%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, cNUMBER: ($i > $o)).
thf(func_def_1, type, cODD: ($i > $o)).
thf(func_def_2, type, cEVEN: ($i > $o)).
thf(func_def_3, type, cS: ($i > $i)).
thf(func_def_8, type, sK0: (($i > $o) > ($i > $o) > $i)).
thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_12, type, sF2: !>[X0: $tType]:(($i > ($i > X0) > X0))).
thf(func_def_14, type, sF4: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > X0 > X1 > X2))).
thf(func_def_15, type, sF5: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X1 > X0) > X1 > X2))).
thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_17, type, sF6: !>[X0: $tType, X1: $tType]:((X1 > (X1 > $i) > ($i > X0) > X0))).
thf(func_def_18, type, sF7: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > ((X0 > X2) > X1) > X1))).
thf(func_def_19, type, sF8: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
thf(func_def_20, type, sF9: !>[X0: $tType]:((X0 > (X0 > $i) > $i))).
thf(func_def_21, type, sF10: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > (X0 > X2 > X1) > X2 > X1))).
thf(f1,conjecture,(
  ((cEVEN @ c0) & ! [X0 : $i] : (((cEVEN @ X0) | (cODD @ X0)) <=> (cNUMBER @ X0)) & (cODD @ (cS @ c0)) & ! [X0 : $i] : ((cEVEN @ X0) => (cEVEN @ (cS @ (cS @ X0)))) & ! [X2 : ($i > $o),X1 : ($i > $o)] : (((X1 @ c0) & (X2 @ c0) & ! [X3 : $i] : (((X2 @ X3) & (X1 @ X3)) => ((X1 @ (cS @ X3)) & (X2 @ (cS @ X3))))) => ! [X3 : $i] : ((X1 @ X3) & (X2 @ X3))) & ! [X0 : $i] : ((cODD @ X0) => (cODD @ (cS @ (cS @ X0))))) => ! [X0 : $i] : (cNUMBER @ X0)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEVEN_ODD_4)).
thf(f2,negated_conjecture,(
  ~(((cEVEN @ c0) & ! [X0 : $i] : (((cEVEN @ X0) | (cODD @ X0)) <=> (cNUMBER @ X0)) & (cODD @ (cS @ c0)) & ! [X0 : $i] : ((cEVEN @ X0) => (cEVEN @ (cS @ (cS @ X0)))) & ! [X2 : ($i > $o),X1 : ($i > $o)] : (((X1 @ c0) & (X2 @ c0) & ! [X3 : $i] : (((X2 @ X3) & (X1 @ X3)) => ((X1 @ (cS @ X3)) & (X2 @ (cS @ X3))))) => ! [X3 : $i] : ((X1 @ X3) & (X2 @ X3))) & ! [X0 : $i] : ((cODD @ X0) => (cODD @ (cS @ (cS @ X0))))) => ! [X0 : $i] : (cNUMBER @ X0))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(((cEVEN @ c0) & ! [X0 : $i] : (((cEVEN @ X0) | (cODD @ X0)) <=> (cNUMBER @ X0)) & (cODD @ (cS @ c0)) & ! [X1 : $i] : ((cEVEN @ X1) => (cEVEN @ (cS @ (cS @ X1)))) & ! [X2 : ($i > $o),X3 : ($i > $o)] : (((X3 @ c0) & (X2 @ c0) & ! [X4 : $i] : (((X2 @ X4) & (X3 @ X4)) => ((X3 @ (cS @ X4)) & (X2 @ (cS @ X4))))) => ! [X5 : $i] : ((X3 @ X5) & (X2 @ X5))) & ! [X6 : $i] : ((cODD @ X6) => (cODD @ (cS @ (cS @ X6))))) => ! [X7 : $i] : (cNUMBER @ X7))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~((! [X1 : $i] : (($true = ((cEVEN @ X1))) => (((cEVEN @ (cS @ (cS @ X1)))) = $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X2 : ($i > $o),X3 : ($i > $o)] : ((($true = ((X3 @ c0))) & (((X2 @ c0)) = $true) & ! [X4 : $i] : ((($true = ((X3 @ X4))) & (((X2 @ X4)) = $true)) => ((((X2 @ (cS @ X4))) = $true) & (((X3 @ (cS @ X4))) = $true)))) => ! [X5 : $i] : (($true = ((X2 @ X5))) & ($true = ((X3 @ X5))))) & ! [X6 : $i] : ((((cODD @ X6)) = $true) => ($true = ((cODD @ (cS @ (cS @ X6)))))) & ! [X0 : $i] : (((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true)) <=> (((cNUMBER @ X0)) = $true)) & (((cEVEN @ c0)) = $true)) => ! [X7 : $i] : ($true = ((cNUMBER @ X7))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X7 : $i] : ($true != ((cNUMBER @ X7))) & (! [X1 : $i] : (($true != ((cEVEN @ X1))) | (((cEVEN @ (cS @ (cS @ X1)))) = $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X2 : ($i > $o),X3 : ($i > $o)] : (! [X5 : $i] : (($true = ((X2 @ X5))) & ($true = ((X3 @ X5)))) | (($true != ((X3 @ c0))) | (((X2 @ c0)) != $true) | ? [X4 : $i] : (((((X2 @ (cS @ X4))) != $true) | (((X3 @ (cS @ X4))) != $true)) & (($true = ((X3 @ X4))) & (((X2 @ X4)) = $true))))) & ! [X6 : $i] : ((((cODD @ X6)) != $true) | ($true = ((cODD @ (cS @ (cS @ X6)))))) & ! [X0 : $i] : (((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true)) <=> (((cNUMBER @ X0)) = $true)) & (((cEVEN @ c0)) = $true))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  (((cODD @ (cS @ c0))) = $true) & ! [X1 : $i] : (($true != ((cEVEN @ X1))) | (((cEVEN @ (cS @ (cS @ X1)))) = $true)) & ! [X3 : ($i > $o),X2 : ($i > $o)] : (($true != ((X3 @ c0))) | ! [X5 : $i] : (($true = ((X2 @ X5))) & ($true = ((X3 @ X5)))) | ? [X4 : $i] : (($true = ((X3 @ X4))) & (((X2 @ X4)) = $true) & ((((X2 @ (cS @ X4))) != $true) | (((X3 @ (cS @ X4))) != $true))) | (((X2 @ c0)) != $true)) & ! [X0 : $i] : (((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true)) <=> (((cNUMBER @ X0)) = $true)) & ? [X7 : $i] : ($true != ((cNUMBER @ X7))) & (((cEVEN @ c0)) = $true) & ! [X6 : $i] : ((((cODD @ X6)) != $true) | ($true = ((cODD @ (cS @ (cS @ X6))))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  (((cODD @ (cS @ c0))) = $true) & ! [X1 : $i] : (($true != ((cEVEN @ X1))) | (((cEVEN @ (cS @ (cS @ X1)))) = $true)) & ! [X3 : ($i > $o),X2 : ($i > $o)] : (($true != ((X3 @ c0))) | ! [X5 : $i] : (($true = ((X2 @ X5))) & ($true = ((X3 @ X5)))) | ? [X4 : $i] : (($true = ((X3 @ X4))) & (((X2 @ X4)) = $true) & ((((X2 @ (cS @ X4))) != $true) | (((X3 @ (cS @ X4))) != $true))) | (((X2 @ c0)) != $true)) & ! [X0 : $i] : ((((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true)) | (((cNUMBER @ X0)) != $true)) & ((((cNUMBER @ X0)) = $true) | ((((cODD @ X0)) != $true) & (((cEVEN @ X0)) != $true)))) & ? [X7 : $i] : ($true != ((cNUMBER @ X7))) & (((cEVEN @ c0)) = $true) & ! [X6 : $i] : ((((cODD @ X6)) != $true) | ($true = ((cODD @ (cS @ (cS @ X6))))))),
  inference(nnf_transformation,[],[f6])).
thf(f8,plain,(
  (((cODD @ (cS @ c0))) = $true) & ! [X1 : $i] : (($true != ((cEVEN @ X1))) | (((cEVEN @ (cS @ (cS @ X1)))) = $true)) & ! [X3 : ($i > $o),X2 : ($i > $o)] : (($true != ((X3 @ c0))) | ! [X5 : $i] : (($true = ((X2 @ X5))) & ($true = ((X3 @ X5)))) | ? [X4 : $i] : (($true = ((X3 @ X4))) & (((X2 @ X4)) = $true) & ((((X2 @ (cS @ X4))) != $true) | (((X3 @ (cS @ X4))) != $true))) | (((X2 @ c0)) != $true)) & ! [X0 : $i] : (((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true) | (((cNUMBER @ X0)) != $true)) & ((((cNUMBER @ X0)) = $true) | ((((cODD @ X0)) != $true) & (((cEVEN @ X0)) != $true)))) & ? [X7 : $i] : ($true != ((cNUMBER @ X7))) & (((cEVEN @ c0)) = $true) & ! [X6 : $i] : ((((cODD @ X6)) != $true) | ($true = ((cODD @ (cS @ (cS @ X6))))))),
  inference(flattening,[],[f7])).
thf(f9,plain,(
  (((cODD @ (cS @ c0))) = $true) & ! [X0 : $i] : ((((cEVEN @ X0)) != $true) | (((cEVEN @ (cS @ (cS @ X0)))) = $true)) & ! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X1 @ c0)) != $true) | ! [X3 : $i] : ((((X2 @ X3)) = $true) & (((X1 @ X3)) = $true)) | ? [X4 : $i] : (($true = ((X1 @ X4))) & (((X2 @ X4)) = $true) & ((((X2 @ (cS @ X4))) != $true) | (((X1 @ (cS @ X4))) != $true))) | (((X2 @ c0)) != $true)) & ! [X5 : $i] : ((($true = ((cODD @ X5))) | (((cEVEN @ X5)) = $true) | ($true != ((cNUMBER @ X5)))) & (($true = ((cNUMBER @ X5))) | (($true != ((cODD @ X5))) & (((cEVEN @ X5)) != $true)))) & ? [X6 : $i] : ($true != ((cNUMBER @ X6))) & (((cEVEN @ c0)) = $true) & ! [X7 : $i] : ((((cODD @ X7)) != $true) | ($true = ((cODD @ (cS @ (cS @ X7))))))),
  inference(rectify,[],[f8])).
thf(f10,plain,(
  (((cODD @ (cS @ c0))) = $true) & ! [X0 : $i] : ((((cEVEN @ X0)) != $true) | (((cEVEN @ (cS @ (cS @ X0)))) = $true)) & ! [X1 : ($i > $o),X2 : ($i > $o)] : ((((X1 @ c0)) != $true) | ! [X3 : $i] : ((((X2 @ X3)) = $true) & (((X1 @ X3)) = $true)) | ((((X1 @ (sK0 @ X2 @ X1))) = $true) & (((X2 @ (sK0 @ X2 @ X1))) = $true) & ((((X2 @ (cS @ (sK0 @ X2 @ X1)))) != $true) | ($true != ((X1 @ (cS @ (sK0 @ X2 @ X1))))))) | (((X2 @ c0)) != $true)) & ! [X5 : $i] : ((($true = ((cODD @ X5))) | (((cEVEN @ X5)) = $true) | ($true != ((cNUMBER @ X5)))) & (($true = ((cNUMBER @ X5))) | (($true != ((cODD @ X5))) & (((cEVEN @ X5)) != $true)))) & ($true != ((cNUMBER @ sK1))) & (((cEVEN @ c0)) = $true) & ! [X7 : $i] : ((((cODD @ X7)) != $true) | ($true = ((cODD @ (cS @ (cS @ X7))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X4,$thf(sK0 @ X2 @ X1)),skolemize(X6,$thf(sK1))],[f9])).
thf(f11,plain,(
  ( ! [X7 : $i] : ((((cODD @ X7)) != $true) | ($true = ((cODD @ (cS @ (cS @ X7)))))) )),
  inference(cnf_transformation,[],[f10])).
thf(f12,plain,(
  (((cEVEN @ c0)) = $true)),
  inference(cnf_transformation,[],[f10])).
thf(f13,plain,(
  ($true != ((cNUMBER @ sK1)))),
  inference(cnf_transformation,[],[f10])).
thf(f14,plain,(
  ( ! [X5 : $i] : ((((cEVEN @ X5)) != $true) | ($true = ((cNUMBER @ X5)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f15,plain,(
  ( ! [X5 : $i] : (($true != ((cODD @ X5))) | ($true = ((cNUMBER @ X5)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f16,plain,(
  ( ! [X5 : $i] : (($true != ((cNUMBER @ X5))) | (((cEVEN @ X5)) = $true) | ($true = ((cODD @ X5)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f17,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : (($true != ((X1 @ (cS @ (sK0 @ X2 @ X1))))) | (((X1 @ c0)) != $true) | (((X2 @ c0)) != $true) | (((X2 @ (cS @ (sK0 @ X2 @ X1)))) != $true) | (((X1 @ X3)) = $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f20,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : (($true != ((X1 @ (cS @ (sK0 @ X2 @ X1))))) | (((X2 @ X3)) = $true) | (((X1 @ c0)) != $true) | (((X2 @ (cS @ (sK0 @ X2 @ X1)))) != $true) | (((X2 @ c0)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f21,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((X2 @ c0)) != $true) | (((X2 @ X3)) = $true) | (((X2 @ (sK0 @ X2 @ X1))) = $true) | (((X1 @ c0)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f22,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((X2 @ c0)) != $true) | (((X1 @ (sK0 @ X2 @ X1))) = $true) | (((X2 @ X3)) = $true) | (((X1 @ c0)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f23,plain,(
  ( ! [X0 : $i] : ((((cEVEN @ X0)) != $true) | (((cEVEN @ (cS @ (cS @ X0)))) = $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f24,plain,(
  (((cODD @ (cS @ c0))) = $true)),
  inference(cnf_transformation,[],[f10])).
thf(f27,plain,(
  (((cNUMBER @ c0)) = $true) | ($true != $true)),
  inference(constrained_superposition,[],[f14,f12])).
thf(f28,plain,(
  (((cNUMBER @ c0)) = $true)),
  inference(trivial_inequality_removal,[],[f27])).
thf(f29,plain,(
  (((cNUMBER @ (cS @ c0))) = $true) | ($true != $true)),
  inference(constrained_superposition,[],[f15,f24])).
thf(f30,plain,(
  (((cNUMBER @ (cS @ c0))) = $true)),
  inference(trivial_inequality_removal,[],[f29])).
thf(f105,definition,(
  spl3_3 <=> ! [X0 : $i] : (((cNUMBER @ X0)) = $true)),
  introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
thf(f106,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ X0)) = $true)) ) | ~spl3_3),
  inference(avatar_component_clause,[],[f105])).
thf(f113,plain,(
  ($true != $true) | ~spl3_3),
  inference(constrained_superposition,[],[f13,f106])).
thf(f117,plain,(
  $false | ~spl3_3),
  inference(trivial_inequality_removal,[],[f113])).
thf(f118,plain,(
  ~spl3_3),
  inference(avatar_contradiction_clause,[],[f117])).
thf(f260,plain,(
  ( ! [X2 : ($i > $o),X3 : $i] : (($true != (((^[Y0 : $i]: ($true)) @ (cS @ (sK0 @ X2 @ (^[Y0 : $i]: ($true))))))) | (((X2 @ c0)) != $true) | (((X2 @ X3)) = $true) | ($true != ((X2 @ (cS @ (sK0 @ X2 @ (^[Y0 : $i]: ($true))))))) | ((((^[Y0 : $i]: ($true)) @ c0)) != $true)) )),
  inference(imitation,[],[f20])).
thf(f261,plain,(
  ( ! [X2 : ($i > $o),X3 : $i] : (($true != ((X2 @ (cS @ (sK0 @ X2 @ (^[Y0 : $i]: ($true))))))) | (((X2 @ c0)) != $true) | ($true != $true) | (((X2 @ X3)) = $true) | ($true != $true)) )),
  inference(beta-eta_normalization,[],[f260])).
thf(f262,plain,(
  ( ! [X2 : ($i > $o),X3 : $i] : (($true != $true) | ($true != ((X2 @ (cS @ (sK0 @ X2 @ (^[Y0 : $i]: ($true))))))) | (((X2 @ c0)) != $true) | (((X2 @ X3)) = $true)) )),
  inference(duplicate_literal_removal,[],[f261])).
thf(f263,plain,(
  ( ! [X2 : ($i > $o),X3 : $i] : (($true != ((X2 @ (cS @ (sK0 @ X2 @ (^[Y0 : $i]: ($true))))))) | (((X2 @ X3)) = $true) | (((X2 @ c0)) != $true)) )),
  inference(trivial_inequality_removal,[],[f262])).
thf(f354,definition,(
  ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : (X0 > X1),X4 : (X3 > X0),X5 : X3] : ((((sF5 @ X0 @ X3 @ X1 @ X2 @ X4 @ X5)) = ((X2 @ (X4 @ X5))))) )),
  introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
thf(f360,plain,(
  ( ! [X0 : $tType,X2 : ($i > X0),X3 : $i,X1 : (X0 > $o),X4 : ($i > $o)] : (($true != ((X4 @ c0))) | ($true = ((sF5 @ X0 @ $i @ $o @ X1 @ X2 @ X3))) | (((X1 @ (X2 @ c0))) != $true) | (((sF5 @ X0 @ $i @ $o @ X1 @ X2 @ (sK0 @ (sF5 @ X0 @ $i @ $o @ X1 @ X2) @ X4))) = $true)) )),
  inference(constrained_superposition,[],[f21,f354])).
thf(f361,plain,(
  ( ! [X0 : $tType,X2 : ($i > X0),X3 : ($i > $o),X1 : (X0 > $o),X4 : $i] : ((((X3 @ (sK0 @ (sF5 @ X0 @ $i @ $o @ X1 @ X2) @ X3))) = $true) | ($true != ((X3 @ c0))) | (((X1 @ (X2 @ c0))) != $true) | ($true = ((sF5 @ X0 @ $i @ $o @ X1 @ X2 @ X4)))) )),
  inference(constrained_superposition,[],[f22,f354])).
thf(f371,plain,(
  ( ! [X0 : $tType,X2 : ($i > X0),X3 : $i,X1 : (X0 > $o),X4 : ($i > $o)] : (($true != ((X4 @ c0))) | ($true = ((X1 @ (X2 @ X3)))) | (((X1 @ (X2 @ c0))) != $true) | (((sF5 @ X0 @ $i @ $o @ X1 @ X2 @ (sK0 @ (sF5 @ X0 @ $i @ $o @ X1 @ X2) @ X4))) = $true)) )),
  inference(forward_demodulation,[],[f360,f354])).
thf(f374,plain,(
  ( ! [X0 : $tType,X2 : ($i > X0),X3 : ($i > $o),X1 : (X0 > $o),X4 : $i] : ((((X1 @ (X2 @ c0))) != $true) | ($true != ((X3 @ c0))) | (((X3 @ (sK0 @ (sF5 @ X0 @ $i @ $o @ X1 @ X2) @ X3))) = $true) | ($true = ((X1 @ (X2 @ X4))))) )),
  inference(forward_demodulation,[],[f361,f354])).
thf(f380,plain,(
  ( ! [X0 : $tType,X2 : ($i > X0),X3 : $i,X1 : (X0 > $o),X4 : ($i > $o)] : ((((X1 @ (X2 @ c0))) != $true) | ($true = ((X1 @ (X2 @ (sK0 @ (sF5 @ X0 @ $i @ $o @ X1 @ X2) @ X4))))) | ($true != ((X4 @ c0))) | ($true = ((X1 @ (X2 @ X3))))) )),
  inference(forward_demodulation,[],[f371,f354])).
thf(f539,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))) = $true) | ($true = ((cNUMBER @ (cS @ X1)))) | (((X0 @ c0)) != $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f374,f30])).
thf(f547,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))) = $true) | (((X0 @ c0)) != $true) | ($true = ((cNUMBER @ (cS @ X1))))) )),
  inference(trivial_inequality_removal,[],[f539])).
thf(f552,definition,(
  spl3_19 <=> ! [X1 : $i] : ($true = ((cNUMBER @ (cS @ X1))))),
  introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition])).
thf(f553,plain,(
  ( ! [X1 : $i] : (($true = ((cNUMBER @ (cS @ X1))))) ) | ~spl3_19),
  inference(avatar_component_clause,[],[f552])).
thf(f555,definition,(
  spl3_20 <=> ! [X0 : ($i > $o)] : ((((X0 @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))) = $true) | (((X0 @ c0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition])).
thf(f556,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | (((X0 @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))) = $true)) ) | ~spl3_20),
  inference(avatar_component_clause,[],[f555])).
thf(f557,plain,(
  spl3_19 | spl3_20),
  inference(avatar_split_clause,[],[f547,f555,f552])).
thf(f575,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ c0)) != $true) | ($true != $true) | (((cNUMBER @ X0)) = $true)) ) | ~spl3_19),
  inference(constrained_superposition,[],[f263,f553])).
thf(f580,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ c0)) != $true) | (((cNUMBER @ X0)) = $true)) ) | ~spl3_19),
  inference(trivial_inequality_removal,[],[f575])).
thf(f586,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ X0)) = $true)) ) | ~spl3_19),
  inference(forward_subsumption_resolution,[],[f580,f28])).
thf(f589,plain,(
  spl3_3 | ~spl3_19),
  inference(avatar_split_clause,[],[f586,f552,f105])).
thf(f652,plain,(
  ($true != $true) | ($true = ((cNUMBER @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ~spl3_20),
  inference(constrained_superposition,[],[f556,f28])).
thf(f657,plain,(
  ($true = ((cNUMBER @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ~spl3_20),
  inference(trivial_inequality_removal,[],[f652])).
thf(f670,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ c0)) != $true) | ($true = ((cNUMBER @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))))) | ($true = ((cNUMBER @ (cS @ X1)))) | ($true != $true)) )),
  inference(constrained_superposition,[],[f380,f30])).
thf(f679,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((cNUMBER @ (cS @ X1)))) | ($true = ((cNUMBER @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))))) | (((X0 @ c0)) != $true)) )),
  inference(trivial_inequality_removal,[],[f670])).
thf(f688,definition,(
  spl3_25 <=> ! [X0 : ($i > $o)] : (($true = ((cNUMBER @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0))))) | (((X0 @ c0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl3_25])],[avatar_definition])).
thf(f689,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | ($true = ((cNUMBER @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ X0)))))) ) | ~spl3_25),
  inference(avatar_component_clause,[],[f688])).
thf(f690,plain,(
  spl3_25 | spl3_19),
  inference(avatar_split_clause,[],[f679,f552,f688])).
thf(f742,plain,(
  ($true = ((cODD @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ($true = ((cEVEN @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ($true != $true) | ~spl3_20),
  inference(constrained_superposition,[],[f16,f657])).
thf(f743,plain,(
  ($true = ((cEVEN @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ($true = ((cODD @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ~spl3_20),
  inference(trivial_inequality_removal,[],[f742])).
thf(f745,definition,(
  spl3_30 <=> ($true = ((cODD @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))),
  introduced(definition,[new_symbols(definition,[spl3_30])],[avatar_definition])).
thf(f747,plain,(
  ($true = ((cODD @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ~spl3_30),
  inference(avatar_component_clause,[],[f745])).
thf(f749,definition,(
  spl3_31 <=> ($true = ((cEVEN @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))),
  introduced(definition,[new_symbols(definition,[spl3_31])],[avatar_definition])).
thf(f751,plain,(
  ($true = ((cEVEN @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) | ~spl3_31),
  inference(avatar_component_clause,[],[f749])).
thf(f752,plain,(
  spl3_30 | spl3_31 | ~spl3_20),
  inference(avatar_split_clause,[],[f743,f555,f749,f745])).
thf(f755,plain,(
  ($true != $true) | ($true = ((cODD @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))))) | ~spl3_30),
  inference(constrained_superposition,[],[f11,f747])).
thf(f757,plain,(
  ($true = ((cODD @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))))) | ~spl3_30),
  inference(trivial_inequality_removal,[],[f755])).
thf(f808,plain,(
  (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) = $true) | ($true != $true) | ~spl3_30),
  inference(constrained_superposition,[],[f15,f757])).
thf(f810,plain,(
  (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) = $true) | ~spl3_30),
  inference(trivial_inequality_removal,[],[f808])).
thf(f1016,plain,(
  ($true = ((cNUMBER @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) | ($true != $true) | ~spl3_25),
  inference(constrained_superposition,[],[f689,f28])).
thf(f1019,plain,(
  ($true = ((cNUMBER @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) | ~spl3_25),
  inference(trivial_inequality_removal,[],[f1016])).
thf(f1024,plain,(
  ( ! [X0 : $i] : (($true != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ X0)) = $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true) | (((cNUMBER @ c0)) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true)) ) | ~spl3_25),
  inference(constrained_superposition,[],[f20,f1019])).
thf(f1025,plain,(
  ( ! [X0 : $i] : ((((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true) | (((cNUMBER @ c0)) != $true) | (((cNUMBER @ X0)) = $true) | ($true != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true)) ) | ~spl3_25),
  inference(constrained_superposition,[],[f17,f1019])).
thf(f1026,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ c0)) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true) | (((cNUMBER @ X0)) = $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true)) ) | ~spl3_25),
  inference(trivial_inequality_removal,[],[f1025])).
thf(f1028,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ c0)) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ X0)) = $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true)) ) | ~spl3_25),
  inference(trivial_inequality_removal,[],[f1024])).
thf(f1029,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ X0)) = $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true)) ) | ~spl3_25),
  inference(forward_subsumption_resolution,[],[f1026,f28])).
thf(f1039,plain,(
  ( ! [X0 : $i] : ((((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ X0)) = $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true)) ) | ~spl3_25),
  inference(forward_subsumption_resolution,[],[f1028,f28])).
thf(f1040,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) != $true) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true) | (((cNUMBER @ X0)) = $true)) ) | ~spl3_25),
  inference(forward_demodulation,[],[f1029,f354])).
thf(f1041,plain,(
  ( ! [X0 : $i] : ((((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))) != $true) | ($true = ((cNUMBER @ (cS @ X0)))) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true)) ) | ~spl3_25),
  inference(forward_demodulation,[],[f1039,f354])).
thf(f1043,plain,(
  ( ! [X0 : $i] : (($true = ((cNUMBER @ (cS @ X0)))) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true) | (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) != $true)) ) | ~spl3_25),
  inference(forward_demodulation,[],[f1041,f354])).
thf(f1045,plain,(
  ( ! [X0 : $i] : (($true = ((cNUMBER @ (cS @ X0)))) | (((sF5 @ $i @ $i @ $o @ cNUMBER @ cS @ c0)) != $true)) ) | (~spl3_25 | ~spl3_30)),
  inference(forward_subsumption_resolution,[],[f1043,f810])).
thf(f1047,plain,(
  ( ! [X0 : $i] : (($true = ((cNUMBER @ (cS @ X0)))) | (((cNUMBER @ (cS @ c0))) != $true)) ) | (~spl3_25 | ~spl3_30)),
  inference(forward_demodulation,[],[f1045,f354])).
thf(f1049,plain,(
  ( ! [X0 : $i] : (($true = ((cNUMBER @ (cS @ X0))))) ) | (~spl3_25 | ~spl3_30)),
  inference(forward_subsumption_resolution,[],[f1047,f30])).
thf(f1050,plain,(
  spl3_19 | ~spl3_25 | ~spl3_30),
  inference(avatar_split_clause,[],[f1049,f745,f688,f552])).
thf(f1052,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ X0)) = $true) | (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) != $true) | (((cNUMBER @ (cS @ c0))) != $true)) ) | ~spl3_25),
  inference(forward_demodulation,[],[f1040,f354])).
thf(f1054,plain,(
  ( ! [X0 : $i] : ((((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) != $true) | (((cNUMBER @ X0)) = $true)) ) | ~spl3_25),
  inference(forward_subsumption_resolution,[],[f1052,f30])).
thf(f1056,definition,(
  spl3_37 <=> (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl3_37])],[avatar_definition])).
thf(f1058,plain,(
  (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) != $true) | spl3_37),
  inference(avatar_component_clause,[],[f1056])).
thf(f1060,plain,(
  ~spl3_37 | spl3_3 | ~spl3_25),
  inference(avatar_split_clause,[],[f1054,f688,f105,f1056])).
thf(f1061,plain,(
  ($true != $true) | ($true = ((cEVEN @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))))) | ~spl3_31),
  inference(constrained_superposition,[],[f23,f751])).
thf(f1063,plain,(
  ($true = ((cEVEN @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER)))))) | ~spl3_31),
  inference(trivial_inequality_removal,[],[f1061])).
thf(f1291,plain,(
  (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) = $true) | ($true != $true) | ~spl3_31),
  inference(constrained_superposition,[],[f14,f1063])).
thf(f1293,plain,(
  (((cNUMBER @ (cS @ (cS @ (sK0 @ (sF5 @ $i @ $i @ $o @ cNUMBER @ cS) @ cNUMBER))))) = $true) | ~spl3_31),
  inference(trivial_inequality_removal,[],[f1291])).
thf(f1294,plain,(
  $false | (~spl3_31 | spl3_37)),
  inference(forward_subsumption_resolution,[],[f1293,f1058])).
thf(f1295,plain,(
  ~spl3_31 | spl3_37),
  inference(avatar_contradiction_clause,[],[f1294])).
cnf(s3, plain, ~spl3_3, inference(sat_conversion,[],[f118])).
cnf(s14, plain, spl3_19 | spl3_20, inference(sat_conversion,[],[f557])).
cnf(s16, plain, spl3_3 | ~spl3_19, inference(sat_conversion,[],[f589])).
cnf(s19, plain, spl3_19 | spl3_25, inference(sat_conversion,[],[f690])).
cnf(s24, plain, ~spl3_20 | spl3_30 | spl3_31, inference(sat_conversion,[],[f752])).
cnf(s30, plain, spl3_19 | ~spl3_25 | ~spl3_30, inference(sat_conversion,[],[f1050])).
cnf(s32, plain, spl3_3 | ~spl3_25 | ~spl3_37, inference(sat_conversion,[],[f1060])).
cnf(s37, plain, ~spl3_31 | spl3_37, inference(sat_conversion,[],[f1295])).
cnf(s39, plain, ~spl3_19, inference(rat,[],[s16,s3])).
cnf(s47, plain, spl3_25, inference(rat,[],[s19,s39])).
cnf(s48, plain, spl3_20, inference(rat,[],[s14,s39])).
cnf(s51, plain, ~spl3_37, inference(rat,[],[s32,s3,s47])).
cnf(s52, plain, ~spl3_30, inference(rat,[],[s30,s39,s47])).
cnf(s54, plain, ~spl3_31, inference(rat,[],[s37,s51])).
cnf(s55, plain, $false, inference(rat,[],[s24,s48,s54,s52])).
thf(f1296,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s55])).
% SZS output end Proof for theBenchmark