%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_4, type, vAND: ($o > $o > $o)).
thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_8, type, vIMP: ($o > $o > $o)).
thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_10, type, sK0: (($i > $o) > $i > $o)).
thf(func_def_12, type, sK2: ($i > $o)).
thf(func_def_13, type, sK3: (($i > $o) > $i)).
thf(func_def_14, type, sK4: (($i > $o) > $i)).
thf(func_def_16, type, sK6: (($i > $o) > $i)).
thf(func_def_17, type, sK7: ($i > $o)).
thf(func_def_18, type, vNOT: ($o > $o)).
thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_21, type, sK9: (($i > $o) > $i)).
thf(f1,conjecture,(
  ! [X0 : (($i > $o) > $i > $o)] : ((! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : (! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)) & (X3 @ X4)))) @ X2))) & (! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) => (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))))) @ X1)))) => ! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) <=> (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM2C_pme)).
thf(f2,negated_conjecture,(
  ~ ! [X0 : (($i > $o) > $i > $o)] : ((! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : (! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)) & (X3 @ X4)))) @ X2))) & (! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) => (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))))) @ X1)))) => ! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) <=> (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : (($i > $o) > $i > $o)] : ((! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X5 : $i] : ((X0 @ X1 @ X5) => (X0 @ (^[X6 : $i] : (? [X7 : ($i > $o)] : (! [X8 : $i] : ((X7 @ X8) => (X0 @ X7 @ X8)) & (X7 @ X6)))) @ X5))) & (! [X9 : $i] : (? [X10 : ($i > $o)] : ((X10 @ X9) & ! [X11 : $i] : ((X10 @ X11) => (X0 @ X10 @ X11))) => (X0 @ (^[X12 : $i] : (? [X13 : ($i > $o)] : (! [X14 : $i] : ((X13 @ X14) => (X0 @ X13 @ X14)) & (X13 @ X12)))) @ X9)) => ! [X15 : $i] : ((X0 @ (^[X16 : $i] : (? [X17 : ($i > $o)] : (! [X18 : $i] : ((X17 @ X18) => (X0 @ X17 @ X18)) & (X17 @ X16)))) @ X15) => (X0 @ (X0 @ (^[X19 : $i] : (? [X20 : ($i > $o)] : (! [X21 : $i] : ((X20 @ X21) => (X0 @ X20 @ X21)) & (X20 @ X19))))) @ X15)))) => ! [X22 : $i] : (? [X23 : ($i > $o)] : ((X23 @ X22) & ! [X24 : $i] : ((X23 @ X24) => (X0 @ X23 @ X24))) <=> (X0 @ (^[X25 : $i] : (? [X26 : ($i > $o)] : (! [X27 : $i] : ((X26 @ X27) => (X0 @ X26 @ X27)) & (X26 @ X25)))) @ X22)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X0 : (($i > $o) > $i > $o)] : ((! [X1 : ($i > $o)] : (! [X2 : $i] : ((((X1 @ X2)) = $true) => ? [X3 : ($i > $o)] : ((((X3 @ X2)) = $true) & ! [X4 : $i] : ((((X3 @ X4)) = $true) => (((X0 @ X3 @ X4)) = $true)))) => ! [X5 : $i] : (($true = ((X0 @ X1 @ X5))) => (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X5)) = $true))) & (! [X9 : $i] : (? [X10 : ($i > $o)] : ((((X10 @ X9)) = $true) & ! [X11 : $i] : ((((X10 @ X11)) = $true) => ($true = ((X0 @ X10 @ X11))))) => (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9)) = $true)) => ! [X15 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X15)) = $true) => (((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2))))))))) @ X15)) = $true)))) => ! [X22 : $i] : (? [X23 : ($i > $o)] : (($true = ((X23 @ X22))) & ! [X24 : $i] : (($true = ((X23 @ X24))) => (((X0 @ X23 @ X24)) = $true))) <=> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X22)) = $true)))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ~ ! [X0 : (($i > $o) > $i > $o)] : ((! [X1 : ($i > $o)] : (! [X2 : $i] : ((((X1 @ X2)) = $true) => ? [X3 : ($i > $o)] : ((((X3 @ X2)) = $true) & ! [X4 : $i] : ((((X3 @ X4)) = $true) => (((X0 @ X3 @ X4)) = $true)))) => ! [X5 : $i] : (($true = ((X0 @ X1 @ X5))) => (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X5)) = $true))) & (! [X6 : $i] : (? [X7 : ($i > $o)] : ((((X7 @ X6)) = $true) & ! [X8 : $i] : ((((X7 @ X8)) = $true) => ($true = ((X0 @ X7 @ X8))))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6)))) => ! [X9 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9)) = $true) => (((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2))))))))) @ X9)) = $true)))) => ! [X10 : $i] : (? [X11 : ($i > $o)] : (($true = ((X11 @ X10))) & ! [X12 : $i] : ((((X11 @ X12)) = $true) => (((X0 @ X11 @ X12)) = $true))) <=> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) = $true)))),
  inference(rectify,[],[f4])).
thf(f6,plain,(
  ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : (? [X11 : ($i > $o)] : (! [X12 : $i] : ((((X0 @ X11 @ X12)) = $true) | (((X11 @ X12)) != $true)) & ($true = ((X11 @ X10)))) <~> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) = $true)) & (! [X1 : ($i > $o)] : (! [X5 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X5)) = $true) | ($true != ((X0 @ X1 @ X5)))) | ? [X2 : $i] : (! [X3 : ($i > $o)] : ((((X3 @ X2)) != $true) | ? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X0 @ X3 @ X4)) != $true))) & (((X1 @ X2)) = $true))) & (! [X9 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9)) != $true) | (((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2))))))))) @ X9)) = $true)) | ? [X6 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6))) & ? [X7 : ($i > $o)] : (! [X8 : $i] : (($true = ((X0 @ X7 @ X8))) | (((X7 @ X8)) != $true)) & (((X7 @ X6)) = $true))))))),
  inference(ennf_transformation,[],[f5])).
thf(f7,plain,(
  ? [X0 : (($i > $o) > $i > $o)] : ((! [X9 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9)) != $true) | (((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2))))))))) @ X9)) = $true)) | ? [X6 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6))) & ? [X7 : ($i > $o)] : (! [X8 : $i] : (($true = ((X0 @ X7 @ X8))) | (((X7 @ X8)) != $true)) & (((X7 @ X6)) = $true)))) & ! [X1 : ($i > $o)] : (! [X5 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X5)) = $true) | ($true != ((X0 @ X1 @ X5)))) | ? [X2 : $i] : (! [X3 : ($i > $o)] : ((((X3 @ X2)) != $true) | ? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X0 @ X3 @ X4)) != $true))) & (((X1 @ X2)) = $true))) & ? [X10 : $i] : (? [X11 : ($i > $o)] : (! [X12 : $i] : ((((X0 @ X11 @ X12)) = $true) | (((X11 @ X12)) != $true)) & ($true = ((X11 @ X10)))) <~> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) = $true)))),
  inference(flattening,[],[f6])).
thf(f8,plain,(
  ? [X0 : (($i > $o) > $i > $o)] : ((! [X9 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9)) != $true) | (((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2))))))))) @ X9)) = $true)) | ? [X6 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6))) & ? [X7 : ($i > $o)] : (! [X8 : $i] : (($true = ((X0 @ X7 @ X8))) | (((X7 @ X8)) != $true)) & (((X7 @ X6)) = $true)))) & ! [X1 : ($i > $o)] : (! [X5 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X5)) = $true) | ($true != ((X0 @ X1 @ X5)))) | ? [X2 : $i] : (! [X3 : ($i > $o)] : ((((X3 @ X2)) != $true) | ? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X0 @ X3 @ X4)) != $true))) & (((X1 @ X2)) = $true))) & ? [X10 : $i] : (((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) != $true) | ! [X11 : ($i > $o)] : (? [X12 : $i] : ((((X0 @ X11 @ X12)) != $true) & (((X11 @ X12)) = $true)) | ($true != ((X11 @ X10))))) & ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) = $true) | ? [X11 : ($i > $o)] : (! [X12 : $i] : ((((X0 @ X11 @ X12)) = $true) | (((X11 @ X12)) != $true)) & ($true = ((X11 @ X10)))))))),
  inference(nnf_transformation,[],[f7])).
thf(f9,plain,(
  ? [X0 : (($i > $o) > $i > $o)] : ((! [X1 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X1)) != $true) | (((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2))))))))) @ X1)) = $true)) | ? [X2 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X2))) & ? [X3 : ($i > $o)] : (! [X4 : $i] : ((((X0 @ X3 @ X4)) = $true) | (((X3 @ X4)) != $true)) & (((X3 @ X2)) = $true)))) & ! [X5 : ($i > $o)] : (! [X6 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6))) | (((X0 @ X5 @ X6)) != $true)) | ? [X7 : $i] : (! [X8 : ($i > $o)] : (($true != ((X8 @ X7))) | ? [X9 : $i] : ((((X8 @ X9)) = $true) & (((X0 @ X8 @ X9)) != $true))) & (((X5 @ X7)) = $true))) & ? [X10 : $i] : (((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) != $true) | ! [X11 : ($i > $o)] : (? [X12 : $i] : ((((X0 @ X11 @ X12)) != $true) & (((X11 @ X12)) = $true)) | ($true != ((X11 @ X10))))) & ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10)) = $true) | ? [X13 : ($i > $o)] : (! [X14 : $i] : ((((X0 @ X13 @ X14)) = $true) | ($true != ((X13 @ X14)))) & (((X13 @ X10)) = $true)))))),
  inference(rectify,[],[f8])).
thf(f10,plain,(
  (! [X1 : $i] : (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | (((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ X1)) = $true)) | (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) & (! [X4 : $i] : ((((sK0 @ sK2 @ X4)) = $true) | (((sK2 @ X4)) != $true)) & (((sK2 @ sK1)) = $true)))) & ! [X5 : ($i > $o)] : (! [X6 : $i] : ((((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6)) = $true) | (((sK0 @ X5 @ X6)) != $true)) | (! [X8 : ($i > $o)] : ((((X8 @ (sK3 @ X5))) != $true) | ((((X8 @ (sK4 @ X8))) = $true) & (((sK0 @ X8 @ (sK4 @ X8))) != $true))) & (((X5 @ (sK3 @ X5))) = $true))) & ((($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | ! [X11 : ($i > $o)] : ((($true != ((sK0 @ X11 @ (sK6 @ X11)))) & (((X11 @ (sK6 @ X11))) = $true)) | (((X11 @ sK5)) != $true))) & (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (! [X14 : $i] : (($true = ((sK0 @ sK7 @ X14))) | ($true != ((sK7 @ X14)))) & ($true = ((sK7 @ sK5))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,sK5,vAPP,sK7]),skolemize(X0,$thf(sK0)),skolemize(X2,$thf(sK1)),skolemize(X3,$thf(sK2)),skolemize(X12,$thf(sK6 @ X11)),skolemize(X12,$thf(sK6 @ X11)),skolemize(X10,$thf(sK5)),skolemize(X12,$thf(sK6 @ X11)),skolemize(X13,$thf(sK7))],[f9])).
thf(f11,plain,(
  ($true = ((sK7 @ sK5))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5)))),
  inference(cnf_transformation,[],[f10])).
thf(f12,plain,(
  ( ! [X14 : $i] : (($true = ((sK0 @ sK7 @ X14))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | ($true != ((sK7 @ X14)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f13,plain,(
  ( ! [X11 : ($i > $o)] : (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (((X11 @ (sK6 @ X11))) = $true) | (((X11 @ sK5)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f14,plain,(
  ( ! [X11 : ($i > $o)] : (($true != ((sK0 @ X11 @ (sK6 @ X11)))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (((X11 @ sK5)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f15,plain,(
  ( ! [X6 : $i,X5 : ($i > $o)] : ((((sK0 @ X5 @ X6)) != $true) | (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6)) = $true) | (((X5 @ (sK3 @ X5))) = $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f16,plain,(
  ( ! [X8 : ($i > $o),X6 : $i,X5 : ($i > $o)] : ((((sK0 @ X8 @ (sK4 @ X8))) != $true) | (((sK0 @ X5 @ X6)) != $true) | (((X8 @ (sK3 @ X5))) != $true) | (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6)) = $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f17,plain,(
  ( ! [X8 : ($i > $o),X6 : $i,X5 : ($i > $o)] : ((((sK0 @ X5 @ X6)) != $true) | (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6)) = $true) | (((X8 @ (sK3 @ X5))) != $true) | (((X8 @ (sK4 @ X8))) = $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f18,plain,(
  ( ! [X1 : $i] : ((((sK2 @ sK1)) = $true) | (((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ X1)) = $true) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f19,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((sK2 @ X4)) != $true) | (((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ X1)) = $true) | (((sK0 @ sK2 @ X4)) = $true) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f20,plain,(
  ( ! [X1 : $i] : ((((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ X1)) = $true) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f24,definition,(
  spl8_1 <=> (((sK2 @ sK1)) = $true)),
  introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
thf(f26,plain,(
  (((sK2 @ sK1)) = $true) | ~spl8_1),
  inference(avatar_component_clause,[],[f24])).
thf(f28,definition,(
  spl8_2 <=> ! [X1 : $i] : ((((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ X1)) = $true) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))))),
  introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
thf(f29,plain,(
  ( ! [X1 : $i] : (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | (((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ X1)) = $true)) ) | ~spl8_2),
  inference(avatar_component_clause,[],[f28])).
thf(f30,plain,(
  spl8_1 | spl8_2),
  inference(avatar_split_clause,[],[f18,f28,f24])).
thf(f32,definition,(
  spl8_3 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5)))),
  introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
thf(f33,plain,(
  ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | ~spl8_3),
  inference(avatar_component_clause,[],[f32])).
thf(f34,plain,(
  ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | spl8_3),
  inference(avatar_component_clause,[],[f32])).
thf(f36,definition,(
  spl8_4 <=> ! [X11 : ($i > $o)] : ((((X11 @ (sK6 @ X11))) = $true) | (((X11 @ sK5)) != $true))),
  introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
thf(f37,plain,(
  ( ! [X11 : ($i > $o)] : ((((X11 @ sK5)) != $true) | (((X11 @ (sK6 @ X11))) = $true)) ) | ~spl8_4),
  inference(avatar_component_clause,[],[f36])).
thf(f38,plain,(
  ~spl8_3 | spl8_4),
  inference(avatar_split_clause,[],[f13,f36,f32])).
thf(f40,definition,(
  spl8_5 <=> ($true = ((sK7 @ sK5)))),
  introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
thf(f42,plain,(
  ($true = ((sK7 @ sK5))) | ~spl8_5),
  inference(avatar_component_clause,[],[f40])).
thf(f43,plain,(
  spl8_5 | spl8_3),
  inference(avatar_split_clause,[],[f11,f32,f40])).
thf(f45,definition,(
  spl8_6 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1)))),
  introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
thf(f47,plain,(
  ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | spl8_6),
  inference(avatar_component_clause,[],[f45])).
thf(f48,plain,(
  ~spl8_6 | spl8_2),
  inference(avatar_split_clause,[],[f20,f28,f45])).
thf(f50,definition,(
  spl8_7 <=> ! [X11 : ($i > $o)] : (($true != ((sK0 @ X11 @ (sK6 @ X11)))) | (((X11 @ sK5)) != $true))),
  introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
thf(f51,plain,(
  ( ! [X11 : ($i > $o)] : (($true != ((sK0 @ X11 @ (sK6 @ X11)))) | (((X11 @ sK5)) != $true)) ) | ~spl8_7),
  inference(avatar_component_clause,[],[f50])).
thf(f52,plain,(
  ~spl8_3 | spl8_7),
  inference(avatar_split_clause,[],[f14,f50,f32])).
thf(f54,definition,(
  spl8_8 <=> ! [X14 : $i] : (($true = ((sK0 @ sK7 @ X14))) | ($true != ((sK7 @ X14))))),
  introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
thf(f55,plain,(
  ( ! [X14 : $i] : (($true != ((sK7 @ X14))) | ($true = ((sK0 @ sK7 @ X14)))) ) | ~spl8_8),
  inference(avatar_component_clause,[],[f54])).
thf(f56,plain,(
  spl8_8 | spl8_3),
  inference(avatar_split_clause,[],[f12,f32,f54])).
thf(f58,definition,(
  spl8_9 <=> ! [X4 : $i] : ((((sK2 @ X4)) != $true) | (((sK0 @ sK2 @ X4)) = $true))),
  introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
thf(f59,plain,(
  ( ! [X4 : $i] : ((((sK2 @ X4)) != $true) | (((sK0 @ sK2 @ X4)) = $true)) ) | ~spl8_9),
  inference(avatar_component_clause,[],[f58])).
thf(f60,plain,(
  spl8_2 | spl8_9),
  inference(avatar_split_clause,[],[f19,f58,f28])).
thf(f75,plain,(
  ($true != $true) | (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ (sK6 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))) = $true) | (~spl8_3 | ~spl8_4)),
  inference(superposition,[],[f37,f33])).
thf(f76,plain,(
  (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ (sK6 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))) = $true) | (~spl8_3 | ~spl8_4)),
  inference(trivial_inequality_removal,[],[f75])).
thf(f162,plain,(
  ($true != $true) | ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ (sK6 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))))))) | (~spl8_2 | ~spl8_3 | ~spl8_4)),
  inference(superposition,[],[f29,f76])).
thf(f163,plain,(
  ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ (sK6 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))))))) | (~spl8_2 | ~spl8_3 | ~spl8_4)),
  inference(trivial_inequality_removal,[],[f162])).
thf(f172,plain,(
  ($true != $true) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (~spl8_2 | ~spl8_3 | ~spl8_4 | ~spl8_7)),
  inference(superposition,[],[f51,f163])).
thf(f179,plain,(
  ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (~spl8_2 | ~spl8_3 | ~spl8_4 | ~spl8_7)),
  inference(trivial_inequality_removal,[],[f172])).
thf(f180,plain,(
  $false | (~spl8_2 | ~spl8_3 | ~spl8_4 | ~spl8_7)),
  inference(forward_subsumption_resolution,[],[f179,f33])).
thf(f181,plain,(
  ~spl8_2 | ~spl8_3 | ~spl8_4 | ~spl8_7),
  inference(avatar_contradiction_clause,[],[f180])).
thf(f182,plain,(
  ($true != $true) | (((sK0 @ sK2 @ sK1)) = $true) | (~spl8_1 | ~spl8_9)),
  inference(superposition,[],[f59,f26])).
thf(f188,plain,(
  (((sK0 @ sK2 @ sK1)) = $true) | (~spl8_1 | ~spl8_9)),
  inference(trivial_inequality_removal,[],[f182])).
thf(f199,plain,(
  ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | ($true != ((X0 @ (sK3 @ sK2)))) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl8_1 | ~spl8_9)),
  inference(superposition,[],[f17,f188])).
thf(f200,plain,(
  ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | (((sK2 @ (sK3 @ sK2))) = $true) | ($true != $true) | (~spl8_1 | ~spl8_9)),
  inference(superposition,[],[f15,f188])).
thf(f201,plain,(
  ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | ($true != ((X0 @ (sK3 @ sK2)))) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl8_1 | ~spl8_9)),
  inference(trivial_inequality_removal,[],[f199])).
thf(f203,plain,(
  ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | (((sK2 @ (sK3 @ sK2))) = $true) | (~spl8_1 | ~spl8_9)),
  inference(trivial_inequality_removal,[],[f200])).
thf(f205,definition,(
  spl8_12 <=> ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK3 @ sK2)))) | (((X0 @ (sK4 @ X0))) = $true))),
  introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition])).
thf(f206,plain,(
  ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK3 @ sK2)))) | (((X0 @ (sK4 @ X0))) = $true)) ) | ~spl8_12),
  inference(avatar_component_clause,[],[f205])).
thf(f207,plain,(
  spl8_12 | spl8_6 | ~spl8_1 | ~spl8_9),
  inference(avatar_split_clause,[],[f201,f58,f24,f45,f205])).
thf(f214,definition,(
  spl8_14 <=> (((sK2 @ (sK3 @ sK2))) = $true)),
  introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition])).
thf(f216,plain,(
  (((sK2 @ (sK3 @ sK2))) = $true) | ~spl8_14),
  inference(avatar_component_clause,[],[f214])).
thf(f217,plain,(
  spl8_6 | spl8_14 | ~spl8_1 | ~spl8_9),
  inference(avatar_split_clause,[],[f203,f58,f24,f214,f45])).
thf(f227,plain,(
  ($true = ((sK2 @ (sK4 @ sK2)))) | ($true != $true) | (~spl8_12 | ~spl8_14)),
  inference(superposition,[],[f206,f216])).
thf(f233,plain,(
  ($true = ((sK2 @ (sK4 @ sK2)))) | (~spl8_12 | ~spl8_14)),
  inference(trivial_inequality_removal,[],[f227])).
thf(f238,plain,(
  ($true != $true) | (((sK0 @ sK2 @ (sK4 @ sK2))) = $true) | (~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(superposition,[],[f59,f233])).
thf(f239,plain,(
  (((sK0 @ sK2 @ (sK4 @ sK2))) = $true) | (~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(trivial_inequality_removal,[],[f238])).
thf(f274,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((sK0 @ X0 @ X1)) != $true) | (((sK2 @ (sK3 @ X0))) != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | ($true != $true)) ) | (~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(superposition,[],[f16,f239])).
thf(f281,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((sK0 @ X0 @ X1)) != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | (((sK2 @ (sK3 @ X0))) != $true)) ) | (~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(trivial_inequality_removal,[],[f274])).
thf(f484,plain,(
  ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | (((sK2 @ (sK3 @ sK2))) != $true) | ($true != $true) | (~spl8_1 | ~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(superposition,[],[f281,f188])).
thf(f492,plain,(
  ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1))) | (((sK2 @ (sK3 @ sK2))) != $true) | (~spl8_1 | ~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(trivial_inequality_removal,[],[f484])).
thf(f501,plain,(
  (((sK2 @ (sK3 @ sK2))) != $true) | (~spl8_1 | spl8_6 | ~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(forward_subsumption_resolution,[],[f492,f47])).
thf(f507,plain,(
  $false | (~spl8_1 | spl8_6 | ~spl8_9 | ~spl8_12 | ~spl8_14)),
  inference(forward_subsumption_resolution,[],[f501,f216])).
thf(f508,plain,(
  ~spl8_1 | spl8_6 | ~spl8_9 | ~spl8_12 | ~spl8_14),
  inference(avatar_contradiction_clause,[],[f507])).
thf(f561,plain,(
  (((sK0 @ sK7 @ sK5)) = $true) | ($true != $true) | (~spl8_5 | ~spl8_8)),
  inference(superposition,[],[f55,f42])).
thf(f569,plain,(
  (((sK0 @ sK7 @ sK5)) = $true) | (~spl8_5 | ~spl8_8)),
  inference(trivial_inequality_removal,[],[f561])).
thf(f576,definition,(
  spl8_34 <=> (((sK0 @ sK7 @ (sK4 @ sK7))) = $true)),
  introduced(definition,[new_symbols(definition,[spl8_34])],[avatar_definition])).
thf(f578,plain,(
  (((sK0 @ sK7 @ (sK4 @ sK7))) = $true) | ~spl8_34),
  inference(avatar_component_clause,[],[f576])).
thf(f631,plain,(
  ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | ($true != $true) | (((X0 @ (sK3 @ sK7))) != $true) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl8_5 | ~spl8_8)),
  inference(superposition,[],[f17,f569])).
thf(f632,plain,(
  ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (((sK7 @ (sK3 @ sK7))) = $true) | (~spl8_5 | ~spl8_8)),
  inference(superposition,[],[f15,f569])).
thf(f636,plain,(
  (((sK7 @ (sK3 @ sK7))) = $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (~spl8_5 | ~spl8_8)),
  inference(trivial_inequality_removal,[],[f632])).
thf(f637,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ (sK3 @ sK7))) != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl8_5 | ~spl8_8)),
  inference(trivial_inequality_removal,[],[f631])).
thf(f641,plain,(
  (((sK7 @ (sK3 @ sK7))) = $true) | (spl8_3 | ~spl8_5 | ~spl8_8)),
  inference(forward_subsumption_resolution,[],[f636,f34])).
thf(f642,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ (sK4 @ X0))) = $true) | (((X0 @ (sK3 @ sK7))) != $true)) ) | (spl8_3 | ~spl8_5 | ~spl8_8)),
  inference(forward_subsumption_resolution,[],[f637,f34])).
thf(f654,definition,(
  spl8_40 <=> (((sK7 @ (sK4 @ sK7))) = $true)),
  introduced(definition,[new_symbols(definition,[spl8_40])],[avatar_definition])).
thf(f656,plain,(
  (((sK7 @ (sK4 @ sK7))) = $true) | ~spl8_40),
  inference(avatar_component_clause,[],[f654])).
thf(f675,definition,(
  spl8_42 <=> ! [X0 : ($i > $o)] : ((((X0 @ (sK3 @ sK7))) != $true) | (((X0 @ (sK4 @ X0))) = $true))),
  introduced(definition,[new_symbols(definition,[spl8_42])],[avatar_definition])).
thf(f676,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ (sK3 @ sK7))) != $true) | (((X0 @ (sK4 @ X0))) = $true)) ) | ~spl8_42),
  inference(avatar_component_clause,[],[f675])).
thf(f692,plain,(
  spl8_42 | spl8_3 | ~spl8_5 | ~spl8_8),
  inference(avatar_split_clause,[],[f642,f54,f40,f32,f675])).
thf(f706,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((sK7 @ (sK3 @ X0))) != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | ($true != $true) | (((sK0 @ X0 @ X1)) != $true)) ) | ~spl8_34),
  inference(superposition,[],[f16,f578])).
thf(f713,plain,(
  ( ! [X0 : ($i > $o),X1 : $i] : ((((sK0 @ X0 @ X1)) != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X1))) | (((sK7 @ (sK3 @ X0))) != $true)) ) | ~spl8_34),
  inference(trivial_inequality_removal,[],[f706])).
thf(f727,plain,(
  ($true != $true) | (((sK7 @ (sK4 @ sK7))) = $true) | (spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_42)),
  inference(superposition,[],[f676,f641])).
thf(f729,plain,(
  (((sK7 @ (sK4 @ sK7))) = $true) | (spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_42)),
  inference(trivial_inequality_removal,[],[f727])).
thf(f739,plain,(
  spl8_40 | spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_42),
  inference(avatar_split_clause,[],[f729,f675,f54,f40,f32,f654])).
thf(f746,plain,(
  ($true != $true) | (((sK0 @ sK7 @ (sK4 @ sK7))) = $true) | (~spl8_8 | ~spl8_40)),
  inference(superposition,[],[f55,f656])).
thf(f747,plain,(
  (((sK0 @ sK7 @ (sK4 @ sK7))) = $true) | (~spl8_8 | ~spl8_40)),
  inference(trivial_inequality_removal,[],[f746])).
thf(f1080,plain,(
  (((sK7 @ (sK3 @ sK7))) != $true) | ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (~spl8_5 | ~spl8_8 | ~spl8_34)),
  inference(superposition,[],[f713,f569])).
thf(f1088,plain,(
  (((sK7 @ (sK3 @ sK7))) != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (~spl8_5 | ~spl8_8 | ~spl8_34)),
  inference(trivial_inequality_removal,[],[f1080])).
thf(f1098,plain,(
  ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK5))) | (spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_34)),
  inference(forward_subsumption_resolution,[],[f1088,f641])).
thf(f1109,plain,(
  $false | (spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_34)),
  inference(forward_subsumption_resolution,[],[f1098,f34])).
thf(f1110,plain,(
  spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_34),
  inference(avatar_contradiction_clause,[],[f1109])).
thf(f1116,plain,(
  spl8_34 | ~spl8_8 | ~spl8_40),
  inference(avatar_split_clause,[],[f747,f654,f54,f576])).
cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f30])).
cnf(s2, plain, ~spl8_3 | spl8_4, inference(sat_conversion,[],[f38])).
cnf(s3, plain, spl8_3 | spl8_5, inference(sat_conversion,[],[f43])).
cnf(s4, plain, spl8_2 | ~spl8_6, inference(sat_conversion,[],[f48])).
cnf(s5, plain, ~spl8_3 | spl8_7, inference(sat_conversion,[],[f52])).
cnf(s6, plain, spl8_3 | spl8_8, inference(sat_conversion,[],[f56])).
cnf(s7, plain, spl8_2 | spl8_9, inference(sat_conversion,[],[f60])).
cnf(s8, plain, ~spl8_2 | ~spl8_3 | ~spl8_4 | ~spl8_7, inference(sat_conversion,[],[f181])).
cnf(s10, plain, ~spl8_1 | spl8_6 | ~spl8_9 | spl8_12, inference(sat_conversion,[],[f207])).
cnf(s12, plain, ~spl8_1 | spl8_6 | ~spl8_9 | spl8_14, inference(sat_conversion,[],[f217])).
cnf(s23, plain, ~spl8_1 | spl8_6 | ~spl8_9 | ~spl8_12 | ~spl8_14, inference(sat_conversion,[],[f508])).
cnf(s40, plain, spl8_3 | ~spl8_5 | ~spl8_8 | spl8_42, inference(sat_conversion,[],[f692])).
cnf(s46, plain, spl8_3 | ~spl8_5 | ~spl8_8 | spl8_40 | ~spl8_42, inference(sat_conversion,[],[f739])).
cnf(s69, plain, spl8_3 | ~spl8_5 | ~spl8_8 | ~spl8_34, inference(sat_conversion,[],[f1110])).
cnf(s73, plain, ~spl8_8 | spl8_34 | ~spl8_40, inference(sat_conversion,[],[f1116])).
cnf(s74, plain, ~spl8_5 | spl8_3 | ~spl8_8, inference(rat,[],[s73,s46,s40,s69])).
cnf(s75, plain, spl8_3, inference(rat,[],[s74,s3,s6])).
cnf(s76, plain, spl8_7, inference(rat,[],[s5,s75])).
cnf(s77, plain, spl8_4, inference(rat,[],[s2,s75])).
cnf(s78, plain, ~spl8_2, inference(rat,[],[s8,s76,s77,s75])).
cnf(s79, plain, spl8_9, inference(rat,[],[s7,s78])).
cnf(s80, plain, ~spl8_6, inference(rat,[],[s4,s78])).
cnf(s81, plain, spl8_1, inference(rat,[],[s1,s78])).
cnf(s82, plain, spl8_14, inference(rat,[],[s12,s80,s79,s81])).
cnf(s84, plain, spl8_12, inference(rat,[],[s10,s80,s79,s81])).
cnf(s85, plain, $false, inference(rat,[],[s23,s81,s80,s79,s82,s84])).
thf(f1117,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s85])).
% SZS output end Proof for theBenchmark