%----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) > $i)).
thf(func_def_5, type, sK1: ((($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 > $o)).
thf(func_def_8, type, sK4: ((($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: $tType]:(X0)).
thf(func_def_16, type, sK7: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_18, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(f1,conjecture,(
  ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X5 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5)) & ! [X2 : ($i > $o),X5 : $i] : ((X1 @ X2 @ X2 @ X5) | (X0 @ X2 @ X2 @ X5)) & ! [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120C_pme)).
thf(f2,negated_conjecture,(
  ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X5 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X5)) & ! [X2 : ($i > $o),X5 : $i] : ((X1 @ X2 @ X2 @ X5) | (X0 @ X2 @ X2 @ X5)) & ! [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : ($true)) @ (^[X4 : $i] : ($false)) @ X2) | (X1 @ (^[X5 : $i] : ($true)) @ (^[X6 : $i] : ($false)) @ X2)) & ! [X7 : ($i > $o),X8 : $i] : ((X0 @ X7 @ X7 @ X8) | (X1 @ X7 @ X7 @ X8)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((X0 @ X11 @ X9 @ X12) | (X1 @ X11 @ X9 @ X12)) & ! [X13 : $i] : ((X1 @ X9 @ X10 @ X13) | (X0 @ X9 @ X10 @ X13))) => ! [X14 : $i] : ((X0 @ X11 @ X10 @ X14) | (X1 @ X11 @ X10 @ X14))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) & ! [X7 : ($i > $o),X8 : $i] : (($true = ((X0 @ X7 @ X7 @ X8))) | ($true = ((X1 @ X7 @ X7 @ X8)))) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((((X0 @ X11 @ X9 @ X12)) = $true) | (((X1 @ X11 @ X9 @ X12)) = $true)) & ! [X13 : $i] : (($true = ((X1 @ X9 @ X10 @ X13))) | (((X0 @ X9 @ X10 @ X13)) = $true))) => ! [X14 : $i] : ((((X0 @ X11 @ X10 @ X14)) = $true) | ($true = ((X1 @ X11 @ X10 @ X14))))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X7 : ($i > $o),X6 : ($i > $o),X5 : ($i > $o)] : ((! [X8 : $i] : ((((X0 @ X7 @ X5 @ X8)) = $true) | (((X1 @ X7 @ X5 @ X8)) = $true)) & ! [X9 : $i] : (($true = ((X1 @ X5 @ X6 @ X9))) | ($true = ((X0 @ X5 @ X6 @ X9))))) => ! [X10 : $i] : ((((X1 @ X7 @ X6 @ X10)) = $true) | (((X0 @ X7 @ X6 @ X10)) = $true))) & ! [X3 : ($i > $o),X4 : $i] : ((((X0 @ X3 @ X3 @ X4)) = $true) | ($true = ((X1 @ X3 @ X3 @ X4)))) & ~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)))),
  inference(rectify,[],[f4])).
thf(f6,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X7 : ($i > $o),X6 : ($i > $o),X5 : ($i > $o)] : (? [X10 : $i] : ((((X0 @ X7 @ X6 @ X10)) != $true) & (((X1 @ X7 @ X6 @ X10)) != $true)) & (! [X8 : $i] : ((((X0 @ X7 @ X5 @ X8)) = $true) | (((X1 @ X7 @ X5 @ X8)) = $true)) & ! [X9 : $i] : (($true = ((X1 @ X5 @ X6 @ X9))) | ($true = ((X0 @ X5 @ X6 @ X9)))))) | ? [X4 : $i,X3 : ($i > $o)] : ((((X0 @ X3 @ X3 @ X4)) != $true) & ($true != ((X1 @ X3 @ X3 @ X4)))) | ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)))),
  inference(ennf_transformation,[],[f5])).
thf(f7,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) | ? [X4 : $i,X3 : ($i > $o)] : ((((X0 @ X3 @ X3 @ X4)) != $true) & ($true != ((X1 @ X3 @ X3 @ X4)))) | ? [X5 : ($i > $o),X7 : ($i > $o),X6 : ($i > $o)] : (! [X9 : $i] : (($true = ((X1 @ X5 @ X6 @ X9))) | ($true = ((X0 @ X5 @ X6 @ X9)))) & ! [X8 : $i] : ((((X0 @ X7 @ X5 @ X8)) = $true) | (((X1 @ X7 @ X5 @ X8)) = $true)) & ? [X10 : $i] : ((((X0 @ X7 @ X6 @ X10)) != $true) & (((X1 @ X7 @ X6 @ X10)) != $true))))),
  inference(flattening,[],[f6])).
thf(f8,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) | ? [X3 : $i,X4 : ($i > $o)] : (($true != ((X0 @ X4 @ X4 @ X3))) & ($true != ((X1 @ X4 @ X4 @ X3)))) | ? [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (! [X8 : $i] : ((((X1 @ X5 @ X7 @ X8)) = $true) | ($true = ((X0 @ X5 @ X7 @ X8)))) & ! [X9 : $i] : (($true = ((X0 @ X6 @ X5 @ X9))) | ($true = ((X1 @ X6 @ X5 @ X9)))) & ? [X10 : $i] : (($true != ((X0 @ X6 @ X7 @ X10))) & (((X1 @ X6 @ X7 @ X10)) != $true))))),
  inference(rectify,[],[f7])).
thf(f9,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) | ((((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0))) != $true) & ($true != ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0))))) | (! [X8 : $i] : (($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8)))) & ! [X9 : $i] : (($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9)))) & ((((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) & ($true != ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))))))),
  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))],[f8])).
thf(f11,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f12,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true != ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f13,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f48,definition,(
  spl6_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
  introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
thf(f49,plain,(
  ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_1),
  inference(avatar_component_clause,[],[f48])).
thf(f50,plain,(
  ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_1),
  inference(avatar_component_clause,[],[f48])).
thf(f55,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | (((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
  inference(primitive_instantiation,[],[f11])).
thf(f61,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
  inference(beta-eta_normalization,[],[f55])).
thf(f62,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
  inference(equality_proxy_clausification,[],[f61])).
thf(f63,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
  inference(equality_proxy_clausification,[],[f62])).
thf(f64,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
  inference(trivial_inequality_removal,[],[f63])).
thf(f77,definition,(
  spl6_3 <=> ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true))),
  introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
thf(f78,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((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) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) ) | ~spl6_3),
  inference(avatar_component_clause,[],[f77])).
thf(f79,plain,(
  spl6_1 | spl6_3),
  inference(avatar_split_clause,[],[f64,f77,f48])).
thf(f140,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9)) = $true)) )),
  inference(primitive_instantiation,[],[f12])).
thf(f146,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) = $true)) )),
  inference(beta-eta_normalization,[],[f140])).
thf(f147,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) = $true) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
  inference(equality_proxy_clausification,[],[f146])).
thf(f148,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
  inference(equality_proxy_clausification,[],[f147])).
thf(f149,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
  inference(equality_proxy_clausification,[],[f148])).
thf(f150,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
  inference(trivial_inequality_removal,[],[f149])).
thf(f169,definition,(
  spl6_7 <=> ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))))),
  introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
thf(f170,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) ) | ~spl6_7),
  inference(avatar_component_clause,[],[f169])).
thf(f171,plain,(
  spl6_7 | spl6_1),
  inference(avatar_split_clause,[],[f150,f48,f169])).
thf(f172,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8)))) )),
  inference(primitive_instantiation,[],[f13])).
thf(f186,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
  inference(beta-eta_normalization,[],[f172])).
thf(f187,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
  inference(equality_proxy_clausification,[],[f186])).
thf(f188,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8)))) )),
  inference(equality_proxy_clausification,[],[f187])).
thf(f189,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
  inference(equality_proxy_clausification,[],[f188])).
thf(f190,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8)))) )),
  inference(trivial_inequality_removal,[],[f189])).
thf(f201,definition,(
  spl6_8 <=> ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))),
  introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
thf(f202,plain,(
  ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | ~spl6_8),
  inference(avatar_component_clause,[],[f201])).
thf(f203,plain,(
  spl6_8 | spl6_1),
  inference(avatar_split_clause,[],[f190,f48,f201])).
thf(f268,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_1),
  inference(argument_congruence,[],[f50])).
thf(f270,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ((((^[Y0 : $i]: ($true)) @ X1)) = $false)) ) | ~spl6_1),
  inference(iff_proxy_clausification,[],[f268])).
thf(f271,plain,(
  ($true = $false) | ($true = $false) | ~spl6_1),
  inference(beta-eta_normalization,[],[f270])).
thf(f272,plain,(
  ($true = $false) | ~spl6_1),
  inference(duplicate_literal_removal,[],[f271])).
thf(f273,plain,(
  $false | ~spl6_1),
  inference(trivial_inequality_removal,[],[f272])).
thf(f274,plain,(
  ~spl6_1),
  inference(avatar_contradiction_clause,[],[f273])).
thf(f287,plain,(
  ( ! [X2 : $i] : (($true != (((^[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))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) ) | ~spl6_3),
  inference(primitive_instantiation,[],[f78])).
thf(f294,plain,(
  ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ($true != (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ~spl6_3),
  inference(beta-eta_normalization,[],[f287])).
thf(f295,plain,(
  ($true != (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_3),
  inference(equality_proxy_clausification,[],[f294])).
thf(f296,plain,(
  (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_3),
  inference(equality_proxy_clausification,[],[f295])).
thf(f307,plain,(
  (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (spl6_1 | ~spl6_3)),
  inference(forward_subsumption_resolution,[],[f296,f49])).
thf(f309,definition,(
  spl6_11 <=> (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[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_11])],[avatar_definition])).
thf(f312,plain,(
  ~spl6_11 | spl6_1 | ~spl6_3),
  inference(avatar_split_clause,[],[f307,f77,f48,f309])).
thf(f313,plain,(
  ( ! [X2 : $i,X9 : $i] : ((((sK3 @ (^[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 > $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))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9)) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) ) | ~spl6_7),
  inference(primitive_instantiation,[],[f170])).
thf(f318,plain,(
  (((sK3 @ (^[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))))))))) | ((((sK3 @ (^[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) | ~spl6_7),
  inference(beta-eta_normalization,[],[f313])).
thf(f319,plain,(
  (((sK3 @ (^[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))))))))) | (((sK3 @ (^[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 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ~spl6_7),
  inference(equality_proxy_clausification,[],[f318])).
thf(f320,plain,(
  (((sK3 @ (^[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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK3 @ (^[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_7),
  inference(equality_proxy_clausification,[],[f319])).
thf(f321,plain,(
  (((sK3 @ (^[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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_7),
  inference(duplicate_literal_removal,[],[f320])).
thf(f335,plain,(
  (((sK3 @ (^[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_1 | ~spl6_7)),
  inference(forward_subsumption_resolution,[],[f321,f49])).
thf(f342,definition,(
  spl6_13 <=> (((sK3 @ (^[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_13])],[avatar_definition])).
thf(f345,plain,(
  spl6_13 | spl6_1 | ~spl6_7),
  inference(avatar_split_clause,[],[f335,f169,f48,f342])).
thf(f346,plain,(
  ( ! [X2 : $i,X8 : $i] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[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)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)))) ) | ~spl6_8),
  inference(primitive_instantiation,[],[f202])).
thf(f351,plain,(
  ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ (^[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) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ~spl6_8),
  inference(beta-eta_normalization,[],[f346])).
thf(f352,plain,(
  (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[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)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ~spl6_8),
  inference(equality_proxy_clausification,[],[f351])).
thf(f353,plain,(
  (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ~spl6_8),
  inference(equality_proxy_clausification,[],[f352])).
thf(f354,plain,(
  ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ~spl6_8),
  inference(duplicate_literal_removal,[],[f353])).
thf(f368,plain,(
  (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (spl6_1 | ~spl6_8)),
  inference(forward_subsumption_resolution,[],[f354,f49])).
thf(f375,definition,(
  spl6_15 <=> (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[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_15])],[avatar_definition])).
thf(f378,plain,(
  spl6_15 | spl6_1 | ~spl6_8),
  inference(avatar_split_clause,[],[f368,f201,f48,f375])).
thf(f379,definition,(
  (((sK3 @ (^[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))))))))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[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)))))))) = ((sK4 @ (^[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_1 | spl6_3, inference(sat_conversion,[],[f79])).
cnf(s6, plain, spl6_1 | spl6_7, inference(sat_conversion,[],[f171])).
cnf(s7, plain, spl6_1 | spl6_8, inference(sat_conversion,[],[f203])).
cnf(s10, plain, ~spl6_1, inference(sat_conversion,[],[f274])).
cnf(s11, plain, spl6_1 | ~spl6_3 | ~spl6_11, inference(sat_conversion,[],[f312])).
cnf(s13, plain, spl6_1 | ~spl6_7 | spl6_13, inference(sat_conversion,[],[f345])).
cnf(s15, plain, spl6_1 | ~spl6_8 | spl6_15, inference(sat_conversion,[],[f378])).
cnf(s16, plain, spl6_11 | ~spl6_13 | ~spl6_15, inference(sat_conversion,[],[f379])).
cnf(s19, plain, spl6_8, inference(rat,[],[s7,s10])).
cnf(s20, plain, spl6_15, inference(rat,[],[s15,s10,s19])).
cnf(s22, plain, spl6_7, inference(rat,[],[s6,s10])).
cnf(s23, plain, spl6_13, inference(rat,[],[s13,s10,s22])).
cnf(s25, plain, spl6_11, inference(rat,[],[s16,s20,s23])).
cnf(s26, plain, ~spl6_3, inference(rat,[],[s11,s10,s25])).
cnf(s29, plain, $false, inference(rat,[],[s2,s26,s10])).
thf(f380,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s29])).
% SZS output end Proof for theBenchmark