%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, u: $tType).
thf(type_def_6, type, d: $tType).
thf(type_def_7, type, du: $tType).
thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
thf(type_def_9, type, mono_2Etyop_2Emin_2Eind: $tType).
thf(func_def_0, type, tyop_2Emin_2Ebool: d).
thf(func_def_1, type, tyop_2Emin_2Efun: (d > d > d)).
thf(func_def_2, type, s: (d > u > du)).
thf(func_def_3, type, app_2E2: (du > du > u)).
thf(func_def_4, type, combin_i_2E0: u).
thf(func_def_5, type, combin_k_2E0: u).
thf(func_def_6, type, combin_s_2E0: u).
thf(func_def_7, type, c_2Ebool_2E_21_2E0: u).
thf(func_def_8, type, c_2Ebool_2E_21_2E1: (du > u)).
thf(func_def_9, type, c_2Ebool_2E_2F_5C_2E0: u).
thf(func_def_10, type, c_2Ebool_2E_2F_5C_2E2: (du > du > u)).
thf(func_def_11, type, c_2Emin_2E_3D_2E0: u).
thf(func_def_12, type, c_2Emin_2E_3D_2E2: (du > du > u)).
thf(func_def_13, type, c_2Emin_2E_3D_3D_3E_2E0: u).
thf(func_def_14, type, c_2Emin_2E_3D_3D_3E_2E2: (du > du > u)).
thf(func_def_15, type, c_2Ebool_2E_3F_2E0: u).
thf(func_def_16, type, c_2Ebool_2E_3F_2E1: (du > u)).
thf(func_def_17, type, c_2Ebool_2EF_2E0: u).
thf(func_def_18, type, c_2Ebool_2ET_2E0: u).
thf(func_def_19, type, c_2Ebool_2E_5C_2F_2E0: u).
thf(func_def_20, type, c_2Ebool_2E_5C_2F_2E2: (du > du > u)).
thf(func_def_21, type, c_2Ebool_2E_7E_2E0: u).
thf(func_def_22, type, c_2Ebool_2E_7E_2E1: (du > u)).
thf(func_def_23, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: (($o > $o) > $o > $o)).
thf(func_def_24, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o > $o) > $o > $o > $o)).
thf(func_def_25, type, mono_2Ec_2Ebool_2E_2F_5C: ($o > $o > $o)).
thf(func_def_26, type, mono_2Ec_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
thf(func_def_27, type, mono_2Ec_2Ebool_2EF: $o).
thf(func_def_28, type, mono_2Ec_2Ebool_2ET: $o).
thf(func_def_29, type, mono_2Ec_2Ebool_2E_5C_2F: ($o > $o > $o)).
thf(func_def_30, type, mono_2Ec_2Ebool_2E_7E: ($o > $o)).
thf(func_def_31, type, i_mono_2Etyop_2Emin_2Ebool: ($o > u)).
thf(func_def_32, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o) > u)).
thf(func_def_33, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (($o > $o > $o) > u)).
thf(func_def_34, type, j_mono_2Etyop_2Emin_2Ebool: (du > $o)).
thf(func_def_35, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (du > $o > $o)).
thf(func_def_36, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (du > $o > $o > $o)).
thf(func_def_37, type, vNOT: ($o > $o)).
thf(func_def_39, type, tyop_2Emin_2Eind: d).
thf(func_def_40, type, c_2Ebool_2E_3F_21_2E0: u).
thf(func_def_41, type, c_2Ebool_2E_3F_21_2E1: (du > u)).
thf(func_def_42, type, c_2Emin_2E_40_2E0: u).
thf(func_def_43, type, c_2Emin_2E_40_2E1: (du > u)).
thf(func_def_44, type, c_2Ebool_2EBOUNDED_2E0: u).
thf(func_def_45, type, c_2Ebool_2EBOUNDED_2E1: (du > u)).
thf(func_def_46, type, c_2Ebool_2ECOND_2E0: u).
thf(func_def_47, type, c_2Ebool_2ECOND_2E3: (du > du > du > u)).
thf(func_def_48, type, c_2Ebool_2EDATATYPE_2E0: u).
thf(func_def_49, type, c_2Ebool_2EDATATYPE_2E1: (du > u)).
thf(func_def_50, type, c_2Ebool_2EIN_2E0: u).
thf(func_def_51, type, c_2Ebool_2EIN_2E2: (du > du > u)).
thf(func_def_52, type, c_2Ebool_2ELET_2E0: u).
thf(func_def_53, type, c_2Ebool_2ELET_2E2: (du > du > u)).
thf(func_def_54, type, c_2Ebool_2EONE__ONE_2E0: u).
thf(func_def_55, type, c_2Ebool_2EONE__ONE_2E1: (du > u)).
thf(func_def_56, type, c_2Ebool_2EONTO_2E0: u).
thf(func_def_57, type, c_2Ebool_2EONTO_2E1: (du > u)).
thf(func_def_58, type, c_2Ebool_2ERES__EXISTS_2E0: u).
thf(func_def_59, type, c_2Ebool_2ERES__EXISTS_2E2: (du > du > u)).
thf(func_def_60, type, c_2Ebool_2ERES__EXISTS__UNIQUE_2E0: u).
thf(func_def_61, type, c_2Ebool_2ERES__EXISTS__UNIQUE_2E2: (du > du > u)).
thf(func_def_62, type, c_2Ebool_2ERES__FORALL_2E0: u).
thf(func_def_63, type, c_2Ebool_2ERES__FORALL_2E2: (du > du > u)).
thf(func_def_64, type, c_2Ebool_2ERES__SELECT_2E0: u).
thf(func_def_65, type, c_2Ebool_2ERES__SELECT_2E2: (du > du > u)).
thf(func_def_66, type, c_2Ebool_2ETYPE__DEFINITION_2E0: u).
thf(func_def_67, type, c_2Ebool_2ETYPE__DEFINITION_2E2: (du > du > u)).
thf(func_def_68, type, c_2Ebool_2Eliteral__case_2E0: u).
thf(func_def_69, type, c_2Ebool_2Eliteral__case_2E2: (du > du > u)).
thf(func_def_70, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_20mono_2Etyop_2Emin_2Ebool: (((mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > $o) > (mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > $o)).
thf(func_def_71, type, mono_2Ec_2Ebool_2EBOUNDED: ($o > $o)).
thf(func_def_72, type, mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind: ((mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > $o)).
thf(func_def_73, type, mono_2Ec_2Ebool_2EONTO_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind: ((mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > $o)).
thf(func_def_74, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29: (((mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > $o) > u)).
thf(func_def_75, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29: ((mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > u)).
thf(func_def_76, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29: (du > (mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind) > $o)).
thf(func_def_77, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29: (du > mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind)).
thf(func_def_80, type, sK0: (u > d > u)).
thf(func_def_81, type, sK1: (u > d > u)).
thf(func_def_82, type, sK2: ($o > $o > $o)).
thf(func_def_83, type, sK3: (d > d > u > u)).
thf(func_def_84, type, sK4: (d > d > u > u)).
thf(func_def_85, type, sK5: (d > u > u > u)).
thf(func_def_86, type, sK6: (u > d > u)).
thf(func_def_87, type, sK7: $o).
thf(func_def_88, type, sK8: (u > d > u > d > u)).
thf(func_def_89, type, sK9: (u > d > d > u)).
thf(func_def_90, type, sK10: (u > d > d > u)).
thf(func_def_91, type, sK11: (u > d > d > u > u)).
thf(func_def_92, type, sK12: (u > d > d > u > u)).
thf(func_def_93, type, sK13: (u > u > d > d > u)).
thf(func_def_94, type, sK14: (mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Emin_2Eind)).
thf(func_def_95, type, sK15: (u > d > u)).
thf(func_def_96, type, sK16: (d > u > u)).
thf(func_def_97, type, sK17: (d > u > $o)).
thf(func_def_98, type, sK18: (d > u > u)).
thf(func_def_99, type, sK19: (d > u > u)).
thf(func_def_100, type, sK20: (d > u > u > u)).
thf(func_def_101, type, sK21: (d > u > u > u)).
thf(func_def_102, type, sK22: (d > u > u > u)).
thf(func_def_103, type, sK23: (d > u > u)).
thf(func_def_104, type, sK24: (d > u > u)).
thf(func_def_105, type, sK25: (d > u > u)).
thf(func_def_106, type, sK26: (u > d > u)).
thf(func_def_107, type, sK27: (u > d > u)).
thf(func_def_108, type, sK28: $o).
thf(func_def_109, type, sK29: ($o > $o > $o)).
thf(func_def_110, type, sK30: (d > u > u > u)).
thf(func_def_111, type, sK31: (u > u > d > d > u)).
thf(func_def_112, type, sK32: (u > d > u)).
thf(func_def_113, type, sK33: (u > d > d > u > u)).
thf(func_def_114, type, sK34: (d > d > u > u)).
thf(func_def_115, type, sK35: (d > u > u)).
thf(func_def_116, type, sK36: (d > u > u)).
thf(func_def_117, type, sK37: (u > d > u)).
thf(func_def_118, type, sK38: (u > d > u)).
thf(func_def_119, type, sK39: (u > d > u)).
thf(f36,axiom,(
  ! [X0 : $o] : (X0 = X0) <=> mono_2Ec_2Ebool_2ET),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF)).
thf(f45,axiom,(
  ! [X0 : d,X1 : u] : (! [X2 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) = mono_2Ec_2Ebool_2ET) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__DEF)).
thf(f83,axiom,(
  ! [X0 : $o] : X0 <=> mono_2Ec_2Ebool_2EF),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__DEF)).
thf(f85,axiom,(
  ! [X0 : $o] : ((X0 = mono_2Ec_2Ebool_2ET) | (X0 = mono_2Ec_2Ebool_2EF))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__CASES__AX)).
thf(f93,conjecture,(
  mono_2Ec_2Ebool_2ET),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH)).
thf(f94,negated_conjecture,(
  ~mono_2Ec_2Ebool_2ET),
  inference(negated_conjecture,[status(cth)],[f93])).
thf(f112,plain,(
  ! [X0 : d,X1 : u] : (! [X2 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) = mono_2Ec_2Ebool_2ET) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))),
  inference(rectify,[],[f45])).
thf(f113,plain,(
  ! [X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) <=> ! [X2 : u] : ((mono_2Ec_2Ebool_2ET = $true) <=> (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) = $true)))),
  inference(fool_elimination,[],[f112])).
thf(f122,plain,(
  ~mono_2Ec_2Ebool_2ET),
  inference(rectify,[],[f94])).
thf(f123,plain,(
  ~ (mono_2Ec_2Ebool_2ET = $true)),
  inference(fool_elimination,[],[f122])).
thf(f132,plain,(
  ! [X0 : $o] : X0 <=> mono_2Ec_2Ebool_2EF),
  inference(rectify,[],[f83])).
thf(f133,plain,(
  ! [X0 : $o] : ($true = X0) <=> (mono_2Ec_2Ebool_2EF = $true)),
  inference(fool_elimination,[],[f132])).
thf(f166,plain,(
  ! [X0 : $o] : (X0 = X0) <=> mono_2Ec_2Ebool_2ET),
  inference(rectify,[],[f36])).
thf(f167,plain,(
  (mono_2Ec_2Ebool_2ET = $true) <=> ! [X0 : $o] : (X0 = X0)),
  inference(fool_elimination,[],[f166])).
thf(f179,plain,(
  (mono_2Ec_2Ebool_2ET != $true)),
  inference(flattening,[],[f123])).
thf(f259,plain,(
  ((mono_2Ec_2Ebool_2ET = $true) | ? [X0 : $o] : (X0 != X0)) & (! [X0 : $o] : (X0 = X0) | (mono_2Ec_2Ebool_2ET != $true))),
  inference(nnf_transformation,[],[f167])).
thf(f260,plain,(
  ((mono_2Ec_2Ebool_2ET = $true) | ? [X0 : $o] : (X0 != X0)) & (! [X1 : $o] : (X1 = X1) | (mono_2Ec_2Ebool_2ET != $true))),
  inference(rectify,[],[f259])).
thf(f261,plain,(
  ((mono_2Ec_2Ebool_2ET = $true) | (sK7 != sK7)) & (! [X1 : $o] : (X1 = X1) | (mono_2Ec_2Ebool_2ET != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,$thf(sK7))],[f260])).
thf(f294,plain,(
  (! [X0 : $o] : ($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | ? [X0 : $o] : ($true != X0))),
  inference(nnf_transformation,[],[f133])).
thf(f295,plain,(
  (! [X0 : $o] : ($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | ? [X1 : $o] : ($true != X1))),
  inference(rectify,[],[f294])).
thf(f296,plain,(
  (! [X0 : $o] : ($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | (sK28 != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X1,$thf(sK28))],[f295])).
thf(f313,plain,(
  ! [X0 : d,X1 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ? [X2 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) != $true) | (mono_2Ec_2Ebool_2ET != $true)) & ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) = $true) | (mono_2Ec_2Ebool_2ET = $true)))) & (! [X2 : u] : (((mono_2Ec_2Ebool_2ET = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) != $true)) & ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) = $true) | (mono_2Ec_2Ebool_2ET != $true))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)))),
  inference(nnf_transformation,[],[f113])).
thf(f314,plain,(
  ! [X0 : d,X1 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ? [X2 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) != $true) | (mono_2Ec_2Ebool_2ET != $true)) & ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X2))))) = $true) | (mono_2Ec_2Ebool_2ET = $true)))) & (! [X3 : u] : (((mono_2Ec_2Ebool_2ET = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) != $true)) & ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) = $true) | (mono_2Ec_2Ebool_2ET != $true))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)))),
  inference(rectify,[],[f313])).
thf(f315,plain,(
  ! [X0 : d,X1 : u] : (((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) = $true) | ((($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ (sK32 @ X1 @ X0))))))) | (mono_2Ec_2Ebool_2ET != $true)) & (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ (sK32 @ X1 @ X0))))))) | (mono_2Ec_2Ebool_2ET = $true)))) & (! [X3 : u] : (((mono_2Ec_2Ebool_2ET = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) != $true)) & ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) = $true) | (mono_2Ec_2Ebool_2ET != $true))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,$thf(sK1 @ X1 @ X0))],[f314])).
thf(f398,plain,(
  (sK7 != sK7) | (mono_2Ec_2Ebool_2ET = $true)),
  inference(cnf_transformation,[],[f261])).
thf(f461,plain,(
  ( ! [X0 : $o] : ((mono_2Ec_2Ebool_2EF != $true) | ($true = X0)) )),
  inference(cnf_transformation,[],[f296])).
thf(f483,plain,(
  ( ! [X0 : $o] : ((mono_2Ec_2Ebool_2EF = X0) | (mono_2Ec_2Ebool_2ET = X0)) )),
  inference(cnf_transformation,[],[f85])).
thf(f491,plain,(
  (mono_2Ec_2Ebool_2ET != $true)),
  inference(cnf_transformation,[],[f179])).
thf(f497,plain,(
  ( ! [X3 : u,X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true) | (mono_2Ec_2Ebool_2ET = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) != $true)) )),
  inference(cnf_transformation,[],[f315])).
thf(f654,plain,(
  ( ! [X0 : $o] : (($true = X0) | (mono_2Ec_2Ebool_2EF = $false) | (mono_2Ec_2Ebool_2ET = X0)) )),
  inference(iff_proxy_clausification,[],[f483])).
thf(f656,plain,(
  ( ! [X0 : $o] : ((mono_2Ec_2Ebool_2ET = $false) | ($true = X0) | ($true = X0) | (mono_2Ec_2Ebool_2EF = $false)) )),
  inference(iff_proxy_clausification,[],[f654])).
thf(f657,plain,(
  ( ! [X0 : $o] : (($true = X0) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2EF = $false)) )),
  inference(duplicate_literal_removal,[],[f656])).
thf(f688,plain,(
  (mono_2Ec_2Ebool_2ET = $true) | (sK7 = $true) | (sK7 = $true)),
  inference(xor_proxy_clausification,[],[f398])).
thf(f689,plain,(
  (sK7 = $false) | (sK7 = $false) | (mono_2Ec_2Ebool_2ET = $true)),
  inference(xor_proxy_clausification,[],[f398])).
thf(f690,plain,(
  (mono_2Ec_2Ebool_2ET = $true) | (sK7 = $false)),
  inference(duplicate_literal_removal,[],[f689])).
thf(f691,plain,(
  (mono_2Ec_2Ebool_2ET = $true) | (sK7 = $true)),
  inference(duplicate_literal_removal,[],[f688])).
thf(f717,definition,(
  spl40_2 <=> (mono_2Ec_2Ebool_2ET = $true)),
  introduced(definition,[new_symbols(definition,[spl40_2])],[avatar_definition])).
thf(f725,definition,(
  spl40_4 <=> (mono_2Ec_2Ebool_2EF = $true)),
  introduced(definition,[new_symbols(definition,[spl40_4])],[avatar_definition])).
thf(f742,definition,(
  spl40_8 <=> ! [X0 : d,X1 : u,X3 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) != $true))),
  introduced(definition,[new_symbols(definition,[spl40_8])],[avatar_definition])).
thf(f743,plain,(
  ( ! [X3 : u,X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ X3))))) != $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)) ) | ~spl40_8),
  inference(avatar_component_clause,[],[f742])).
thf(f744,plain,(
  spl40_8 | spl40_2),
  inference(avatar_split_clause,[],[f497,f717,f742])).
thf(f763,definition,(
  spl40_13 <=> (mono_2Ec_2Ebool_2ET = $false)),
  introduced(definition,[new_symbols(definition,[spl40_13])],[avatar_definition])).
thf(f767,definition,(
  spl40_14 <=> ! [X0 : $o] : ($true = X0)),
  introduced(definition,[new_symbols(definition,[spl40_14])],[avatar_definition])).
thf(f768,plain,(
  ( ! [X0 : $o] : (($true = X0)) ) | ~spl40_14),
  inference(avatar_component_clause,[],[f767])).
thf(f770,definition,(
  spl40_15 <=> (mono_2Ec_2Ebool_2EF = $false)),
  introduced(definition,[new_symbols(definition,[spl40_15])],[avatar_definition])).
thf(f773,plain,(
  spl40_13 | spl40_14 | spl40_15),
  inference(avatar_split_clause,[],[f657,f770,f767,f763])).
thf(f775,plain,(
  spl40_14 | ~spl40_4),
  inference(avatar_split_clause,[],[f461,f725,f767])).
thf(f793,plain,(
  ~spl40_2),
  inference(avatar_split_clause,[],[f491,f717])).
thf(f800,definition,(
  spl40_21 <=> (sK7 = $false)),
  introduced(definition,[new_symbols(definition,[spl40_21])],[avatar_definition])).
thf(f803,plain,(
  spl40_2 | spl40_21),
  inference(avatar_split_clause,[],[f690,f800,f717])).
thf(f805,definition,(
  spl40_22 <=> (sK7 = $true)),
  introduced(definition,[new_symbols(definition,[spl40_22])],[avatar_definition])).
thf(f808,plain,(
  spl40_22 | spl40_2),
  inference(avatar_split_clause,[],[f691,f717,f805])).
thf(f850,definition,(
  (mono_2Ec_2Ebool_2ET != $false) | (sK7 != $false) | (sK7 != $true) | (mono_2Ec_2Ebool_2ET = $true)),
  introduced(theory,[theory_tautology_sat_conflict])).
thf(f876,plain,(
  ( ! [X0 : d,X1 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2E_21_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) != $true)) ) | (~spl40_8 | ~spl40_14)),
  inference(forward_subsumption_resolution,[],[f743,f768])).
thf(f877,plain,(
  $false | (~spl40_8 | ~spl40_14)),
  inference(forward_subsumption_resolution,[],[f876,f768])).
thf(f878,plain,(
  ~spl40_8 | ~spl40_14),
  inference(avatar_contradiction_clause,[],[f877])).
thf(f879,definition,(
  (mono_2Ec_2Ebool_2EF != $false) | (sK7 != $false) | (sK7 != $true) | (mono_2Ec_2Ebool_2EF = $true)),
  introduced(theory,[theory_tautology_sat_conflict])).
cnf(s6, plain, spl40_2 | spl40_8, inference(sat_conversion,[],[f744])).
cnf(s12, plain, spl40_13 | spl40_14 | spl40_15, inference(sat_conversion,[],[f773])).
cnf(s14, plain, ~spl40_4 | spl40_14, inference(sat_conversion,[],[f775])).
cnf(s19, plain, ~spl40_2, inference(sat_conversion,[],[f793])).
cnf(s21, plain, spl40_2 | spl40_21, inference(sat_conversion,[],[f803])).
cnf(s22, plain, spl40_2 | spl40_22, inference(sat_conversion,[],[f808])).
cnf(s33, plain, spl40_2 | ~spl40_13 | ~spl40_21 | ~spl40_22, inference(sat_conversion,[],[f850])).
cnf(s34, plain, ~spl40_8 | ~spl40_14, inference(sat_conversion,[],[f878])).
cnf(s35, plain, spl40_4 | ~spl40_15 | ~spl40_21 | ~spl40_22, inference(sat_conversion,[],[f879])).
cnf(s39, plain, spl40_22, inference(rat,[],[s22,s19])).
cnf(s40, plain, spl40_21, inference(rat,[],[s21,s19])).
cnf(s41, plain, ~spl40_13, inference(rat,[],[s33,s39,s19,s40])).
cnf(s47, plain, spl40_14 | spl40_15, inference(rat,[],[s12,s41])).
cnf(s49, plain, spl40_8, inference(rat,[],[s6,s19])).
cnf(s50, plain, ~spl40_14, inference(rat,[],[s34,s49])).
cnf(s51, plain, ~spl40_4, inference(rat,[],[s14,s50])).
cnf(s52, plain, spl40_15, inference(rat,[],[s47,s50])).
cnf(s53, plain, $false, inference(rat,[],[s35,s39,s40,s52,s51])).
thf(f880,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s53])).
% SZS output end Proof for theBenchmark