3 @ X5)) != $true) & (((X0 @ X2 @ X3 @ X5)) != $true)) & ! [X6 : $i] : ((((X1 @ X4 @ X3 @ X6)) = $true) | ($true = ((X0 @ X4 @ X3 @ X6)))) & ! [X7 : $i] : ((((X0 @ X2 @ X4 @ X7)) = $true) | ($true = ((X1 @ X2 @ X4 @ X7))))) | ! [X8 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) | ? [X9 : ($i > $o),X10 : $i] : ((((X1 @ X9 @ X9 @ X10)) != $true) & (((X0 @ X9 @ X9 @ X10)) != $true)))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : ((((((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) & (((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true)) & ! [X6 : $i] : (($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | (((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6)) = $true)) & ! [X7 : $i] : (($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))))) | ! [X8 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) | ((((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) & (((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X10,$thf(sK5 @ X1 @ X0)),skolemize(X10,$thf(sK5 @ X1 @ X0)),skolemize(X10,$thf(sK5 @ X1 @ X0)),skolemize(X10,$thf(sK5 @ X1 @ X0)),skolemize(X10,$thf(sK5 @ X1 @ X0)),skolemize(X10,$thf(sK5 @ X1 @ X0))],[f7])).
thf(f9,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : ((((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f14,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f50,definition,(
  spl6_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
  introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
thf(f51,plain,(
  ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_2),
  inference(avatar_component_clause,[],[f50])).
thf(f52,plain,(
  ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2),
  inference(avatar_component_clause,[],[f50])).
thf(f54,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
  inference(primitive_instantiation,[],[f14])).
thf(f60,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
  inference(beta-eta_normalization,[],[f54])).
thf(f61,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
  inference(equality_proxy_clausification,[],[f60])).
thf(f62,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
  inference(equality_proxy_clausification,[],[f61])).
thf(f63,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
  inference(trivial_inequality_removal,[],[f62])).
thf(f76,definition,(
  spl6_3 <=> ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true))),
  introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
thf(f77,plain,(
  ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) ) | ~spl6_3),
  inference(avatar_component_clause,[],[f76])).
thf(f78,plain,(
  spl6_2 | spl6_3),
  inference(avatar_split_clause,[],[f63,f76,f50])).
thf(f107,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_2),
  inference(argument_congruence,[],[f52])).
thf(f108,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = $true) | ($false = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_2),
  inference(iff_proxy_clausification,[],[f107])).
thf(f111,plain,(
  ($false = $true) | ($false = $true) | ~spl6_2),
  inference(beta-eta_normalization,[],[f108])).
thf(f112,plain,(
  ($false = $true) | ~spl6_2),
  inference(duplicate_literal_removal,[],[f111])).
thf(f113,plain,(
  $false | ~spl6_2),
  inference(trivial_inequality_removal,[],[f112])).
thf(f114,plain,(
  ~spl6_2),
  inference(avatar_contradiction_clause,[],[f113])).
thf(f152,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7)))) )),
  inference(primitive_instantiation,[],[f9])).
thf(f160,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true)) )),
  inference(beta-eta_normalization,[],[f152])).
thf(f161,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true)) )),
  inference(equality_proxy_clausification,[],[f160])).
thf(f162,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | ((((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
  inference(equality_proxy_clausification,[],[f161])).
thf(f163,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) )),
  inference(equality_proxy_clausification,[],[f162])).
thf(f164,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
  inference(trivial_inequality_removal,[],[f163])).
thf(f180,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) ) | spl6_2),
  inference(forward_subsumption_resolution,[],[f164,f51])).
thf(f210,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : ((((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
  inference(primitive_instantiation,[],[f11])).
thf(f216,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (((((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
  inference(beta-eta_normalization,[],[f210])).
thf(f217,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))))) )),
  inference(equality_proxy_clausification,[],[f216])).
thf(f218,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true)) )),
  inference(equality_proxy_clausification,[],[f217])).
thf(f219,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : ((((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
  inference(equality_proxy_clausification,[],[f218])).
thf(f220,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
  inference(trivial_inequality_removal,[],[f219])).
thf(f238,plain,(
  ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : ((((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) ) | spl6_2),
  inference(forward_subsumption_resolution,[],[f220,f51])).
thf(f274,plain,(
  ( ! [X8 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) ) | ~spl6_3),
  inference(primitive_instantiation,[],[f77])).
thf(f280,plain,(
  ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true) | ~spl6_3),
  inference(beta-eta_normalization,[],[f274])).
thf(f281,plain,(
  ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_3),
  inference(equality_proxy_clausification,[],[f280])).
thf(f282,plain,(
  (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_3),
  inference(equality_proxy_clausification,[],[f281])).
thf(f294,plain,(
  (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (spl6_2 | ~spl6_3)),
  inference(forward_subsumption_resolution,[],[f282,f51])).
thf(f296,definition,(
  spl6_7 <=> (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))),
  introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
thf(f299,plain,(
  ~spl6_7 | spl6_2 | ~spl6_3),
  inference(avatar_split_clause,[],[f294,f76,f50,f296])).
thf(f300,plain,(
  ( ! [X8 : $i,X7 : $i] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7)))) ) | spl6_2),
  inference(primitive_instantiation,[],[f180])).
thf(f305,plain,(
  (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_2),
  inference(beta-eta_normalization,[],[f300])).
thf(f306,plain,(
  ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_2),
  inference(equality_proxy_clausification,[],[f305])).
thf(f307,plain,(
  (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
  inference(equality_proxy_clausification,[],[f306])).
thf(f308,plain,(
  (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_2),
  inference(duplicate_literal_removal,[],[f307])).
thf(f322,plain,(
  (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
  inference(forward_subsumption_resolution,[],[f308,f51])).
thf(f329,definition,(
  spl6_9 <=> (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))),
  introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
thf(f332,plain,(
  spl6_9 | spl6_2),
  inference(avatar_split_clause,[],[f322,f50,f329])).
thf(f383,plain,(
  ( ! [X8 : $i,X6 : $i] : ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6)) = $true)) ) | spl6_2),
  inference(primitive_instantiation,[],[f238])).
thf(f398,plain,(
  ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
  inference(beta-eta_normalization,[],[f383])).
thf(f399,plain,(
  ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_2),
  inference(equality_proxy_clausification,[],[f398])).
thf(f400,plain,(
  (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
  inference(equality_proxy_clausification,[],[f399])).
thf(f401,plain,(
  ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
  inference(duplicate_literal_removal,[],[f400])).
thf(f405,plain,(
  (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
  inference(forward_subsumption_resolution,[],[f401,f51])).
thf(f412,definition,(
  spl6_16 <=> (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))),
  introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition])).
thf(f415,plain,(
  spl6_16 | spl6_2),
  inference(avatar_split_clause,[],[f405,f50,f412])).
thf(f416,definition,(
  (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))),
  introduced(theory,[theory_tautology_sat_conflict])).
cnf(s2, plain, spl6_2 | spl6_3, inference(sat_conversion,[],[f78])).
cnf(s5, plain, ~spl6_2, inference(sat_conversion,[],[f114])).
cnf(s7, plain, spl6_2 | ~spl6_3 | ~spl6_7, inference(sat_conversion,[],[f299])).
cnf(s9, plain, spl6_2 | spl6_9, inference(sat_conversion,[],[f332])).
cnf(s16, plain, spl6_2 | spl6_16, inference(sat_conversion,[],[f415])).
cnf(s17, plain, spl6_7 | ~spl6_9 | ~spl6_16, inference(sat_conversion,[],[f416])).
cnf(s18, plain, spl6_16, inference(rat,[],[s16,s5])).
cnf(s21, plain, spl6_9, inference(rat,[],[s9,s5])).
cnf(s24, plain, spl6_7, inference(rat,[],[s17,s18,s21])).
cnf(s25, plain, ~spl6_3, inference(rat,[],[s7,s5,s24])).
cnf(s27, plain, $false, inference(rat,[],[s2,s25,s5])).
thf(f417,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s27])).
% SZS output end Proof for theBenchmark