%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, p: $o).
thf(func_def_2, type, vOR: ($o > $o > $o)).
thf(func_def_3, type, vNOT: ($o > $o)).
thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_5, type, vAND: ($o > $o > $o)).
thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_12, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
thf(func_def_13, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_20, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_21, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_23, type, sK11: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(func_def_24, type, sK12: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
thf(f1,conjecture,(
  ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : ($i > $o),X2 : $i] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : ((! [X2 : $i] : ((X0 @ X3 @ X4 @ X2) | (X1 @ X3 @ X4 @ X2)) & ! [X2 : $i] : ((X1 @ X4 @ X5 @ X2) | (X0 @ X4 @ X5 @ X2))) => ! [X2 : $i] : ((X1 @ X3 @ X5 @ X2) | (X0 @ X3 @ X5 @ X2))) & ~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : (~p | p)) @ (^[X3 : $i] : (~p & p)) @ X2) | (X1 @ (^[X3 : $i] : (~p | p)) @ (^[X3 : $i] : (p & ~p)) @ X2)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120F_pme)).
thf(f2,negated_conjecture,(
  ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : ($i > $o),X2 : $i] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : ((! [X2 : $i] : ((X0 @ X3 @ X4 @ X2) | (X1 @ X3 @ X4 @ X2)) & ! [X2 : $i] : ((X1 @ X4 @ X5 @ X2) | (X0 @ X4 @ X5 @ X2))) => ! [X2 : $i] : ((X1 @ X3 @ X5 @ X2) | (X0 @ X3 @ X5 @ X2))) & ~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : (~p | p)) @ (^[X3 : $i] : (~p & p)) @ X2) | (X1 @ (^[X3 : $i] : (~p | p)) @ (^[X3 : $i] : (p & ~p)) @ X2)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((! [X7 : $i] : ((X1 @ X4 @ X6 @ X7) | (X0 @ X4 @ X6 @ X7)) & ! [X8 : $i] : ((X0 @ X6 @ X5 @ X8) | (X1 @ X6 @ X5 @ X8))) => ! [X9 : $i] : ((X0 @ X4 @ X5 @ X9) | (X1 @ X4 @ X5 @ X9))) & ~ ! [X10 : $i] : ((X1 @ (^[X11 : $i] : (~p | p)) @ (^[X12 : $i] : (~p & p)) @ X10) | (X0 @ (^[X13 : $i] : (~p | p)) @ (^[X14 : $i] : (p & ~p)) @ X10)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X10 : $i] : (($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))) & ! [X2 : ($i > $o),X3 : $i] : (($true = ((X1 @ X2 @ X2 @ X3))) | ($true = ((X0 @ X2 @ X2 @ X3)))) & ! [X5 : ($i > $o),X6 : ($i > $o),X4 : ($i > $o)] : ((! [X8 : $i] : (($true = ((X1 @ X6 @ X5 @ X8))) | ($true = ((X0 @ X6 @ X5 @ X8)))) & ! [X7 : $i] : (($true = ((X1 @ X4 @ X6 @ X7))) | ($true = ((X0 @ X4 @ X6 @ X7))))) => ! [X9 : $i] : (($true = ((X1 @ X4 @ X5 @ X9))) | ($true = ((X0 @ X4 @ X5 @ X9))))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X10 : $i] : (($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))) | ? [X2 : ($i > $o),X3 : $i] : (($true != ((X1 @ X2 @ X2 @ X3))) & ($true != ((X0 @ X2 @ X2 @ X3)))) | ? [X5 : ($i > $o),X6 : ($i > $o),X4 : ($i > $o)] : (? [X9 : $i] : (($true != ((X1 @ X4 @ X5 @ X9))) & ($true != ((X0 @ X4 @ X5 @ X9)))) & (! [X8 : $i] : (($true = ((X1 @ X6 @ X5 @ X8))) | ($true = ((X0 @ X6 @ X5 @ X8)))) & ! [X7 : $i] : (($true = ((X1 @ X4 @ X6 @ X7))) | ($true = ((X0 @ X4 @ X6 @ X7)))))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X5 : ($i > $o),X6 : ($i > $o),X4 : ($i > $o)] : (! [X8 : $i] : (($true = ((X1 @ X6 @ X5 @ X8))) | ($true = ((X0 @ X6 @ X5 @ X8)))) & ! [X7 : $i] : (($true = ((X1 @ X4 @ X6 @ X7))) | ($true = ((X0 @ X4 @ X6 @ X7)))) & ? [X9 : $i] : (($true != ((X1 @ X4 @ X5 @ X9))) & ($true != ((X0 @ X4 @ X5 @ X9))))) | ? [X2 : ($i > $o),X3 : $i] : (($true != ((X1 @ X2 @ X2 @ X3))) & ($true != ((X0 @ X2 @ X2 @ X3)))) | ! [X10 : $i] : (($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (! [X5 : $i] : (($true = ((X0 @ X3 @ X2 @ X5))) | ($true = ((X1 @ X3 @ X2 @ X5)))) & ! [X6 : $i] : (($true = ((X0 @ X4 @ X3 @ X6))) | ($true = ((X1 @ X4 @ X3 @ X6)))) & ? [X7 : $i] : (($true != ((X0 @ X4 @ X2 @ X7))) & ($true != ((X1 @ X4 @ X2 @ X7))))) | ? [X8 : ($i > $o),X9 : $i] : (($true != ((X0 @ X8 @ X8 @ X9))) & ($true != ((X1 @ X8 @ X8 @ X9)))) | ! [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : ((! [X5 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)))) & ! [X6 : $i] : (($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6)))) & (($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))))) | (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) & ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) | ! [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X9,$thf(sK5 @ X1 @ X0)),skolemize(X9,$thf(sK5 @ X1 @ X0)),skolemize(X9,$thf(sK5 @ X1 @ X0)),skolemize(X9,$thf(sK5 @ X1 @ X0)),skolemize(X9,$thf(sK5 @ X1 @ X0)),skolemize(X9,$thf(sK5 @ X1 @ X0))],[f7])).
thf(f11,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f14,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f16,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f19,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10)))) )),
  inference(boolean_simplification,[],[f16])).
thf(f20,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)))) )),
  inference(boolean_simplification,[],[f19])).
thf(f21,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)))) )),
  inference(boolean_simplification,[],[f20])).
thf(f22,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)))) )),
  inference(boolean_simplification,[],[f21])).
thf(f23,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10)))) )),
  inference(boolean_simplification,[],[f14])).
thf(f24,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6)))) )),
  inference(boolean_simplification,[],[f23])).
thf(f25,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6)))) )),
  inference(boolean_simplification,[],[f24])).
thf(f26,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X6)))) )),
  inference(boolean_simplification,[],[f25])).
thf(f47,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10)))) )),
  inference(boolean_simplification,[],[f11])).
thf(f48,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) )),
  inference(boolean_simplification,[],[f47])).
thf(f49,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) )),
  inference(boolean_simplification,[],[f48])).
thf(f50,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(boolean_simplification,[],[f49])).
thf(f72,definition,(
  spl6_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
  introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
thf(f73,plain,(
  ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_1),
  inference(avatar_component_clause,[],[f72])).
thf(f74,plain,(
  ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_1),
  inference(avatar_component_clause,[],[f72])).
thf(f253,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_1),
  inference(argument_congruence,[],[f73])).
thf(f255,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ((((^[Y0 : $i]: ($true)) @ X1)) = $false)) ) | ~spl6_1),
  inference(iff_proxy_clausification,[],[f253])).
thf(f256,plain,(
  ($true = $false) | ($true = $false) | ~spl6_1),
  inference(beta-eta_normalization,[],[f255])).
thf(f257,plain,(
  ($true = $false) | ~spl6_1),
  inference(duplicate_literal_removal,[],[f256])).
thf(f258,plain,(
  $false | ~spl6_1),
  inference(trivial_inequality_removal,[],[f257])).
thf(f259,plain,(
  ~spl6_1),
  inference(avatar_contradiction_clause,[],[f258])).
thf(f383,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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))))) )),
  inference(primitive_instantiation,[],[f50])).
thf(f389,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true != ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($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 = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))) )),
  inference(beta-eta_normalization,[],[f383])).
thf(f390,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[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))))) | (((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 = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(equality_proxy_clausification,[],[f389])).
thf(f391,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true != ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[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 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(equality_proxy_clausification,[],[f390])).
thf(f392,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
  inference(trivial_inequality_removal,[],[f391])).
thf(f404,plain,(
  ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) ) | spl6_1),
  inference(forward_subsumption_resolution,[],[f392,f74])).
thf(f405,plain,(
  ( ! [X10 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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))))))) @ (sK0 @ (^[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 : $i]: (Y0 = Y1))))))))))) ) | spl6_1),
  inference(primitive_instantiation,[],[f404])).
thf(f417,plain,(
  ($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))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_1),
  inference(beta-eta_normalization,[],[f405])).
thf(f418,plain,(
  ($true != (((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)))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_1),
  inference(equality_proxy_clausification,[],[f417])).
thf(f419,plain,(
  ((^[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)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
  inference(equality_proxy_clausification,[],[f418])).
thf(f425,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_1),
  inference(forward_subsumption_resolution,[],[f419,f74])).
thf(f447,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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 = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5)))) )),
  inference(primitive_instantiation,[],[f22])).
thf(f453,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($true = (((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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(beta-eta_normalization,[],[f447])).
thf(f454,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($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 = (((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
  inference(equality_proxy_clausification,[],[f453])).
thf(f455,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : ((((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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = (((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
  inference(equality_proxy_clausification,[],[f454])).
thf(f456,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : ((((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)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(equality_proxy_clausification,[],[f455])).
thf(f457,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(trivial_inequality_removal,[],[f456])).
thf(f475,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X5 : $i] : (($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) ) | spl6_1),
  inference(forward_subsumption_resolution,[],[f457,f74])).
thf(f481,plain,(
  ( ! [X10 : $i,X5 : $i] : (($true = (((^[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))))))) @ X5))) | (((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 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) ) | spl6_1),
  inference(primitive_instantiation,[],[f475])).
thf(f489,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 : $i]: (Y0 = Y1))))))))) | ($true = (((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 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | spl6_1),
  inference(beta-eta_normalization,[],[f481])).
thf(f490,plain,(
  ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((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))))))))) | (((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_1),
  inference(equality_proxy_clausification,[],[f489])).
thf(f491,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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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_1),
  inference(equality_proxy_clausification,[],[f490])).
thf(f492,plain,(
  ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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_1),
  inference(duplicate_literal_removal,[],[f491])).
thf(f520,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_1),
  inference(forward_subsumption_resolution,[],[f492,f74])).
thf(f525,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = (((^[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 != (((^[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)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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)))) )),
  inference(primitive_instantiation,[],[f26])).
thf(f548,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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 = (((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 = ((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)))) )),
  inference(beta-eta_normalization,[],[f525])).
thf(f549,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),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)))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($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)))) )),
  inference(equality_proxy_clausification,[],[f548])).
thf(f550,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($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))) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(equality_proxy_clausification,[],[f549])).
thf(f551,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),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))))))))) | (((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 @ (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)) @ X10))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
  inference(equality_proxy_clausification,[],[f550])).
thf(f552,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($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))) | ((^[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 : $i]: (Y0 = Y1))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
  inference(trivial_inequality_removal,[],[f551])).
thf(f553,plain,(
  ( ! [X10 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($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 = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) ) | spl6_1),
  inference(forward_subsumption_resolution,[],[f552,f74])).
thf(f558,plain,(
  ( ! [X10 : $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)))))) @ (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 = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) ) | spl6_1),
  inference(primitive_instantiation,[],[f553])).
thf(f592,plain,(
  ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((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 : $i]: (Y0 = Y1)))))))))) | spl6_1),
  inference(beta-eta_normalization,[],[f558])).
thf(f593,plain,(
  ($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)))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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_1),
  inference(equality_proxy_clausification,[],[f592])).
thf(f594,plain,(
  ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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))))))))) | (((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_1),
  inference(equality_proxy_clausification,[],[f593])).
thf(f595,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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_1),
  inference(duplicate_literal_removal,[],[f594])).
thf(f613,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_1),
  inference(forward_subsumption_resolution,[],[f595,f74])).
thf(f617,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_1),
  inference(forward_demodulation,[],[f613,f520])).
thf(f622,plain,(
  $false | spl6_1),
  inference(forward_subsumption_resolution,[],[f617,f425])).
thf(f623,plain,(
  spl6_1),
  inference(avatar_contradiction_clause,[],[f622])).
cnf(s8, plain, ~spl6_1, inference(sat_conversion,[],[f259])).
cnf(s17, plain, spl6_1, inference(sat_conversion,[],[f623])).
cnf(s18, plain, $false, inference(rat,[],[s8,s17])).
thf(f624,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s18])).
% SZS output end Proof for theBenchmark