%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, qML_mu: $tType).
thf(type_def_6, type, qML_i: $tType).
thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, scott_G: (qML_mu > qML_i > $o)).
thf(func_def_1, type, scott_NE_QML_mu: (qML_mu > qML_i > $o)).
thf(func_def_2, type, scott_P: ((qML_mu > qML_i > $o) > qML_i > $o)).
thf(func_def_3, type, scott_ess_QML_mu: ((qML_mu > qML_i > $o) > qML_mu > qML_i > $o)).
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, db0: !>[X0: $tType]:(X0)).
thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_12, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_14, type, vAND: ($o > $o > $o)).
thf(func_def_15, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_16, type, vNOT: ($o > $o)).
thf(func_def_17, type, sK0: ((qML_mu > qML_i > $o) > (qML_mu > qML_i > $o) > qML_mu)).
thf(func_def_18, type, sK1: ((qML_mu > qML_i > $o) > (qML_mu > qML_i > $o) > qML_i)).
thf(func_def_19, type, sK2: qML_i).
thf(func_def_20, type, sK3: (qML_mu > qML_i > qML_mu > qML_i > $o)).
thf(func_def_21, type, sK4: ((qML_mu > qML_i > $o) > qML_i > qML_mu)).
thf(func_def_22, type, sK5: (qML_mu > qML_i > qML_mu > qML_i > $o)).
thf(func_def_23, type, sK6: (qML_mu > qML_i > qML_i)).
thf(func_def_24, type, sK7: (qML_i > (qML_mu > qML_i > $o) > qML_mu > qML_mu > qML_i > $o)).
thf(func_def_25, type, sK8: (qML_i > (qML_mu > qML_i > $o) > qML_mu > qML_mu)).
thf(func_def_26, type, sK9: (qML_i > (qML_mu > qML_i > $o) > qML_mu > qML_i)).
thf(f1,axiom,(
  ! [X1 : (qML_mu > qML_i > $o),X0 : qML_i] : ((scott_P @ (^[X2 : qML_mu, X3 : qML_i] : (~(X1 @ X2 @ X3))) @ X0) => ~(scott_P @ X1 @ X0))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_A1a)).
thf(f2,axiom,(
  ! [X0 : qML_i] : (scott_P @ scott_NE_QML_mu @ X0)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_A5)).
thf(f3,axiom,(
  ! [X1 : (qML_mu > qML_i > $o),X2 : (qML_mu > qML_i > $o),X0 : qML_i] : ((! [X4 : qML_mu,X3 : qML_i] : ((X1 @ X4 @ X3) => (X2 @ X4 @ X3)) & (scott_P @ X1 @ X0)) => (scott_P @ X2 @ X0))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_A2)).
thf(f4,conjecture,(
  ! [X0 : qML_i,X1 : qML_i] : ? [X2 : qML_mu] : (scott_G @ X2 @ X1)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
thf(f5,negated_conjecture,(
  ~ ! [X0 : qML_i,X1 : qML_i] : ? [X2 : qML_mu] : (scott_G @ X2 @ X1)),
  inference(negated_conjecture,[status(cth)],[f4])).
thf(f6,axiom,(
  ((^[X0 : qML_mu, X1 : qML_i] : (! [X2 : (qML_mu > qML_i > $o)] : ((scott_ess_QML_mu @ X2 @ X0 @ X1) => ! [X3 : qML_i] : ? [X4 : qML_mu] : (X2 @ X4 @ X3)))) = scott_NE_QML_mu)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_NE__def)).
thf(f7,axiom,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : (~(scott_P @ X1 @ X0) => (scott_P @ (^[X2 : qML_mu, X3 : qML_i] : (~(X1 @ X2 @ X3))) @ X0))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_A1b)).
thf(f8,axiom,(
  (scott_G = (^[X0 : qML_mu, X1 : qML_i] : (! [X2 : (qML_mu > qML_i > $o)] : ((scott_P @ X2 @ X1) => (X2 @ X0 @ X1)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_G__def)).
thf(f9,axiom,(
  (scott_ess_QML_mu = (^[X0 : (qML_mu > qML_i > $o), X1 : qML_mu, X2 : qML_i] : (! [X3 : (qML_mu > qML_i > $o)] : ((X3 @ X1 @ X2) => ! [X4 : qML_i,X5 : qML_mu] : ((X0 @ X5 @ X4) => (X3 @ X5 @ X4))) & (X0 @ X1 @ X2))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ess__def)).
thf(f10,axiom,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((scott_P @ X1 @ X0) => ! [X2 : qML_i] : (scott_P @ X1 @ X2))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_A4)).
thf(f11,axiom,(
  ! [X0 : qML_i] : (scott_P @ scott_G @ X0)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_A3)).
thf(f12,plain,(
  ! [X0 : qML_i] : (scott_P @ scott_NE_QML_mu @ X0)),
  inference(rectify,[],[f2])).
thf(f13,plain,(
  ! [X0 : qML_i] : (((scott_P @ scott_NE_QML_mu @ X0)) = $true)),
  inference(fool_elimination,[],[f12])).
thf(f14,plain,(
  ~ ! [X1 : qML_i] : ? [X2 : qML_mu] : (scott_G @ X2 @ X1)),
  inference(rectify,[],[f5])).
thf(f15,plain,(
  ~ ! [X1 : qML_i] : ? [X2 : qML_mu] : (((scott_G @ X2 @ X1)) = $true)),
  inference(fool_elimination,[],[f14])).
thf(f16,plain,(
  ((^[X0 : qML_mu, X1 : qML_i] : (! [X2 : (qML_mu > qML_i > $o)] : ((scott_ess_QML_mu @ X2 @ X0 @ X1) => ! [X3 : qML_i] : ? [X4 : qML_mu] : (X2 @ X4 @ X3)))) = scott_NE_QML_mu)),
  inference(rectify,[],[f6])).
thf(f17,plain,(
  (scott_NE_QML_mu = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y2 @ Y0 @ Y1) => (!! @ qML_i @ (^[Y3 : qML_i]: (?? @ qML_mu @ (^[Y4 : qML_mu]: (Y2 @ Y4 @ Y3))))))))))))),
  inference(fool_elimination,[],[f16])).
thf(f18,plain,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((scott_P @ X1 @ X0) => ! [X2 : qML_i] : (scott_P @ X1 @ X2))),
  inference(rectify,[],[f10])).
thf(f19,plain,(
  ! [X1 : (qML_mu > qML_i > $o),X0 : qML_i] : ((((scott_P @ X1 @ X0)) = $true) => ! [X2 : qML_i] : (((scott_P @ X1 @ X2)) = $true))),
  inference(fool_elimination,[],[f18])).
thf(f20,plain,(
  (scott_ess_QML_mu = (^[X0 : (qML_mu > qML_i > $o), X1 : qML_mu, X2 : qML_i] : (! [X3 : (qML_mu > qML_i > $o)] : ((X3 @ X1 @ X2) => ! [X4 : qML_i,X5 : qML_mu] : ((X0 @ X5 @ X4) => (X3 @ X5 @ X4))) & (X0 @ X1 @ X2))))),
  inference(rectify,[],[f9])).
thf(f21,plain,(
  (scott_ess_QML_mu = (^[Y0 : qML_mu > qML_i > $o]: ((^[Y1 : qML_mu]: ((^[Y2 : qML_i]: ((Y0 @ Y1 @ Y2) & (!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((Y3 @ Y1 @ Y2) => (!! @ qML_mu @ (^[Y4 : qML_mu]: (!! @ qML_i @ (^[Y5 : qML_i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))))))))))))),
  inference(fool_elimination,[],[f20])).
thf(f22,plain,(
  ! [X0 : qML_i] : (scott_P @ scott_G @ X0)),
  inference(rectify,[],[f11])).
thf(f23,plain,(
  ! [X0 : qML_i] : (((scott_P @ scott_G @ X0)) = $true)),
  inference(fool_elimination,[],[f22])).
thf(f24,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : (qML_mu > qML_i > $o),X2 : qML_i] : ((! [X3 : qML_mu,X4 : qML_i] : ((X0 @ X3 @ X4) => (X1 @ X3 @ X4)) & (scott_P @ X0 @ X2)) => (scott_P @ X1 @ X2))),
  inference(rectify,[],[f3])).
thf(f25,plain,(
  ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : (qML_mu > qML_i > $o)] : ((! [X3 : qML_mu,X4 : qML_i] : ((((X0 @ X3 @ X4)) = $true) => ($true = ((X1 @ X3 @ X4)))) & ($true = ((scott_P @ X0 @ X2)))) => (((scott_P @ X1 @ X2)) = $true))),
  inference(fool_elimination,[],[f24])).
thf(f26,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((scott_P @ (^[X2 : qML_mu, X3 : qML_i] : (~(X0 @ X2 @ X3))) @ X1) => ~(scott_P @ X0 @ X1))),
  inference(rectify,[],[f1])).
thf(f27,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) => ~ ($true = ((scott_P @ X0 @ X1))))),
  inference(fool_elimination,[],[f26])).
thf(f28,plain,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : (~(scott_P @ X1 @ X0) => (scott_P @ (^[X2 : qML_mu, X3 : qML_i] : (~(X1 @ X2 @ X3))) @ X0))),
  inference(rectify,[],[f7])).
thf(f29,plain,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : (~ (((scott_P @ X1 @ X0)) = $true) => (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X1 @ Y0 @ Y1))))) @ X0)) = $true))),
  inference(fool_elimination,[],[f28])).
thf(f30,plain,(
  (scott_G = (^[X0 : qML_mu, X1 : qML_i] : (! [X2 : (qML_mu > qML_i > $o)] : ((scott_P @ X2 @ X1) => (X2 @ X0 @ X1)))))),
  inference(rectify,[],[f8])).
thf(f31,plain,(
  (scott_G = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))),
  inference(fool_elimination,[],[f30])).
thf(f32,plain,(
  ~ ! [X0 : qML_i] : ? [X1 : qML_mu] : (((scott_G @ X1 @ X0)) = $true)),
  inference(rectify,[],[f15])).
thf(f33,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) => ($true != ((scott_P @ X0 @ X1))))),
  inference(flattening,[],[f27])).
thf(f34,plain,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_P @ X1 @ X0)) != $true) => (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X1 @ Y0 @ Y1))))) @ X0)) = $true))),
  inference(flattening,[],[f29])).
thf(f35,plain,(
  ? [X0 : qML_i] : ! [X1 : qML_mu] : (((scott_G @ X1 @ X0)) != $true)),
  inference(ennf_transformation,[],[f32])).
thf(f36,plain,(
  ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : (qML_mu > qML_i > $o)] : ((((scott_P @ X1 @ X2)) = $true) | (? [X3 : qML_mu,X4 : qML_i] : (($true != ((X1 @ X3 @ X4))) & (((X0 @ X3 @ X4)) = $true)) | ($true != ((scott_P @ X0 @ X2)))))),
  inference(ennf_transformation,[],[f25])).
thf(f37,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X2 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_P @ X1 @ X2)) = $true) | ($true != ((scott_P @ X0 @ X2))) | ? [X3 : qML_mu,X4 : qML_i] : (($true != ((X1 @ X3 @ X4))) & (((X0 @ X3 @ X4)) = $true)))),
  inference(flattening,[],[f36])).
thf(f38,plain,(
  ! [X1 : (qML_mu > qML_i > $o),X0 : qML_i] : (! [X2 : qML_i] : (((scott_P @ X1 @ X2)) = $true) | (((scott_P @ X1 @ X0)) != $true))),
  inference(ennf_transformation,[],[f19])).
thf(f39,plain,(
  ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_P @ X1 @ X0)) = $true) | (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X1 @ Y0 @ Y1))))) @ X0)) = $true))),
  inference(ennf_transformation,[],[f34])).
thf(f40,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true != ((scott_P @ X0 @ X1))) | ($true != ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))))),
  inference(ennf_transformation,[],[f33])).
thf(f41,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i,X2 : (qML_mu > qML_i > $o)] : ((((scott_P @ X2 @ X1)) = $true) | ($true != ((scott_P @ X0 @ X1))) | ? [X3 : qML_mu,X4 : qML_i] : (($true != ((X2 @ X3 @ X4))) & (((X0 @ X3 @ X4)) = $true)))),
  inference(rectify,[],[f37])).
thf(f42,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i,X2 : (qML_mu > qML_i > $o)] : ((((scott_P @ X2 @ X1)) = $true) | ($true != ((scott_P @ X0 @ X1))) | ((((X2 @ (sK0 @ X2 @ X0) @ (sK1 @ X2 @ X0))) != $true) & (((X0 @ (sK0 @ X2 @ X0) @ (sK1 @ X2 @ X0))) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,$thf(sK1 @ X2 @ X0)),skolemize(X4,$thf(sK1 @ X2 @ X0))],[f41])).
thf(f43,plain,(
  ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (! [X2 : qML_i] : ($true = ((scott_P @ X0 @ X2))) | ($true != ((scott_P @ X0 @ X1))))),
  inference(rectify,[],[f38])).
thf(f44,plain,(
  ! [X1 : qML_mu] : (((scott_G @ X1 @ sK2)) != $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,$thf(sK2))],[f35])).
thf(f45,plain,(
  (scott_ess_QML_mu = (^[Y0 : qML_mu > qML_i > $o]: ((^[Y1 : qML_mu]: ((^[Y2 : qML_i]: ((Y0 @ Y1 @ Y2) & (!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((Y3 @ Y1 @ Y2) => (!! @ qML_mu @ (^[Y4 : qML_mu]: (!! @ qML_i @ (^[Y5 : qML_i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))))))))))))),
  inference(cnf_transformation,[],[f21])).
thf(f46,plain,(
  ( ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true != ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) | ($true != ((scott_P @ X0 @ X1)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f47,plain,(
  ( ! [X0 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X1 @ Y0 @ Y1))))) @ X0)) = $true) | (((scott_P @ X1 @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f39])).
thf(f48,plain,(
  ( ! [X2 : (qML_mu > qML_i > $o),X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((X0 @ (sK0 @ X2 @ X0) @ (sK1 @ X2 @ X0))) = $true) | ($true != ((scott_P @ X0 @ X1))) | (((scott_P @ X2 @ X1)) = $true)) )),
  inference(cnf_transformation,[],[f42])).
thf(f50,plain,(
  (scott_NE_QML_mu = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y2 @ Y0 @ Y1) => (!! @ qML_i @ (^[Y3 : qML_i]: (?? @ qML_mu @ (^[Y4 : qML_mu]: (Y2 @ Y4 @ Y3))))))))))))),
  inference(cnf_transformation,[],[f17])).
thf(f51,plain,(
  ( ! [X0 : qML_i] : ((((scott_P @ scott_G @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f23])).
thf(f52,plain,(
  (scott_G = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))),
  inference(cnf_transformation,[],[f31])).
thf(f53,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ X0 @ X2))) | ($true != ((scott_P @ X0 @ X1)))) )),
  inference(cnf_transformation,[],[f43])).
thf(f54,plain,(
  ( ! [X1 : qML_mu] : ((((scott_G @ X1 @ sK2)) != $true)) )),
  inference(cnf_transformation,[],[f44])).
thf(f55,plain,(
  ( ! [X0 : qML_i] : ((((scott_P @ scott_NE_QML_mu @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f57,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f60,plain,(
  ( ! [X0 : qML_mu] : (($true != $true) | (((scott_G @ X0 @ sK2)) = $false)) )),
  inference(superposition,[],[f54,f57])).
thf(f66,plain,(
  ( ! [X0 : qML_mu] : ((((scott_G @ X0 @ sK2)) = $false)) )),
  inference(trivial_inequality_removal,[],[f60])).
thf(f67,plain,(
  ( ! [X1 : qML_mu] : ((((scott_G @ X1)) = (((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ X1)))) )),
  inference(argument_congruence,[],[f52])).
thf(f68,plain,(
  ( ! [X1 : qML_mu] : ((((scott_G @ X1)) = (^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (Y1 @ X1 @ Y0))))))) )),
  inference(beta-eta_normalization,[],[f67])).
thf(f78,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : (((((^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (Y1 @ X1 @ Y0))))) @ X2)) = ((scott_G @ X1 @ X2)))) )),
  inference(argument_congruence,[],[f68])).
thf(f79,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : (($true = (((^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (Y1 @ X1 @ Y0))))) @ X2))) | (((scott_G @ X1 @ X2)) = $false)) )),
  inference(iff_proxy_clausification,[],[f78])).
thf(f86,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : ((((scott_G @ X1 @ X2)) = $false) | ($true = ((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ X2) => (Y0 @ X1 @ X2))))))) )),
  inference(beta-eta_normalization,[],[f79])).
thf(f87,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu] : ((((scott_G @ X1 @ X2)) = $false) | ((((^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ X2) => (Y0 @ X1 @ X2))) @ X3)) = $true)) )),
  inference(pi_proxy_clausification,[],[f86])).
thf(f88,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu] : (($true = (((scott_P @ X3 @ X2) => (X3 @ X1 @ X2)))) | (((scott_G @ X1 @ X2)) = $false)) )),
  inference(beta-eta_normalization,[],[f87])).
thf(f89,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu] : (($false = ((scott_P @ X3 @ X2))) | (((scott_G @ X1 @ X2)) = $false) | (((X3 @ X1 @ X2)) = $true)) )),
  inference(imp_proxy_clausification,[],[f88])).
thf(f90,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((scott_P @ X0 @ X3)) != $true) | (((scott_G @ X2 @ X1)) = $false) | ($true = $false) | ($true = ((X0 @ X2 @ X1)))) )),
  inference(superposition,[],[f89,f53])).
thf(f92,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : (($true = ((scott_NE_QML_mu @ X1 @ X0))) | (((scott_G @ X1 @ X0)) = $false) | ($true = $false)) )),
  inference(superposition,[],[f89,f55])).
thf(f101,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((scott_P @ X0 @ X3)) != $true) | ($true = ((X0 @ X2 @ X1))) | (((scott_G @ X2 @ X1)) = $false)) )),
  inference(trivial_inequality_removal,[],[f90])).
thf(f108,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : (($true = ((scott_NE_QML_mu @ X1 @ X0))) | (((scott_G @ X1 @ X0)) = $false)) )),
  inference(trivial_inequality_removal,[],[f92])).
thf(f115,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((scott_G @ X2 @ X3)) = $false) | ($true != $true) | (((X0 @ X2 @ X3)) = $true) | (((scott_P @ X0 @ X1)) = $false)) )),
  inference(superposition,[],[f101,f57])).
thf(f116,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((scott_P @ X0 @ X1)) = $false) | (((scott_G @ X2 @ X3)) = $false) | (((X0 @ X2 @ X3)) = $true)) )),
  inference(trivial_inequality_removal,[],[f115])).
thf(f205,plain,(
  ( ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($false = ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) | ($true != ((scott_P @ X0 @ X1))) | ($true != $true)) )),
  inference(superposition,[],[f46,f57])).
thf(f209,plain,(
  ( ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($false = ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) | ($true != ((scott_P @ X0 @ X1)))) )),
  inference(trivial_inequality_removal,[],[f205])).
thf(f210,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((scott_G @ X2 @ X3)) = $false) | ($true = (((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X2 @ X3))) | ($true = ((scott_P @ X0 @ X1))) | ($true = $false)) )),
  inference(superposition,[],[f47,f116])).
thf(f216,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ X0 @ X1))) | (((scott_G @ X2 @ X3)) = $false) | ($true = (((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X2 @ X3)))) )),
  inference(trivial_inequality_removal,[],[f210])).
thf(f217,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : ((((~ (X0 @ X2 @ X3))) = $true) | ($true = ((scott_P @ X0 @ X1))) | (((scott_G @ X2 @ X3)) = $false)) )),
  inference(beta-eta_normalization,[],[f216])).
thf(f218,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ X0 @ X1))) | (((X0 @ X2 @ X3)) = $false) | (((scott_G @ X2 @ X3)) = $false)) )),
  inference(not_proxy_clausification,[],[f217])).
thf(f222,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X4 : qML_mu,X5 : qML_i] : ((((X0 @ X4 @ X5)) = $true) | ($true = $false) | (((X0 @ X2 @ X3)) = $false) | (((scott_G @ X4 @ X5)) = $false) | (((scott_G @ X2 @ X3)) = $false)) )),
  inference(superposition,[],[f218,f116])).
thf(f226,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : (qML_mu > qML_i > $o),X4 : qML_mu,X5 : qML_i] : ((((scott_G @ X4 @ X5)) = $false) | (((scott_G @ X2 @ X3)) = $false) | (((X0 @ X2 @ X3)) = $false) | (((X0 @ X4 @ X5)) = $true)) )),
  inference(trivial_inequality_removal,[],[f222])).
thf(f232,plain,(
  ( ! [X1 : qML_mu] : ((((scott_NE_QML_mu @ X1)) = (((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y2 @ Y0 @ Y1) => (!! @ qML_i @ (^[Y3 : qML_i]: (?? @ qML_mu @ (^[Y4 : qML_mu]: (Y2 @ Y4 @ Y3))))))))))) @ X1)))) )),
  inference(argument_congruence,[],[f50])).
thf(f233,plain,(
  ( ! [X1 : qML_mu] : ((((scott_NE_QML_mu @ X1)) = (^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y1 @ X1 @ Y0) => (!! @ qML_i @ (^[Y2 : qML_i]: (?? @ qML_mu @ (^[Y3 : qML_mu]: (Y1 @ Y3 @ Y2))))))))))) )),
  inference(beta-eta_normalization,[],[f232])).
thf(f234,plain,(
  ( ! [X1 : (qML_mu > qML_i > $o)] : (((((^[Y0 : qML_mu > qML_i > $o]: ((^[Y1 : qML_mu]: ((^[Y2 : qML_i]: ((Y0 @ Y1 @ Y2) & (!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((Y3 @ Y1 @ Y2) => (!! @ qML_mu @ (^[Y4 : qML_mu]: (!! @ qML_i @ (^[Y5 : qML_i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))))))))))) @ X1)) = ((scott_ess_QML_mu @ X1)))) )),
  inference(argument_congruence,[],[f45])).
thf(f235,plain,(
  ( ! [X1 : (qML_mu > qML_i > $o)] : (((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: ((X1 @ Y0 @ Y1) & (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((Y2 @ Y0 @ Y1) => (!! @ qML_mu @ (^[Y3 : qML_mu]: (!! @ qML_i @ (^[Y4 : qML_i]: ((X1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))))))))) = ((scott_ess_QML_mu @ X1)))) )),
  inference(beta-eta_normalization,[],[f234])).
thf(f260,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true != ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X2))) | ($true = $false) | ($true != ((scott_P @ X0 @ X1)))) )),
  inference(superposition,[],[f53,f209])).
thf(f261,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true != ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X2))) | ($true != ((scott_P @ X0 @ X1)))) )),
  inference(trivial_inequality_removal,[],[f260])).
thf(f285,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : ((((scott_NE_QML_mu @ X1 @ X2)) = (((^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y1 @ X1 @ Y0) => (!! @ qML_i @ (^[Y2 : qML_i]: (?? @ qML_mu @ (^[Y3 : qML_mu]: (Y1 @ Y3 @ Y2))))))))) @ X2)))) )),
  inference(argument_congruence,[],[f233])).
thf(f287,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : (($true = (((^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y1 @ X1 @ Y0) => (!! @ qML_i @ (^[Y2 : qML_i]: (?? @ qML_mu @ (^[Y3 : qML_mu]: (Y1 @ Y3 @ Y2))))))))) @ X2))) | (((scott_NE_QML_mu @ X1 @ X2)) = $false)) )),
  inference(iff_proxy_clausification,[],[f285])).
thf(f288,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : (($true = ((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y0 @ X1 @ X2) => (!! @ qML_i @ (^[Y1 : qML_i]: (?? @ qML_mu @ (^[Y2 : qML_mu]: (Y0 @ Y2 @ Y1)))))))))) | (((scott_NE_QML_mu @ X1 @ X2)) = $false)) )),
  inference(beta-eta_normalization,[],[f287])).
thf(f289,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu] : ((((scott_NE_QML_mu @ X1 @ X2)) = $false) | ($true = (((^[Y0 : qML_mu > qML_i > $o]: ((scott_ess_QML_mu @ Y0 @ X1 @ X2) => (!! @ qML_i @ (^[Y1 : qML_i]: (?? @ qML_mu @ (^[Y2 : qML_mu]: (Y0 @ Y2 @ Y1))))))) @ X3)))) )),
  inference(pi_proxy_clausification,[],[f288])).
thf(f290,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu] : ((((scott_NE_QML_mu @ X1 @ X2)) = $false) | ($true = (((scott_ess_QML_mu @ X3 @ X1 @ X2) => (!! @ qML_i @ (^[Y0 : qML_i]: (?? @ qML_mu @ (^[Y1 : qML_mu]: (X3 @ Y1 @ Y0))))))))) )),
  inference(beta-eta_normalization,[],[f289])).
thf(f291,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu] : ((((scott_NE_QML_mu @ X1 @ X2)) = $false) | (((scott_ess_QML_mu @ X3 @ X1 @ X2)) = $false) | (((!! @ qML_i @ (^[Y0 : qML_i]: (?? @ qML_mu @ (^[Y1 : qML_mu]: (X3 @ Y1 @ Y0)))))) = $true)) )),
  inference(imp_proxy_clausification,[],[f290])).
thf(f292,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu,X4 : qML_i] : ((((scott_ess_QML_mu @ X3 @ X1 @ X2)) = $false) | (((scott_NE_QML_mu @ X1 @ X2)) = $false) | ($true = (((^[Y0 : qML_i]: (?? @ qML_mu @ (^[Y1 : qML_mu]: (X3 @ Y1 @ Y0)))) @ X4)))) )),
  inference(pi_proxy_clausification,[],[f291])).
thf(f293,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu,X4 : qML_i] : ((((scott_NE_QML_mu @ X1 @ X2)) = $false) | ($true = ((?? @ qML_mu @ (^[Y0 : qML_mu]: (X3 @ Y0 @ X4))))) | (((scott_ess_QML_mu @ X3 @ X1 @ X2)) = $false)) )),
  inference(beta-eta_normalization,[],[f292])).
thf(f294,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu,X4 : qML_i] : ((((scott_ess_QML_mu @ X3 @ X1 @ X2)) = $false) | ((((^[Y0 : qML_mu]: (X3 @ Y0 @ X4)) @ (sK4 @ X3 @ X4))) = $true) | (((scott_NE_QML_mu @ X1 @ X2)) = $false)) )),
  inference(sigma_proxy_clausification,[],[f293])).
thf(f295,plain,(
  ( ! [X2 : qML_i,X3 : (qML_mu > qML_i > $o),X1 : qML_mu,X4 : qML_i] : (($true = ((X3 @ (sK4 @ X3 @ X4) @ X4))) | (((scott_NE_QML_mu @ X1 @ X2)) = $false) | (((scott_ess_QML_mu @ X3 @ X1 @ X2)) = $false)) )),
  inference(beta-eta_normalization,[],[f294])).
thf(f307,plain,(
  ( ! [X2 : qML_mu,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2)) = (((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: ((X1 @ Y0 @ Y1) & (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((Y2 @ Y0 @ Y1) => (!! @ qML_mu @ (^[Y3 : qML_mu]: (!! @ qML_i @ (^[Y4 : qML_i]: ((X1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))))))))) @ X2)))) )),
  inference(argument_congruence,[],[f235])).
thf(f308,plain,(
  ( ! [X2 : qML_mu,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2)) = (^[Y0 : qML_i]: ((X1 @ X2 @ Y0) & (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((Y1 @ X2 @ Y0) => (!! @ qML_mu @ (^[Y2 : qML_mu]: (!! @ qML_i @ (^[Y3 : qML_i]: ((X1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))))) )),
  inference(beta-eta_normalization,[],[f307])).
thf(f312,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($false = ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) | ($true != $true) | ($true != ((scott_P @ X0 @ X2)))) )),
  inference(superposition,[],[f261,f57])).
thf(f313,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($false = ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X0 @ Y0 @ Y1))))) @ X1))) | ($true != ((scott_P @ X0 @ X2)))) )),
  inference(trivial_inequality_removal,[],[f312])).
thf(f320,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : (((((^[Y0 : qML_i]: ((X1 @ X2 @ Y0) & (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((Y1 @ X2 @ Y0) => (!! @ qML_mu @ (^[Y2 : qML_mu]: (!! @ qML_i @ (^[Y3 : qML_i]: ((X1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))) @ X3)) = ((scott_ess_QML_mu @ X1 @ X2 @ X3)))) )),
  inference(argument_congruence,[],[f308])).
thf(f322,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | ((((^[Y0 : qML_i]: ((X1 @ X2 @ Y0) & (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((Y1 @ X2 @ Y0) => (!! @ qML_mu @ (^[Y2 : qML_mu]: (!! @ qML_i @ (^[Y3 : qML_i]: ((X1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))) @ X3)) = $false)) )),
  inference(iff_proxy_clausification,[],[f320])).
thf(f323,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : (((((X1 @ X2 @ X3) & (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ X2 @ X3) => (!! @ qML_mu @ (^[Y1 : qML_mu]: (!! @ qML_i @ (^[Y2 : qML_i]: ((X1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))))))) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true)) )),
  inference(beta-eta_normalization,[],[f322])).
thf(f324,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | ($false = ((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ X2 @ X3) => (!! @ qML_mu @ (^[Y1 : qML_mu]: (!! @ qML_i @ (^[Y2 : qML_i]: ((X1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))))))) | (((X1 @ X2 @ X3)) = $false)) )),
  inference(and_proxy_clausification,[],[f323])).
thf(f325,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : (((((^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ X2 @ X3) => (!! @ qML_mu @ (^[Y1 : qML_mu]: (!! @ qML_i @ (^[Y2 : qML_i]: ((X1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))))) @ (sK7 @ X3 @ X1 @ X2))) = $false) | (((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true)) )),
  inference(sigma_proxy_clausification,[],[f324])).
thf(f326,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : (((((sK7 @ X3 @ X1 @ X2 @ X2 @ X3) => (!! @ qML_mu @ (^[Y0 : qML_mu]: (!! @ qML_i @ (^[Y1 : qML_i]: ((X1 @ Y0 @ Y1) => (sK7 @ X3 @ X1 @ X2 @ Y0 @ Y1)))))))) = $false) | (((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true)) )),
  inference(beta-eta_normalization,[],[f325])).
thf(f327,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | ($false = ((!! @ qML_mu @ (^[Y0 : qML_mu]: (!! @ qML_i @ (^[Y1 : qML_i]: ((X1 @ Y0 @ Y1) => (sK7 @ X3 @ X1 @ X2 @ Y0 @ Y1))))))))) )),
  inference(imp_proxy_clausification,[],[f326])).
thf(f328,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : (($true = ((sK7 @ X3 @ X1 @ X2 @ X2 @ X3))) | (((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true)) )),
  inference(imp_proxy_clausification,[],[f326])).
thf(f329,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | (((X1 @ X2 @ X3)) = $false) | ((((^[Y0 : qML_mu]: (!! @ qML_i @ (^[Y1 : qML_i]: ((X1 @ Y0 @ Y1) => (sK7 @ X3 @ X1 @ X2 @ Y0 @ Y1))))) @ (sK8 @ X3 @ X1 @ X2))) = $false)) )),
  inference(sigma_proxy_clausification,[],[f327])).
thf(f330,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | (((!! @ qML_i @ (^[Y0 : qML_i]: ((X1 @ (sK8 @ X3 @ X1 @ X2) @ Y0) => (sK7 @ X3 @ X1 @ X2 @ (sK8 @ X3 @ X1 @ X2) @ Y0))))) = $false) | (((X1 @ X2 @ X3)) = $false)) )),
  inference(beta-eta_normalization,[],[f329])).
thf(f331,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | ((((^[Y0 : qML_i]: ((X1 @ (sK8 @ X3 @ X1 @ X2) @ Y0) => (sK7 @ X3 @ X1 @ X2 @ (sK8 @ X3 @ X1 @ X2) @ Y0))) @ (sK9 @ X3 @ X1 @ X2))) = $false) | (((X1 @ X2 @ X3)) = $false)) )),
  inference(sigma_proxy_clausification,[],[f330])).
thf(f332,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true) | ($false = (((X1 @ (sK8 @ X3 @ X1 @ X2) @ (sK9 @ X3 @ X1 @ X2)) => (sK7 @ X3 @ X1 @ X2 @ (sK8 @ X3 @ X1 @ X2) @ (sK9 @ X3 @ X1 @ X2)))))) )),
  inference(beta-eta_normalization,[],[f331])).
thf(f333,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : ((((sK7 @ X3 @ X1 @ X2 @ (sK8 @ X3 @ X1 @ X2) @ (sK9 @ X3 @ X1 @ X2))) = $false) | (((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true)) )),
  inference(imp_proxy_clausification,[],[f332])).
thf(f334,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X1 : (qML_mu > qML_i > $o)] : (($true = ((X1 @ (sK8 @ X3 @ X1 @ X2) @ (sK9 @ X3 @ X1 @ X2)))) | (((X1 @ X2 @ X3)) = $false) | (((scott_ess_QML_mu @ X1 @ X2 @ X3)) = $true)) )),
  inference(imp_proxy_clausification,[],[f332])).
thf(f374,plain,(
  ( ! [X0 : qML_mu,X1 : qML_i] : ((((scott_NE_QML_mu @ X0 @ X1)) = $false) | ($true = $false) | (((scott_ess_QML_mu @ scott_G @ X0 @ X1)) = $false)) )),
  inference(superposition,[],[f295,f66])).
thf(f389,plain,(
  ( ! [X0 : qML_mu,X1 : qML_i] : ((((scott_NE_QML_mu @ X0 @ X1)) = $false) | (((scott_ess_QML_mu @ scott_G @ X0 @ X1)) = $false)) )),
  inference(trivial_inequality_removal,[],[f374])).
thf(f397,definition,(
  spl10_2 <=> ! [X2 : qML_i,X1 : qML_mu] : ((((scott_NE_QML_mu @ X1 @ X2)) = $false) | ($false = ((scott_ess_QML_mu @ scott_G @ X1 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
thf(f398,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : (($false = ((scott_ess_QML_mu @ scott_G @ X1 @ X2))) | (((scott_NE_QML_mu @ X1 @ X2)) = $false)) ) | ~spl10_2),
  inference(avatar_component_clause,[],[f397])).
thf(f400,plain,(
  spl10_2),
  inference(avatar_split_clause,[],[f389,f397])).
thf(f606,definition,(
  spl10_14 <=> ! [X2 : qML_i,X1 : qML_mu] : ((((scott_G @ X1 @ X2)) = $false) | (((scott_NE_QML_mu @ X1 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition])).
thf(f607,plain,(
  ( ! [X2 : qML_i,X1 : qML_mu] : ((((scott_NE_QML_mu @ X1 @ X2)) = $false) | (((scott_G @ X1 @ X2)) = $false)) ) | ~spl10_14),
  inference(avatar_component_clause,[],[f606])).
thf(f609,definition,(
  spl10_15 <=> ! [X0 : (qML_mu > qML_i > $o),X3 : qML_i] : (((scott_P @ X0 @ X3)) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition])).
thf(f610,plain,(
  ( ! [X3 : qML_i,X0 : (qML_mu > qML_i > $o)] : ((((scott_P @ X0 @ X3)) = $true)) ) | ~spl10_15),
  inference(avatar_component_clause,[],[f609])).
thf(f647,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : ((((scott_G @ X1 @ X0)) = $false) | ($true = $false)) ) | ~spl10_14),
  inference(backward_subsumption_demodulation,[],[f108,f607])).
thf(f657,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : ((((scott_G @ X1 @ X0)) = $false)) ) | ~spl10_14),
  inference(trivial_inequality_removal,[],[f647])).
thf(f673,plain,(
  ( ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true != ((scott_P @ scott_G @ X1))) | ($true = ((scott_P @ X0 @ X1))) | ($true = $false)) ) | ~spl10_14),
  inference(superposition,[],[f657,f48])).
thf(f684,plain,(
  ( ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ X0 @ X1))) | ($true != ((scott_P @ scott_G @ X1)))) ) | ~spl10_14),
  inference(trivial_inequality_removal,[],[f673])).
thf(f690,plain,(
  ( ! [X0 : (qML_mu > qML_i > $o),X1 : qML_i] : (($true = ((scott_P @ X0 @ X1)))) ) | ~spl10_14),
  inference(forward_subsumption_resolution,[],[f684,f51])).
thf(f692,plain,(
  spl10_15 | ~spl10_14),
  inference(avatar_split_clause,[],[f690,f606,f609])).
thf(f698,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o)] : (($true = $false) | ($true != ((scott_P @ X0 @ X2)))) ) | ~spl10_15),
  inference(superposition,[],[f313,f610])).
thf(f703,plain,(
  ( ! [X2 : qML_i,X0 : (qML_mu > qML_i > $o)] : (($true != ((scott_P @ X0 @ X2)))) ) | ~spl10_15),
  inference(trivial_inequality_removal,[],[f698])).
thf(f709,plain,(
  $false | ~spl10_15),
  inference(forward_subsumption_resolution,[],[f703,f610])).
thf(f710,plain,(
  ~spl10_15),
  inference(avatar_contradiction_clause,[],[f709])).
thf(f1057,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : qML_i,X1 : qML_mu,X4 : (qML_mu > qML_i > $o)] : ((((scott_G @ X2 @ X3)) = $false) | ($true = $false) | (((scott_G @ X1 @ X0)) = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | ($true = ((X4 @ (sK8 @ X0 @ scott_G @ X1) @ (sK9 @ X0 @ scott_G @ X1)))) | (((X4 @ X2 @ X3)) = $false)) )),
  inference(superposition,[],[f334,f226])).
thf(f1081,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : qML_i,X1 : qML_mu,X4 : (qML_mu > qML_i > $o)] : (($true = ((X4 @ (sK8 @ X0 @ scott_G @ X1) @ (sK9 @ X0 @ scott_G @ X1)))) | (((X4 @ X2 @ X3)) = $false) | (((scott_G @ X1 @ X0)) = $false) | (((scott_G @ X2 @ X3)) = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0)))) )),
  inference(trivial_inequality_removal,[],[f1057])).
thf(f3005,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : qML_i,X1 : qML_mu] : (($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | (((scott_G @ X1 @ X0)) = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | ($true = $false) | (((scott_G @ X1 @ X0)) = $false) | (((sK7 @ X0 @ scott_G @ X1 @ X2 @ X3)) = $false) | (((scott_G @ X2 @ X3)) = $false)) )),
  inference(superposition,[],[f1081,f333])).
thf(f3079,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : qML_i,X1 : qML_mu] : ((((scott_G @ X1 @ X0)) = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | (((scott_G @ X2 @ X3)) = $false) | (((sK7 @ X0 @ scott_G @ X1 @ X2 @ X3)) = $false) | ($true = $false)) )),
  inference(duplicate_literal_removal,[],[f3005])).
thf(f3080,plain,(
  ( ! [X2 : qML_mu,X3 : qML_i,X0 : qML_i,X1 : qML_mu] : ((((sK7 @ X0 @ scott_G @ X1 @ X2 @ X3)) = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | (((scott_G @ X2 @ X3)) = $false) | (((scott_G @ X1 @ X0)) = $false)) )),
  inference(trivial_inequality_removal,[],[f3079])).
thf(f3913,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : ((((scott_G @ X1 @ X0)) = $false) | (((scott_G @ X1 @ X0)) = $false) | (((scott_G @ X1 @ X0)) = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | ($true = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0)))) )),
  inference(superposition,[],[f328,f3080])).
thf(f3932,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : (($true = $false) | ($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | (((scott_G @ X1 @ X0)) = $false)) )),
  inference(duplicate_literal_removal,[],[f3913])).
thf(f3933,plain,(
  ( ! [X0 : qML_i,X1 : qML_mu] : (($true = ((scott_ess_QML_mu @ scott_G @ X1 @ X0))) | (((scott_G @ X1 @ X0)) = $false)) )),
  inference(trivial_inequality_removal,[],[f3932])).
thf(f3962,plain,(
  ( ! [X0 : qML_mu,X1 : qML_i] : (($true = $false) | (((scott_G @ X0 @ X1)) = $false) | (((scott_NE_QML_mu @ X0 @ X1)) = $false)) ) | ~spl10_2),
  inference(superposition,[],[f3933,f398])).
thf(f3996,plain,(
  ( ! [X0 : qML_mu,X1 : qML_i] : ((((scott_NE_QML_mu @ X0 @ X1)) = $false) | (((scott_G @ X0 @ X1)) = $false)) ) | ~spl10_2),
  inference(trivial_inequality_removal,[],[f3962])).
thf(f4035,plain,(
  spl10_14 | ~spl10_2),
  inference(avatar_split_clause,[],[f3996,f397,f606])).
cnf(s2, plain, spl10_2, inference(sat_conversion,[],[f400])).
cnf(s32, plain, ~spl10_14 | spl10_15, inference(sat_conversion,[],[f692])).
cnf(s36, plain, ~spl10_15, inference(sat_conversion,[],[f710])).
cnf(s304, plain, ~spl10_2 | spl10_14, inference(sat_conversion,[],[f4035])).
cnf(s353, plain, ~spl10_14, inference(rat,[],[s32,s36])).
cnf(s354, plain, ~spl10_2, inference(rat,[],[s304,s353])).
cnf(s373, plain, $false, inference(rat,[],[s2,s354])).
thf(f4050,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s373])).
% SZS output end Proof for theBenchmark