%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, a: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, sK0: (a > a > $o)).
thf(func_def_4, type, sK1: ((a > $o) > a)).
thf(func_def_5, type, sK2: (a > (a > $o) > a)).
thf(func_def_6, type, sK3: (a > a)).
thf(func_def_7, type, sF4: (a > a > $o)).
thf(func_def_8, type, sF5: ((a > $o) > a)).
thf(func_def_9, type, sF6: ((a > $o) > a > $o)).
thf(func_def_10, type, sF7: (a > (a > $o) > $o)).
thf(func_def_11, type, sF8: ((a > $o) > a > a)).
thf(func_def_12, type, sF9: (a > (a > $o) > $o)).
thf(func_def_13, type, sF10: (a > (a > $o) > $o)).
thf(func_def_14, type, sF11: (a > (a > $o) > $o)).
thf(func_def_15, type, sF12: (a > a)).
thf(func_def_16, type, sF13: (a > a > $o)).
thf(func_def_17, type, sF14: (a > $o)).
thf(func_def_18, type, sF15: (a > $o)).
thf(func_def_19, type, vNOT: ($o > $o)).
thf(func_def_20, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_21, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X5 : a] : ((X2 @ X5) => (X0 @ X5 @ (X1 @ X2))) & ! [X3 : a] : (! [X4 : a] : (((X2 @ X4) & (X2 @ X4)) => (X0 @ X4 @ X3)) => ((X0 @ (X1 @ X2) @ X3) & (X0 @ (X1 @ X2) @ X3))) & ! [X5 : a] : ((X2 @ X5) => (X0 @ X5 @ (X1 @ X2)))) & ! [X7 : a,X5 : a,X6 : a] : (((X0 @ X6 @ X7) & (X0 @ X7 @ X5)) => (X0 @ X6 @ X5))) => ! [X8 : (a > a)] : ((! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X0 @ (X8 @ X6) @ (X8 @ X7))) & ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X0 @ (X8 @ X6) @ (X8 @ X7)))) => ? [X9 : a] : ((X0 @ (X8 @ X9) @ X9) & (X0 @ X9 @ (X8 @ X9)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM145_A_pme)).
thf(f2,negated_conjecture,(
  ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X5 : a] : ((X2 @ X5) => (X0 @ X5 @ (X1 @ X2))) & ! [X3 : a] : (! [X4 : a] : (((X2 @ X4) & (X2 @ X4)) => (X0 @ X4 @ X3)) => ((X0 @ (X1 @ X2) @ X3) & (X0 @ (X1 @ X2) @ X3))) & ! [X5 : a] : ((X2 @ X5) => (X0 @ X5 @ (X1 @ X2)))) & ! [X7 : a,X5 : a,X6 : a] : (((X0 @ X6 @ X7) & (X0 @ X7 @ X5)) => (X0 @ X6 @ X5))) => ! [X8 : (a > a)] : ((! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X0 @ (X8 @ X6) @ (X8 @ X7))) & ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X0 @ (X8 @ X6) @ (X8 @ X7)))) => ? [X9 : a] : ((X0 @ (X8 @ X9) @ X9) & (X0 @ X9 @ (X8 @ X9)))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X3 : a] : ((X2 @ X3) => (X0 @ X3 @ (X1 @ X2))) & ! [X4 : a] : (! [X5 : a] : (((X2 @ X5) & (X2 @ X5)) => (X0 @ X5 @ X4)) => ((X0 @ (X1 @ X2) @ X4) & (X0 @ (X1 @ X2) @ X4))) & ! [X6 : a] : ((X2 @ X6) => (X0 @ X6 @ (X1 @ X2)))) & ! [X7 : a,X8 : a,X9 : a] : (((X0 @ X9 @ X7) & (X0 @ X7 @ X8)) => (X0 @ X9 @ X8))) => ! [X10 : (a > a)] : ((! [X11 : a,X12 : a] : ((X0 @ X12 @ X11) => (X0 @ (X10 @ X12) @ (X10 @ X11))) & ! [X13 : a,X14 : a] : ((X0 @ X14 @ X13) => (X0 @ (X10 @ X14) @ (X10 @ X13)))) => ? [X15 : a] : ((X0 @ (X10 @ X15) @ X15) & (X0 @ X15 @ (X10 @ X15)))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X6 : a] : (($true = ((X2 @ X6))) => ($true = ((X0 @ X6 @ (X1 @ X2))))) & ! [X4 : a] : (! [X5 : a] : (((((X2 @ X5)) = $true) & (((X2 @ X5)) = $true)) => (((X0 @ X5 @ X4)) = $true)) => ((((X0 @ (X1 @ X2) @ X4)) = $true) & (((X0 @ (X1 @ X2) @ X4)) = $true))) & ! [X3 : a] : (($true = ((X2 @ X3))) => (((X0 @ X3 @ (X1 @ X2))) = $true))) & ! [X8 : a,X9 : a,X7 : a] : ((($true = ((X0 @ X9 @ X7))) & ($true = ((X0 @ X7 @ X8)))) => ($true = ((X0 @ X9 @ X8))))) => ! [X10 : (a > a)] : ((! [X11 : a,X12 : a] : (($true = ((X0 @ X12 @ X11))) => (((X0 @ (X10 @ X12) @ (X10 @ X11))) = $true)) & ! [X13 : a,X14 : a] : (($true = ((X0 @ X14 @ X13))) => ($true = ((X0 @ (X10 @ X14) @ (X10 @ X13)))))) => ? [X15 : a] : ((((X0 @ (X10 @ X15) @ X15)) = $true) & (((X0 @ X15 @ (X10 @ X15))) = $true))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X10 : (a > a)] : (! [X15 : a] : ((((X0 @ (X10 @ X15) @ X15)) != $true) | (((X0 @ X15 @ (X10 @ X15))) != $true)) & (! [X11 : a,X12 : a] : ((((X0 @ (X10 @ X12) @ (X10 @ X11))) = $true) | ($true != ((X0 @ X12 @ X11)))) & ! [X13 : a,X14 : a] : (($true != ((X0 @ X14 @ X13))) | ($true = ((X0 @ (X10 @ X14) @ (X10 @ X13))))))) & (! [X2 : (a > $o)] : (! [X6 : a] : (($true != ((X2 @ X6))) | ($true = ((X0 @ X6 @ (X1 @ X2))))) & ! [X4 : a] : (((((X0 @ (X1 @ X2) @ X4)) = $true) & (((X0 @ (X1 @ X2) @ X4)) = $true)) | ? [X5 : a] : ((((X0 @ X5 @ X4)) != $true) & ((((X2 @ X5)) = $true) & (((X2 @ X5)) = $true)))) & ! [X3 : a] : ((((X0 @ X3 @ (X1 @ X2))) = $true) | ($true != ((X2 @ X3))))) & ! [X8 : a,X9 : a,X7 : a] : (($true = ((X0 @ X9 @ X8))) | (($true != ((X0 @ X9 @ X7))) | ($true != ((X0 @ X7 @ X8)))))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (! [X8 : a,X7 : a,X9 : a] : (($true != ((X0 @ X7 @ X8))) | ($true = ((X0 @ X9 @ X8))) | ($true != ((X0 @ X9 @ X7)))) & ! [X2 : (a > $o)] : (! [X3 : a] : ((((X0 @ X3 @ (X1 @ X2))) = $true) | ($true != ((X2 @ X3)))) & ! [X6 : a] : (($true != ((X2 @ X6))) | ($true = ((X0 @ X6 @ (X1 @ X2))))) & ! [X4 : a] : (? [X5 : a] : ((((X2 @ X5)) = $true) & (((X0 @ X5 @ X4)) != $true) & (((X2 @ X5)) = $true)) | ((((X0 @ (X1 @ X2) @ X4)) = $true) & (((X0 @ (X1 @ X2) @ X4)) = $true)))) & ? [X10 : (a > a)] : (! [X13 : a,X14 : a] : (($true != ((X0 @ X14 @ X13))) | ($true = ((X0 @ (X10 @ X14) @ (X10 @ X13))))) & ! [X11 : a,X12 : a] : ((((X0 @ (X10 @ X12) @ (X10 @ X11))) = $true) | ($true != ((X0 @ X12 @ X11)))) & ! [X15 : a] : ((((X0 @ (X10 @ X15) @ X15)) != $true) | (((X0 @ X15 @ (X10 @ X15))) != $true))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (! [X2 : a,X3 : a,X4 : a] : (($true != ((X0 @ X3 @ X2))) | (((X0 @ X4 @ X2)) = $true) | (((X0 @ X4 @ X3)) != $true)) & ! [X5 : (a > $o)] : (! [X6 : a] : (($true = ((X0 @ X6 @ (X1 @ X5)))) | ($true != ((X5 @ X6)))) & ! [X7 : a] : (($true != ((X5 @ X7))) | ($true = ((X0 @ X7 @ (X1 @ X5))))) & ! [X8 : a] : (? [X9 : a] : ((((X5 @ X9)) = $true) & ($true != ((X0 @ X9 @ X8))) & (((X5 @ X9)) = $true)) | (($true = ((X0 @ (X1 @ X5) @ X8))) & ($true = ((X0 @ (X1 @ X5) @ X8)))))) & ? [X10 : (a > a)] : (! [X11 : a,X12 : a] : (($true != ((X0 @ X12 @ X11))) | (((X0 @ (X10 @ X12) @ (X10 @ X11))) = $true)) & ! [X13 : a,X14 : a] : (($true = ((X0 @ (X10 @ X14) @ (X10 @ X13)))) | ($true != ((X0 @ X14 @ X13)))) & ! [X15 : a] : ((((X0 @ (X10 @ X15) @ X15)) != $true) | (((X0 @ X15 @ (X10 @ X15))) != $true))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X2 : a,X3 : a,X4 : a] : (($true != ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X4 @ X2))) | (((sK0 @ X4 @ X3)) != $true)) & ! [X5 : (a > $o)] : (! [X6 : a] : ((((sK0 @ X6 @ (sK1 @ X5))) = $true) | ($true != ((X5 @ X6)))) & ! [X7 : a] : (($true != ((X5 @ X7))) | (((sK0 @ X7 @ (sK1 @ X5))) = $true)) & ! [X8 : a] : ((($true = ((X5 @ (sK2 @ X8 @ X5)))) & ($true != ((sK0 @ (sK2 @ X8 @ X5) @ X8))) & ($true = ((X5 @ (sK2 @ X8 @ X5))))) | ((((sK0 @ (sK1 @ X5) @ X8)) = $true) & (((sK0 @ (sK1 @ X5) @ X8)) = $true)))) & (! [X11 : a,X12 : a] : ((((sK0 @ X12 @ X11)) != $true) | (((sK0 @ (sK3 @ X12) @ (sK3 @ X11))) = $true)) & ! [X13 : a,X14 : a] : (($true = ((sK0 @ (sK3 @ X14) @ (sK3 @ X13)))) | ($true != ((sK0 @ X14 @ X13)))) & ! [X15 : a] : (($true != ((sK0 @ (sK3 @ X15) @ X15))) | (((sK0 @ X15 @ (sK3 @ X15))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X9,$thf(sK2 @ X8 @ X5)),skolemize(X10,$thf(sK3))],[f7])).
thf(f9,plain,(
  ( ! [X15 : a] : (($true != ((sK0 @ (sK3 @ X15) @ X15))) | (((sK0 @ X15 @ (sK3 @ X15))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X11 : a,X12 : a] : ((((sK0 @ X12 @ X11)) != $true) | (((sK0 @ (sK3 @ X12) @ (sK3 @ X11))) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f15,plain,(
  ( ! [X8 : a,X5 : (a > $o)] : (($true != ((sK0 @ (sK2 @ X8 @ X5) @ X8))) | (((sK0 @ (sK1 @ X5) @ X8)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f17,plain,(
  ( ! [X8 : a,X5 : (a > $o)] : (($true = ((X5 @ (sK2 @ X8 @ X5)))) | (((sK0 @ (sK1 @ X5) @ X8)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f18,plain,(
  ( ! [X7 : a,X5 : (a > $o)] : (($true != ((X5 @ X7))) | (((sK0 @ X7 @ (sK1 @ X5))) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f20,plain,(
  ( ! [X2 : a,X3 : a,X4 : a] : (($true != ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X4 @ X2))) | (((sK0 @ X4 @ X3)) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f23,definition,(
  ( ! [X2 : a,X3 : a] : ((((sF4 @ X2 @ X3)) = ((sK0 @ X3 @ X2)))) )),
  introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
thf(f24,plain,(
  ( ! [X2 : a,X3 : a] : ((((sK0 @ X3 @ X2)) = ((sF4 @ X2 @ X3)))) )),
  inference(reorient_equations,[],[f23])).
thf(f25,plain,(
  ( ! [X2 : a,X3 : a,X4 : a] : (($true != ((sF4 @ X3 @ X4))) | ($true != ((sF4 @ X2 @ X3))) | (((sF4 @ X2 @ X4)) = $true)) )),
  inference(definition_folding,[],[f20,f24,f24,f24])).
thf(f26,definition,(
  ( ! [X5 : (a > $o)] : ((((sF5 @ X5)) = ((sK1 @ X5)))) )),
  introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
thf(f27,definition,(
  ( ! [X6 : a,X5 : (a > $o)] : ((((sF6 @ X5 @ X6)) = ((sK0 @ X6 @ (sF5 @ X5))))) )),
  introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
thf(f28,definition,(
  ( ! [X6 : a,X5 : (a > $o)] : ((((sF7 @ X6 @ X5)) = ((X5 @ X6)))) )),
  introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
thf(f30,plain,(
  ( ! [X7 : a,X5 : (a > $o)] : ((((sF7 @ X7 @ X5)) != $true) | (((sF6 @ X5 @ X7)) = $true)) )),
  inference(definition_folding,[],[f18,f27,f26,f28])).
thf(f31,definition,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sF8 @ X5 @ X8)) = ((sK2 @ X8 @ X5)))) )),
  introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
thf(f32,definition,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sF9 @ X8 @ X5)) = ((X5 @ (sF8 @ X5 @ X8))))) )),
  introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
thf(f33,definition,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sF10 @ X8 @ X5)) = ((sK0 @ (sF5 @ X5) @ X8)))) )),
  introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
thf(f34,plain,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sK0 @ (sF5 @ X5) @ X8)) = ((sF10 @ X8 @ X5)))) )),
  inference(reorient_equations,[],[f33])).
thf(f35,plain,(
  ( ! [X8 : a,X5 : (a > $o)] : (($true = ((sF10 @ X8 @ X5))) | ($true = ((sF9 @ X8 @ X5)))) )),
  inference(definition_folding,[],[f17,f34,f26,f32,f31])).
thf(f37,definition,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sF11 @ X8 @ X5)) = ((sK0 @ (sF8 @ X5 @ X8) @ X8)))) )),
  introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
thf(f38,plain,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sK0 @ (sF8 @ X5 @ X8) @ X8)) = ((sF11 @ X8 @ X5)))) )),
  inference(reorient_equations,[],[f37])).
thf(f39,plain,(
  ( ! [X8 : a,X5 : (a > $o)] : ((((sF11 @ X8 @ X5)) != $true) | ($true = ((sF10 @ X8 @ X5)))) )),
  inference(definition_folding,[],[f15,f34,f26,f38,f31])).
thf(f43,definition,(
  ( ! [X12 : a] : ((((sF12 @ X12)) = ((sK3 @ X12)))) )),
  introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
thf(f44,plain,(
  ( ! [X12 : a] : ((((sK3 @ X12)) = ((sF12 @ X12)))) )),
  inference(reorient_equations,[],[f43])).
thf(f45,definition,(
  ( ! [X11 : a,X12 : a] : ((((sF13 @ X11 @ X12)) = ((sK0 @ (sF12 @ X12) @ (sF12 @ X11))))) )),
  introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
thf(f46,plain,(
  ( ! [X11 : a,X12 : a] : ((((sF4 @ X11 @ X12)) != $true) | (((sF13 @ X11 @ X12)) = $true)) )),
  inference(definition_folding,[],[f11,f45,f44,f44,f24])).
thf(f48,definition,(
  ( ! [X15 : a] : ((((sF14 @ X15)) = ((sK0 @ (sF12 @ X15) @ X15)))) )),
  introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
thf(f49,definition,(
  ( ! [X15 : a] : ((((sF15 @ X15)) = ((sK0 @ X15 @ (sF12 @ X15))))) )),
  introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
thf(f50,plain,(
  ( ! [X15 : a] : (($true != ((sF14 @ X15))) | (((sF15 @ X15)) != $true)) )),
  inference(definition_folding,[],[f9,f49,f44,f48,f44])).
thf(f65,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK0 @ X0 @ X1)) != $true) | (((sF13 @ X1 @ X0)) = $true)) )),
  inference(superposition,[],[f46,f24])).
thf(f68,plain,(
  ( ! [X0 : a] : ((((sF15 @ X0)) != $true) | (((sF13 @ (sF12 @ X0) @ X0)) = $true)) )),
  inference(superposition,[],[f65,f49])).
thf(f70,plain,(
  ( ! [X0 : (a > $o)] : ((((sF6 @ X0 @ (sF12 @ (sF5 @ X0)))) = ((sF14 @ (sF5 @ X0))))) )),
  inference(superposition,[],[f27,f48])).
thf(f73,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((sF6 @ X0 @ X1)) != $true) | ($true = ((sF13 @ (sF5 @ X0) @ X1)))) )),
  inference(superposition,[],[f65,f27])).
thf(f78,plain,(
  ( ! [X0 : a] : ((((sF13 @ (sF12 @ X0) @ X0)) = ((sF15 @ (sF12 @ X0))))) )),
  inference(superposition,[],[f49,f45])).
thf(f81,plain,(
  ( ! [X0 : a,X1 : a] : ((((sF13 @ X0 @ X1)) = ((sF4 @ (sF12 @ X0) @ (sF12 @ X1))))) )),
  inference(superposition,[],[f24,f45])).
thf(f92,plain,(
  ( ! [X0 : (a > $o),X1 : a] : (($true != ((X0 @ X1))) | (((sF6 @ X0 @ X1)) = $true)) )),
  inference(superposition,[],[f30,f28])).
thf(f131,plain,(
  ( ! [X0 : a] : (($true != ((sF9 @ X0 @ sF15))) | ($true = ((sF13 @ (sF12 @ (sF8 @ sF15 @ X0)) @ (sF8 @ sF15 @ X0))))) )),
  inference(superposition,[],[f68,f32])).
thf(f139,plain,(
  ( ! [X0 : a] : (($true != ((sF9 @ X0 @ sF15))) | ($true = ((sF15 @ (sF12 @ (sF8 @ sF15 @ X0)))))) )),
  inference(forward_demodulation,[],[f131,f78])).
thf(f148,plain,(
  ( ! [X0 : (a > $o)] : ((((sF10 @ (sF12 @ (sF5 @ X0)) @ X0)) = ((sF15 @ (sF5 @ X0))))) )),
  inference(superposition,[],[f49,f34])).
thf(f205,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : ((((sF4 @ X2 @ X1)) != $true) | (((sK0 @ X0 @ X1)) != $true) | (((sF4 @ X2 @ X0)) = $true)) )),
  inference(superposition,[],[f25,f24])).
thf(f409,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : ((((sF4 @ X0 @ (sF8 @ X1 @ X0))) = ((sF11 @ X0 @ X1)))) )),
  inference(superposition,[],[f24,f38])).
thf(f474,plain,(
  ( ! [X0 : (a > $o)] : ((((sF9 @ (sF12 @ (sF5 @ X0)) @ X0)) = $true) | ($true = ((sF15 @ (sF5 @ X0))))) )),
  inference(superposition,[],[f148,f35])).
thf(f691,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : ((((sK0 @ X2 @ X0)) != $true) | (((sK0 @ X0 @ X1)) != $true) | (((sF4 @ X1 @ X2)) = $true)) )),
  inference(superposition,[],[f205,f24])).
thf(f776,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK0 @ (sF12 @ X0) @ X1)) != $true) | (((sF15 @ X0)) != $true) | (((sF4 @ X1 @ X0)) = $true)) )),
  inference(superposition,[],[f691,f49])).
thf(f786,plain,(
  ( ! [X0 : a,X1 : a] : ((((sF13 @ X0 @ X1)) != $true) | ($true != ((sF15 @ X1))) | ($true = ((sF4 @ (sF12 @ X0) @ X1)))) )),
  inference(superposition,[],[f776,f45])).
thf(f1202,plain,(
  ($true != $true) | (((sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) = $true) | ($true = ((sF15 @ (sF5 @ sF15))))),
  inference(superposition,[],[f139,f474])).
thf(f1203,plain,(
  (((sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) = $true) | ($true = ((sF15 @ (sF5 @ sF15))))),
  inference(trivial_inequality_removal,[],[f1202])).
thf(f1205,definition,(
  spl16_1 <=> (((sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition])).
thf(f1207,plain,(
  (((sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) = $true) | ~spl16_1),
  inference(avatar_component_clause,[],[f1205])).
thf(f1209,definition,(
  spl16_2 <=> ($true = ((sF15 @ (sF5 @ sF15))))),
  introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition])).
thf(f1210,plain,(
  ($true != ((sF15 @ (sF5 @ sF15)))) | spl16_2),
  inference(avatar_component_clause,[],[f1209])).
thf(f1211,plain,(
  ($true = ((sF15 @ (sF5 @ sF15)))) | ~spl16_2),
  inference(avatar_component_clause,[],[f1209])).
thf(f1212,plain,(
  spl16_1 | spl16_2),
  inference(avatar_split_clause,[],[f1203,f1209,f1205])).
thf(f1216,plain,(
  ($true != $true) | (((sF13 @ (sF12 @ (sF5 @ sF15)) @ (sF5 @ sF15))) = $true) | ~spl16_2),
  inference(superposition,[],[f68,f1211])).
thf(f1220,plain,(
  (((sF13 @ (sF12 @ (sF5 @ sF15)) @ (sF5 @ sF15))) = $true) | ~spl16_2),
  inference(trivial_inequality_removal,[],[f1216])).
thf(f1225,plain,(
  (((sF15 @ (sF12 @ (sF5 @ sF15)))) = $true) | ~spl16_2),
  inference(forward_demodulation,[],[f1220,f78])).
thf(f1235,plain,(
  ($true != $true) | ($true = ((sF6 @ sF15 @ (sF12 @ (sF5 @ sF15))))) | ~spl16_2),
  inference(superposition,[],[f92,f1225])).
thf(f1238,plain,(
  ($true = ((sF6 @ sF15 @ (sF12 @ (sF5 @ sF15))))) | ~spl16_2),
  inference(trivial_inequality_removal,[],[f1235])).
thf(f1246,plain,(
  (((sF14 @ (sF5 @ sF15))) = $true) | ~spl16_2),
  inference(forward_demodulation,[],[f1238,f70])).
thf(f1253,plain,(
  ($true != $true) | ($true != ((sF15 @ (sF5 @ sF15)))) | ~spl16_2),
  inference(superposition,[],[f50,f1246])).
thf(f1256,plain,(
  ($true != ((sF15 @ (sF5 @ sF15)))) | ~spl16_2),
  inference(trivial_inequality_removal,[],[f1253])).
thf(f1262,plain,(
  $false | ~spl16_2),
  inference(forward_subsumption_resolution,[],[f1256,f1211])).
thf(f1263,plain,(
  ~spl16_2),
  inference(avatar_contradiction_clause,[],[f1262])).
thf(f1273,plain,(
  ($true != $true) | ($true = ((sF6 @ sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))))) | ~spl16_1),
  inference(superposition,[],[f92,f1207])).
thf(f1282,plain,(
  ($true = ((sF6 @ sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))))) | ~spl16_1),
  inference(trivial_inequality_removal,[],[f1273])).
thf(f1287,definition,(
  spl16_3 <=> (((sF9 @ (sF12 @ (sF5 @ sF15)) @ sF15)) = $true)),
  introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition])).
thf(f1288,plain,(
  (((sF9 @ (sF12 @ (sF5 @ sF15)) @ sF15)) = $true) | ~spl16_3),
  inference(avatar_component_clause,[],[f1287])).
thf(f1289,plain,(
  (((sF9 @ (sF12 @ (sF5 @ sF15)) @ sF15)) != $true) | spl16_3),
  inference(avatar_component_clause,[],[f1287])).
thf(f1295,plain,(
  ($true = ((sF15 @ (sF5 @ sF15)))) | ($true != $true) | spl16_3),
  inference(superposition,[],[f1289,f474])).
thf(f1296,plain,(
  ($true = ((sF15 @ (sF5 @ sF15)))) | spl16_3),
  inference(trivial_inequality_removal,[],[f1295])).
thf(f1297,plain,(
  $false | (spl16_2 | spl16_3)),
  inference(forward_subsumption_resolution,[],[f1296,f1210])).
thf(f1298,plain,(
  spl16_2 | spl16_3),
  inference(avatar_contradiction_clause,[],[f1297])).
thf(f1385,plain,(
  ($true != $true) | (((sF13 @ (sF5 @ sF15) @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) = $true) | ~spl16_1),
  inference(superposition,[],[f73,f1282])).
thf(f1388,plain,(
  (((sF13 @ (sF5 @ sF15) @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) = $true) | ~spl16_1),
  inference(trivial_inequality_removal,[],[f1385])).
thf(f1450,plain,(
  ($true != $true) | ($true = ((sF4 @ (sF12 @ (sF5 @ sF15)) @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))))) | (((sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) != $true) | ~spl16_1),
  inference(superposition,[],[f786,f1388])).
thf(f1457,plain,(
  (((sF15 @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15)))))) != $true) | ($true = ((sF4 @ (sF12 @ (sF5 @ sF15)) @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))))) | ~spl16_1),
  inference(trivial_inequality_removal,[],[f1450])).
thf(f1461,plain,(
  ($true = ((sF4 @ (sF12 @ (sF5 @ sF15)) @ (sF12 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))))) | ~spl16_1),
  inference(forward_subsumption_resolution,[],[f1457,f1207])).
thf(f1462,plain,(
  (((sF13 @ (sF5 @ sF15) @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))) = $true) | ~spl16_1),
  inference(forward_demodulation,[],[f1461,f81])).
thf(f1463,plain,(
  ($true != $true) | (((sF4 @ (sF12 @ (sF5 @ sF15)) @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))) = $true) | (((sF15 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))) != $true) | ~spl16_1),
  inference(superposition,[],[f786,f1462])).
thf(f1471,plain,(
  (((sF4 @ (sF12 @ (sF5 @ sF15)) @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))) = $true) | (((sF15 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))) != $true) | ~spl16_1),
  inference(trivial_inequality_removal,[],[f1463])).
thf(f1474,plain,(
  ($true = ((sF11 @ (sF12 @ (sF5 @ sF15)) @ sF15))) | (((sF15 @ (sF8 @ sF15 @ (sF12 @ (sF5 @ sF15))))) != $true) | ~spl16_1),
  inference(forward_demodulation,[],[f1471,f409])).
thf(f1475,plain,(
  (((sF9 @ (sF12 @ (sF5 @ sF15)) @ sF15)) != $true) | ($true = ((sF11 @ (sF12 @ (sF5 @ sF15)) @ sF15))) | ~spl16_1),
  inference(forward_demodulation,[],[f1474,f32])).
thf(f1476,plain,(
  ($true = ((sF11 @ (sF12 @ (sF5 @ sF15)) @ sF15))) | (~spl16_1 | ~spl16_3)),
  inference(forward_subsumption_resolution,[],[f1475,f1288])).
thf(f1477,plain,(
  ($true != $true) | ($true = ((sF10 @ (sF12 @ (sF5 @ sF15)) @ sF15))) | (~spl16_1 | ~spl16_3)),
  inference(superposition,[],[f39,f1476])).
thf(f1478,plain,(
  ($true = ((sF10 @ (sF12 @ (sF5 @ sF15)) @ sF15))) | (~spl16_1 | ~spl16_3)),
  inference(trivial_inequality_removal,[],[f1477])).
thf(f1479,plain,(
  ($true = ((sF15 @ (sF5 @ sF15)))) | (~spl16_1 | ~spl16_3)),
  inference(forward_demodulation,[],[f1478,f148])).
thf(f1480,plain,(
  $false | (~spl16_1 | spl16_2 | ~spl16_3)),
  inference(forward_subsumption_resolution,[],[f1479,f1210])).
thf(f1481,plain,(
  ~spl16_1 | spl16_2 | ~spl16_3),
  inference(avatar_contradiction_clause,[],[f1480])).
cnf(s1, plain, spl16_1 | spl16_2, inference(sat_conversion,[],[f1212])).
cnf(s2, plain, ~spl16_2, inference(sat_conversion,[],[f1263])).
cnf(s4, plain, spl16_2 | spl16_3, inference(sat_conversion,[],[f1298])).
cnf(s8, plain, ~spl16_1 | spl16_2 | ~spl16_3, inference(sat_conversion,[],[f1481])).
cnf(s9, plain, spl16_3, inference(rat,[],[s4,s2])).
cnf(s10, plain, ~spl16_1, inference(rat,[],[s8,s2,s9])).
cnf(s11, plain, $false, inference(rat,[],[s1,s2,s10])).
thf(f1482,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s11])).
% SZS output end Proof for theBenchmark