%----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(func_def_0, type, tyop_2Emin_2Ebool: d).
thf(func_def_1, type, tyop_2Emin_2Efun: (d > d > d)).
thf(func_def_2, type, tyop_2Eoption_2Eoption: (d > d)).
thf(func_def_3, type, s: (d > u > du)).
thf(func_def_4, type, app_2E2: (du > du > u)).
thf(func_def_5, type, combin_i_2E0: u).
thf(func_def_6, type, combin_k_2E0: u).
thf(func_def_7, type, combin_s_2E0: u).
thf(func_def_8, type, c_2Ebool_2E_21_2E0: u).
thf(func_def_9, type, c_2Ebool_2E_21_2E1: (du > u)).
thf(func_def_10, type, c_2Ebool_2E_2F_5C_2E0: u).
thf(func_def_11, type, c_2Ebool_2E_2F_5C_2E2: (du > du > u)).
thf(func_def_12, type, c_2Emin_2E_3D_2E0: u).
thf(func_def_13, type, c_2Emin_2E_3D_2E2: (du > du > u)).
thf(func_def_14, type, c_2Emin_2E_3D_3D_3E_2E0: u).
thf(func_def_15, type, c_2Emin_2E_3D_3D_3E_2E2: (du > du > u)).
thf(func_def_16, type, c_2Ebool_2E_3F_2E0: u).
thf(func_def_17, type, c_2Ebool_2E_3F_2E1: (du > u)).
thf(func_def_18, type, c_2Ebool_2EF_2E0: u).
thf(func_def_19, type, c_2Eoption_2EIS__NONE_2E0: u).
thf(func_def_20, type, c_2Eoption_2EIS__NONE_2E1: (du > u)).
thf(func_def_21, type, c_2Eoption_2EIS__SOME_2E0: u).
thf(func_def_22, type, c_2Eoption_2EIS__SOME_2E1: (du > u)).
thf(func_def_23, type, c_2Eoption_2ENONE_2E0: u).
thf(func_def_24, type, c_2Eoption_2EOPTION__JOIN_2E0: u).
thf(func_def_25, type, c_2Eoption_2EOPTION__JOIN_2E1: (du > u)).
thf(func_def_26, type, c_2Eoption_2EOPTION__MAP_2E0: u).
thf(func_def_27, type, c_2Eoption_2EOPTION__MAP_2E2: (du > du > u)).
thf(func_def_28, type, c_2Eoption_2EOPTREL_2E0: u).
thf(func_def_29, type, c_2Eoption_2EOPTREL_2E3: (du > du > du > u)).
thf(func_def_30, type, c_2Eoption_2ESOME_2E0: u).
thf(func_def_31, type, c_2Eoption_2ESOME_2E1: (du > u)).
thf(func_def_32, type, c_2Ebool_2ET_2E0: u).
thf(func_def_33, type, c_2Eoption_2ETHE_2E0: u).
thf(func_def_34, type, c_2Eoption_2ETHE_2E1: (du > u)).
thf(func_def_35, type, c_2Ebool_2E_5C_2F_2E0: u).
thf(func_def_36, type, c_2Ebool_2E_5C_2F_2E2: (du > du > u)).
thf(func_def_37, type, c_2Eoption_2Eoption__CASE_2E0: u).
thf(func_def_38, type, c_2Eoption_2Eoption__CASE_2E3: (du > du > du > u)).
thf(func_def_39, type, c_2Ebool_2E_7E_2E0: u).
thf(func_def_40, type, c_2Ebool_2E_7E_2E1: (du > u)).
thf(func_def_41, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: (($o > $o) > $o > $o)).
thf(func_def_42, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o > $o) > $o > $o > $o)).
thf(func_def_43, type, mono_2Ec_2Ebool_2E_2F_5C: ($o > $o > $o)).
thf(func_def_44, type, mono_2Ec_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
thf(func_def_45, type, mono_2Ec_2Ebool_2EF: $o).
thf(func_def_46, type, mono_2Ec_2Ebool_2ET: $o).
thf(func_def_47, type, mono_2Ec_2Ebool_2E_5C_2F: ($o > $o > $o)).
thf(func_def_48, type, mono_2Ec_2Ebool_2E_7E: ($o > $o)).
thf(func_def_49, type, i_mono_2Etyop_2Emin_2Ebool: ($o > u)).
thf(func_def_50, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o) > u)).
thf(func_def_51, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (($o > $o > $o) > u)).
thf(func_def_52, type, j_mono_2Etyop_2Emin_2Ebool: (du > $o)).
thf(func_def_53, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (du > $o > $o)).
thf(func_def_54, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (du > $o > $o > $o)).
thf(func_def_56, type, vNOT: ($o > $o)).
thf(func_def_59, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_60, type, sK0: (u > d > u)).
thf(func_def_61, type, sK1: (d > u > u > u > d > u)).
thf(func_def_62, type, sK2: (d > u > u > u > d > u)).
thf(func_def_63, type, sK3: u).
thf(func_def_64, type, sK4: u).
thf(func_def_65, type, sK5: d).
thf(func_def_66, type, sK6: u).
thf(func_def_67, type, sK7: (d > u > u)).
thf(func_def_68, type, sK8: (d > u > d > u > u)).
thf(func_def_70, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_71, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f9,axiom,(
  ! [X1 : u,X0 : d] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0) @ (s @ X0 @ X1)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a)).
thf(f26,axiom,(
  ! [X3 : u,X4 : u,X0 : d,X2 : u,X1 : d] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) <=> (? [X6 : u,X5 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6)))) & (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))) & (((s @ (tyop_2Eoption_2Eoption @ X1) @ X4)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)))))) | ((((s @ (tyop_2Eoption_2Eoption @ X1) @ X4)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0))) & (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def)).
thf(f32,axiom,(
  ! [X2 : u,X4 : u,X1 : d,X0 : d,X3 : u] : (! [X23 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X23))))))) = mono_2Ec_2Ebool_2ET) & ! [X9 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9)))) => (((s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)))) = ((s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9)))))))) & ! [X15 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X15)))))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ X15))) & ! [X5 : u] : (((s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))) = ((s @ X0 @ X5))) & ! [X16 : u] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X16) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0))) & ! [X10 : u,X11 : u] : (((s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X10) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X11)))) = ((s @ X1 @ X10))) & ! [X6 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X6)))) => (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X6)))))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ X6)))) & (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) & ! [X24 : u] : (~ (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) = mono_2Ec_2Ebool_2EF) & ! [X20 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20)))) => (((s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)))) = ((s @ X1 @ X4)))) & ! [X26 : u,X27 : u] : ((((s @ X0 @ X26)) = ((s @ X0 @ X27))) <=> (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27)))))) & ! [X12 : u,X14 : u,X13 : u] : (((s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X12))) @ (s @ X1 @ X13) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X14)))) = ((s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X14) @ (s @ X0 @ X12))))) & ! [X7 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) & ! [X8 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ X8))) & ! [X17 : u,X18 : u] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X17) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X18)))))) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X17) @ (s @ X0 @ X18))))))) & ! [X19 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X19)))) => (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X19) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ X19)))) & ! [X21 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21))))) <=> (((s @ (tyop_2Eoption_2Eoption @ X0) @ X21)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) & ! [X22 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X22)))) <=> (((s @ (tyop_2Eoption_2Eoption @ X0) @ X22)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) & ! [X25 : u] : (~ (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25)))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES)).
thf(f37,axiom,(
  ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2EF) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2ET) <=> X0) & (X0 <=> (mono_2Ec_2Ebool_2ET = X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES)).
thf(f38,conjecture,(
  ! [X3 : u,X1 : u,X2 : u,X0 : d] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1))))))) = mono_2Ec_2Ebool_2EF) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) = mono_2Ec_2Ebool_2EF) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) = mono_2Ec_2Ebool_2ET) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1))))))) = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X0 @ X2))) @ (s @ X0 @ X1)))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def)).
thf(f39,negated_conjecture,(
  ~ ! [X3 : u,X1 : u,X2 : u,X0 : d] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1))))))) = mono_2Ec_2Ebool_2EF) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) = mono_2Ec_2Ebool_2EF) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) = mono_2Ec_2Ebool_2ET) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1))))))) = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X0 @ X2))) @ (s @ X0 @ X1)))))))),
  inference(negated_conjecture,[status(cth)],[f38])).
thf(f44,axiom,(
  mono_2Ec_2Ebool_2ET),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH)).
thf(f52,plain,(
  mono_2Ec_2Ebool_2ET),
  inference(rectify,[],[f44])).
thf(f53,plain,(
  (mono_2Ec_2Ebool_2ET = $true)),
  inference(fool_elimination,[],[f52])).
thf(f54,plain,(
  ! [X0 : u,X1 : u,X2 : d,X3 : d,X4 : u] : (! [X5 : u] : (mono_2Ec_2Ebool_2ET = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5)))))))) & ! [X6 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6)))) => (((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0) @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6)))))) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))))) & ! [X7 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X7)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X7))))))) & ! [X8 : u] : (((s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X8)))))) = ((s @ X3 @ X8))) & ! [X9 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))))) & ! [X10 : u,X11 : u] : (((s @ X2 @ X10)) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ X2 @ X10) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X11))))) & ! [X12 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))) => (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))) & (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ENONE_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) & ! [X13 : u] : (~ (((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X13)))))) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) & ! [X14 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14)))) => (((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))) = ((s @ X2 @ X1)))) & ! [X15 : u,X16 : u] : ((((s @ X3 @ X16)) = ((s @ X3 @ X15))) <=> (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X15)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X16)))))) & ! [X17 : u,X18 : u,X19 : u] : (((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X17))) @ (s @ X2 @ X19) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18)))) = ((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18) @ (s @ X3 @ X17))))) & ! [X20 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X20)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))) & ! [X21 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X21)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))) & ! [X22 : u,X23 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ X3 @ X23)))))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X23))))))) & ! [X24 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24)))) => (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X4) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X24)))) & ! [X25 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X25))))) <=> (((s @ (tyop_2Eoption_2Eoption @ X3) @ X25)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))) & ! [X26 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))) <=> (((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))) & ! [X27 : u] : (~ (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X27)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))),
  inference(rectify,[],[f32])).
thf(f55,plain,(
  ! [X1 : u,X0 : u,X2 : d,X4 : u,X3 : d] : (! [X6 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6))))) = $true) => (((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0) @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6)))))) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))))) & ! [X13 : u] : ($true = ((~ ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X13))))))) & ! [X25 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X3) @ X25)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) <=> (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X25)))))) = $true)) & ! [X18 : u,X17 : u,X19 : u] : (((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X17))) @ (s @ X2 @ X19) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18)))) = ((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18) @ (s @ X3 @ X17))))) & ! [X11 : u,X10 : u] : (((s @ X2 @ X10)) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ X2 @ X10) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X11))))) & ! [X21 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X21)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))) & ! [X14 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14)))))) => (((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))) = ((s @ X2 @ X1)))) & ! [X5 : u] : (mono_2Ec_2Ebool_2ET = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5)))))))) & ! [X8 : u] : (((s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X8)))))) = ((s @ X3 @ X8))) & (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ENONE_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) & ! [X12 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) => (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))) & ! [X26 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))))) <=> (((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))) & ! [X7 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X7)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X7))))))) & ! [X24 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24))))) = $true) => (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X4) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X24)))) & ! [X27 : u] : (((~ ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X27))) = (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))) = $true) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) & ! [X23 : u,X22 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ X3 @ X23)))))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X23))))))) & ! [X20 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X20)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))) & ! [X9 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))))) & ! [X16 : u,X15 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X15)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X16))))) <=> (((s @ X3 @ X16)) = ((s @ X3 @ X15)))))),
  inference(fool_elimination,[],[f54])).
thf(f72,plain,(
  ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2EF) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2ET) <=> X0) & (X0 <=> (mono_2Ec_2Ebool_2ET = X0)))),
  inference(rectify,[],[f37])).
thf(f73,plain,(
  ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) <=> (((~ X0)) = $true)) & ((mono_2Ec_2Ebool_2EF = X0) <=> (((~ X0)) = $true)) & ((mono_2Ec_2Ebool_2ET = X0) <=> ($true = X0)) & ((mono_2Ec_2Ebool_2ET = X0) <=> ($true = X0)))),
  inference(fool_elimination,[],[f72])).
thf(f76,plain,(
  ! [X0 : u,X1 : u,X2 : d,X3 : u,X4 : d] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) <=> (? [X5 : u,X6 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X6))) @ (s @ X4 @ X5)))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X5)))) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) | ((((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))))))),
  inference(rectify,[],[f26])).
thf(f77,plain,(
  ! [X4 : d,X3 : u,X0 : u,X1 : u,X2 : d] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))))) <=> (? [X5 : u,X6 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X6))) @ (s @ X4 @ X5)))))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X5)))) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) | ((((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))))))),
  inference(fool_elimination,[],[f76])).
thf(f88,plain,(
  ~ ! [X2 : u,X3 : d,X1 : u,X0 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X1))))))) = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ X3 @ X2))) @ (s @ X3 @ X1)))))) & (mono_2Ec_2Ebool_2ET = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X1)))))))))),
  inference(rectify,[],[f39])).
thf(f95,plain,(
  ! [X0 : u,X1 : d] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0) @ (s @ X1 @ X0)))) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X0)))))),
  inference(rectify,[],[f9])).
thf(f99,plain,(
  ! [X2 : d,X3 : d,X1 : u,X0 : u,X4 : u] : (! [X25 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X3) @ X25)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) <=> (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X25)))))) = $true)) & ! [X24 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X4) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X24))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24))))) != $true)) & ! [X14 : u] : ((((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))) = ((s @ X2 @ X1))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14))))))) & ! [X26 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))))) <=> (((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))) & ! [X16 : u,X15 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X15)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X16))))) <=> (((s @ X3 @ X16)) = ((s @ X3 @ X15)))) & (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ENONE_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) & ! [X8 : u] : (((s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X8)))))) = ((s @ X3 @ X8))) & ! [X5 : u] : (mono_2Ec_2Ebool_2ET = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5)))))))) & ! [X13 : u] : ($true = ((~ ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X13))))))) & ! [X11 : u,X10 : u] : (((s @ X2 @ X10)) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ X2 @ X10) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X11))))) & ! [X6 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6))))) != $true) | (((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0) @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6)))))) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))))) & ! [X7 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X7)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X7))))))) & ! [X9 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))))) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) & ! [X21 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X21)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))) & ! [X18 : u,X17 : u,X19 : u] : (((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X17))) @ (s @ X2 @ X19) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18)))) = ((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18) @ (s @ X3 @ X17))))) & ! [X23 : u,X22 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ X3 @ X23)))))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X23))))))) & ! [X12 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) | (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))) & ! [X27 : u] : (((~ ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X27))) = (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))) = $true) & ! [X20 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X20)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))))),
  inference(ennf_transformation,[],[f55])).
thf(f104,plain,(
  ? [X1 : u,X0 : u,X3 : d,X2 : u] : ((mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X1)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X1))))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ X3 @ X2))) @ (s @ X3 @ X1)))))) | (mono_2Ec_2Ebool_2ET != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool)) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))))),
  inference(ennf_transformation,[],[f88])).
thf(f105,plain,(
  ! [X0 : $o] : ((((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0))) & (((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0))) & (((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0))) & (((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0))))),
  inference(nnf_transformation,[],[f73])).
thf(f106,plain,(
  ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0)) & ((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0)))),
  inference(flattening,[],[f105])).
thf(f115,plain,(
  ! [X4 : d,X3 : u,X0 : u,X1 : u,X2 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))))) | (! [X5 : u,X6 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X6))) @ (s @ X4 @ X5)))))) | (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) != ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X5)))) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) & ((((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1))) | (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0)))))) & ((? [X5 : u,X6 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X6))) @ (s @ X4 @ X5)))))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X5)))) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) | ((((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X1))))))))),
  inference(nnf_transformation,[],[f77])).
thf(f116,plain,(
  ! [X4 : d,X3 : u,X0 : u,X1 : u,X2 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))))) | (! [X5 : u,X6 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X6))) @ (s @ X4 @ X5)))))) | (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) != ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X5)))) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) & ((((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1))) | (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0)))))) & (? [X5 : u,X6 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X6))) @ (s @ X4 @ X5)))))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X5)))) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1)))) | ((((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X1))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0)))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X1))))))))),
  inference(flattening,[],[f115])).
thf(f117,plain,(
  ! [X0 : d,X1 : u,X2 : u,X3 : u,X4 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (! [X5 : u,X6 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X4 @ X6))) @ (s @ X0 @ X5)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X6)))) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X2))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) != ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))) & ((((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) != ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)))))) & (? [X7 : u,X8 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X4 @ X8))) @ (s @ X0 @ X7)))))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X8)))) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ X2))) & (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X7)))))) | ((((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))))))))),
  inference(rectify,[],[f116])).
thf(f118,plain,(
  ! [X0 : d,X1 : u,X2 : u,X3 : u,X4 : d] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (! [X5 : u,X6 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X4 @ X6))) @ (s @ X0 @ X5)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X6)))) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X2))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) != ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))) & ((((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) != ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)))))) & ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X4 @ (sK2 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X0 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (sK2 @ X4 @ X3 @ X2 @ X1 @ X0)))))) & (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))))) | ((((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) & (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK0 @ X1 @ X0)),skolemize(X2,$thf(sK0 @ X1 @ X0))],[f117])).
thf(f123,plain,(
  ! [X2 : d,X3 : d,X1 : u,X0 : u,X4 : u] : (! [X25 : u] : (((((s @ (tyop_2Eoption_2Eoption @ X3) @ X25)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) | (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X25)))))) != $true)) & ((((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X25)))))) = $true) | (((s @ (tyop_2Eoption_2Eoption @ X3) @ X25)) != ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))))) & ! [X24 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X4) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X24))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X24))))) != $true)) & ! [X14 : u] : ((((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))) = ((s @ X2 @ X1))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X14))))))) & ! [X26 : u] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))))) | (((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))) & ((((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X26))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X26)))))))) & ! [X16 : u,X15 : u] : (((((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X15)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X16))))) | (((s @ X3 @ X16)) != ((s @ X3 @ X15)))) & ((((s @ X3 @ X16)) = ((s @ X3 @ X15))) | (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X15)))) != ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X16))))))) & (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ENONE_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) & ! [X8 : u] : (((s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X8)))))) = ((s @ X3 @ X8))) & ! [X5 : u] : (mono_2Ec_2Ebool_2ET = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5)))))))) & ! [X13 : u] : ($true = ((~ ((s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X13))))))) & ! [X11 : u,X10 : u] : (((s @ X2 @ X10)) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ X2 @ X10) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X11))))) & ! [X6 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6))))) != $true) | (((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0) @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6)))))) = ((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X6) @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X0)))))) & ! [X7 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X7)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X7))))))) & ! [X9 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))))) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))))) & ! [X21 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X21)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X21) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))) & ! [X18 : u,X17 : u,X19 : u] : (((s @ X2 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X17))) @ (s @ X2 @ X19) @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18)))) = ((s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X18) @ (s @ X3 @ X17))))) & ! [X23 : u,X22 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ X3 @ X23)))))) = ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X2) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X23))))))) & ! [X12 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) | (((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))))) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ X12)))) & ! [X27 : u] : (((~ ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X27))) = (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))) = $true) & ! [X20 : u] : (((s @ (tyop_2Eoption_2Eoption @ X3) @ X20)) = ((s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X3) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Eoption_2Eoption @ X3)) @ c_2Eoption_2ESOME_2E0))))))),
  inference(nnf_transformation,[],[f99])).
thf(f124,plain,(
  ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (! [X5 : u] : (((((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ X5))) | ($true != ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X5)))))))) & (($true = ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X5))))))) | (((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X1) @ X5))))) & ! [X6 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X6) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0)))) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ X6))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X6))))))) & ! [X7 : u] : ((((s @ X0 @ X2)) = ((s @ X0 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X7) @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X7))))) != $true)) & ! [X8 : u] : ((($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X8)))))) | (((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X1) @ X8)))) & ((((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ X8))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X8)))))))) & ! [X9 : u,X10 : u] : (((((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X10)))) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X9))))) | (((s @ X1 @ X10)) != ((s @ X1 @ X9)))) & ((((s @ X1 @ X10)) = ((s @ X1 @ X9))) | (((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X10)))) != ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X9))))))) & (((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ENONE_2E0))))) & ! [X11 : u] : (((s @ X1 @ X11)) = ((s @ X1 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X11))))))) & ! [X12 : u] : (mono_2Ec_2Ebool_2ET = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X12)))))))) & ! [X13 : u] : ($true = ((~ ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X13))))))) & ! [X14 : u,X15 : u] : (((s @ X0 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ X0 @ X15) @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14)))) = ((s @ X0 @ X15))) & ! [X16 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X16)))))) | (((s @ X0 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X16) @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3)))) = ((s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X16)))))))) & ! [X17 : u] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ X17)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X1)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X17))))))) & ! [X18 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X18) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0))))) & (mono_2Ec_2Ebool_2EF = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)))))) & ! [X19 : u] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ X19)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X19) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X19) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0))))) & ! [X20 : u,X21 : u,X22 : u] : (((s @ X0 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X21))) @ (s @ X0 @ X22) @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X20)))) = ((s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X20) @ (s @ X1 @ X21))))) & ! [X23 : u,X24 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X24) @ (s @ X1 @ X23)))))) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X24) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X23))))))) & ! [X25 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X25))))) != $true) | (((s @ (tyop_2Eoption_2Eoption @ X1) @ X25)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X25)))))))) & ! [X26 : u] : (((~ ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X26))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)))) = $true) & ! [X27 : u] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ X27)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X27) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0))))))),
  inference(rectify,[],[f123])).
thf(f126,plain,(
  ? [X0 : u,X1 : u,X2 : d,X3 : u] : ((mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X3))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0))))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X2 @ X3))) @ (s @ X2 @ X0)))))) | (mono_2Ec_2Ebool_2ET != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X3))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))))))),
  inference(rectify,[],[f104])).
thf(f127,plain,(
  (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2ET != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,$thf(sK3)),skolemize(X1,$thf(sK4)),skolemize(X2,$thf(sK5)),skolemize(X3,$thf(sK6))],[f126])).
thf(f145,plain,(
  ( ! [X0 : $o] : ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0)) )),
  inference(cnf_transformation,[],[f106])).
thf(f185,plain,(
  ( ! [X2 : u,X3 : u,X0 : d,X1 : u,X4 : d] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))))) )),
  inference(cnf_transformation,[],[f118])).
thf(f187,plain,(
  ( ! [X2 : u,X3 : u,X0 : d,X1 : u,X4 : d] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (sK2 @ X4 @ X3 @ X2 @ X1 @ X0)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)))) )),
  inference(cnf_transformation,[],[f118])).
thf(f188,plain,(
  ( ! [X2 : u,X3 : u,X0 : d,X1 : u,X4 : d] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (sK2 @ X4 @ X3 @ X2 @ X1 @ X0))))))) )),
  inference(cnf_transformation,[],[f118])).
thf(f189,plain,(
  ( ! [X2 : u,X3 : u,X0 : d,X1 : u,X4 : d] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) = ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X4 @ (sK2 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X0 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0)))))))) )),
  inference(cnf_transformation,[],[f118])).
thf(f191,plain,(
  ( ! [X2 : u,X3 : u,X0 : d,X1 : u,X4 : d] : ((((s @ (tyop_2Eoption_2Eoption @ X4) @ X2)) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)))))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) != ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) )),
  inference(cnf_transformation,[],[f118])).
thf(f192,plain,(
  ( ! [X2 : u,X3 : u,X0 : d,X1 : u,X6 : u,X4 : d,X5 : u] : (($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ X4 @ X6))) @ (s @ X0 @ X5)))))) | (((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ X6)))) != ((s @ (tyop_2Eoption_2Eoption @ X4) @ X2))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) != ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X4 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X4) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))))))) )),
  inference(cnf_transformation,[],[f118])).
thf(f196,plain,(
  ( ! [X0 : u,X1 : d] : ((((s @ (tyop_2Eoption_2Eoption @ X1) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0) @ (s @ X1 @ X0)))) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X0)))))) )),
  inference(cnf_transformation,[],[f95])).
thf(f200,plain,(
  ( ! [X1 : d,X27 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X1) @ X27)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X27) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0)))))) )),
  inference(cnf_transformation,[],[f124])).
thf(f201,plain,(
  ( ! [X1 : d,X26 : u] : ((((~ ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X26))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)))) = $true)) )),
  inference(cnf_transformation,[],[f124])).
thf(f204,plain,(
  ( ! [X21 : u,X0 : d,X1 : d,X22 : u,X20 : u] : ((((s @ X0 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X21))) @ (s @ X0 @ X22) @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X20)))) = ((s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X20) @ (s @ X1 @ X21)))))) )),
  inference(cnf_transformation,[],[f124])).
thf(f205,plain,(
  ( ! [X1 : d,X19 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X1) @ X19)) = ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X19) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X19) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0)))))) )),
  inference(cnf_transformation,[],[f124])).
thf(f207,plain,(
  ( ! [X0 : d,X1 : d,X18 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) = ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X18) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)))))) )),
  inference(cnf_transformation,[],[f124])).
thf(f210,plain,(
  ( ! [X0 : d,X1 : d,X14 : u,X15 : u] : ((((s @ X0 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ X0 @ X15) @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14)))) = ((s @ X0 @ X15)))) )),
  inference(cnf_transformation,[],[f124])).
thf(f215,plain,(
  ( ! [X10 : u,X1 : d,X9 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X10)))) != ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X9))))) | (((s @ X1 @ X10)) = ((s @ X1 @ X9)))) )),
  inference(cnf_transformation,[],[f124])).
thf(f224,plain,(
  (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2ET != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))))),
  inference(cnf_transformation,[],[f127])).
thf(f229,plain,(
  (mono_2Ec_2Ebool_2ET = $true)),
  inference(cnf_transformation,[],[f53])).
thf(f239,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f255,plain,(
  ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  inference(definition_unfolding,[],[f224,f229])).
thf(f260,plain,(
  (((~ mono_2Ec_2Ebool_2EF)) = $true)),
  inference(equality_resolution,[],[f145])).
thf(f292,plain,(
  (mono_2Ec_2Ebool_2EF = $false)),
  inference(not_proxy_clausification,[],[f260])).
thf(f306,plain,(
  ( ! [X1 : d,X26 : u] : (((((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X26))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0))) = $false)) )),
  inference(not_proxy_clausification,[],[f201])).
thf(f307,plain,(
  ( ! [X1 : d,X26 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) != ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X26)))))) )),
  inference(equality_proxy_clausification,[],[f306])).
thf(f324,plain,(
  ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2EF = $true) | (mono_2Ec_2Ebool_2EF != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  inference(xor_proxy_clausification,[],[f255])).
thf(f334,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2EF = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF = $true)),
  inference(xor_proxy_clausification,[],[f324])).
thf(f338,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2EF = $true) | (mono_2Ec_2Ebool_2EF = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true)),
  inference(xor_proxy_clausification,[],[f334])).
thf(f339,plain,(
  (mono_2Ec_2Ebool_2EF = $true) | ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (mono_2Ec_2Ebool_2EF = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $false) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  inference(xor_proxy_clausification,[],[f334])).
thf(f340,plain,(
  (mono_2Ec_2Ebool_2EF = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $false) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  inference(duplicate_literal_removal,[],[f339])).
thf(f341,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (mono_2Ec_2Ebool_2EF = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  inference(duplicate_literal_removal,[],[f338])).
thf(f380,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | ($true = $false) | ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $false)),
  inference(forward_demodulation,[],[f340,f292])).
thf(f381,plain,(
  ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $false) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true)),
  inference(trivial_inequality_removal,[],[f380])).
thf(f382,plain,(
  ($true = $false) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true)),
  inference(forward_demodulation,[],[f341,f292])).
thf(f383,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true)),
  inference(trivial_inequality_removal,[],[f382])).
thf(f396,definition,(
  spl9_4 <=> ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))))),
  introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
thf(f398,plain,(
  ($true != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | spl9_4),
  inference(avatar_component_clause,[],[f396])).
thf(f400,definition,(
  spl9_5 <=> ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition])).
thf(f402,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ~spl9_5),
  inference(avatar_component_clause,[],[f400])).
thf(f404,definition,(
  spl9_6 <=> (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition])).
thf(f406,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) = $true) | ~spl9_6),
  inference(avatar_component_clause,[],[f404])).
thf(f408,definition,(
  spl9_7 <=> (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $false)),
  introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition])).
thf(f410,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $false) | ~spl9_7),
  inference(avatar_component_clause,[],[f408])).
thf(f412,definition,(
  spl9_8 <=> ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
thf(f414,plain,(
  ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ~spl9_8),
  inference(avatar_component_clause,[],[f412])).
thf(f415,plain,(
  ~spl9_4 | spl9_5 | spl9_6 | spl9_7 | spl9_8),
  inference(avatar_split_clause,[],[f381,f412,f408,f404,f400,f396])).
thf(f417,definition,(
  spl9_9 <=> ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
  introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition])).
thf(f419,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ~spl9_9),
  inference(avatar_component_clause,[],[f417])).
thf(f421,definition,(
  spl9_10 <=> (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition])).
thf(f423,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true) | ~spl9_10),
  inference(avatar_component_clause,[],[f421])).
thf(f424,plain,(
  spl9_9 | spl9_5 | spl9_6 | ~spl9_4 | spl9_10),
  inference(avatar_split_clause,[],[f383,f421,f396,f404,f400,f417])).
thf(f447,plain,(
  ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))))) | spl9_4),
  inference(unit_resulting_resolution,[],[f239,f398])).
thf(f1067,plain,(
  ( ! [X2 : u,X3 : d,X0 : d,X1 : d,X4 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ X0) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0))) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0))))))))) )),
  inference(unit_resulting_resolution,[],[f191,f205,f207])).
thf(f1105,plain,(
  ( ! [X2 : u,X0 : d,X1 : d] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X1 @ (tyop_2Eoption_2Eoption @ X1)) @ c_2Eoption_2ESOME_2E0))))))) = $true)) )),
  inference(forward_demodulation,[],[f1067,f207])).
thf(f1154,plain,(
  ( ! [X2 : u,X0 : d,X1 : d] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0))))))) )),
  inference(forward_demodulation,[],[f1105,f210])).
thf(f1203,plain,(
  ($true = $false) | spl9_4),
  inference(backward_demodulation,[],[f447,f1154])).
thf(f1204,plain,(
  $false | spl9_4),
  inference(trivial_inequality_removal,[],[f1203])).
thf(f1205,plain,(
  spl9_4),
  inference(avatar_contradiction_clause,[],[f1204])).
thf(f1297,plain,(
  $false | ~spl9_5),
  inference(unit_resulting_resolution,[],[f188,f307,f307,f402])).
thf(f1300,plain,(
  ~spl9_5),
  inference(avatar_contradiction_clause,[],[f1297])).
thf(f1318,plain,(
  $false | ~spl9_6),
  inference(unit_resulting_resolution,[],[f185,f307,f307,f406])).
thf(f1319,plain,(
  ~spl9_6),
  inference(avatar_contradiction_clause,[],[f1318])).
thf(f1363,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ (sK2 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5)))) @ (s @ sK5 @ (sK1 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5)))))) = $true) | ~spl9_9),
  inference(unit_resulting_resolution,[],[f189,f307,f419])).
thf(f1365,plain,(
  (((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK2 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5))))) = ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))))) | ~spl9_9),
  inference(unit_resulting_resolution,[],[f187,f307,f419])).
thf(f1367,plain,(
  (((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK1 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5))))) = ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))) | ~spl9_9),
  inference(unit_resulting_resolution,[],[f185,f307,f419])).
thf(f1374,plain,(
  (((s @ sK5 @ sK6)) = ((s @ sK5 @ (sK2 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5)))) | ~spl9_9),
  inference(unit_resulting_resolution,[],[f215,f1365])).
thf(f1376,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ (sK1 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5)))))) = $true) | ~spl9_9),
  inference(backward_demodulation,[],[f1363,f1374])).
thf(f1385,plain,(
  (((s @ sK5 @ (sK1 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6)) @ sK4 @ sK5))) = ((s @ sK5 @ sK3))) | ~spl9_9),
  inference(unit_resulting_resolution,[],[f215,f1367])).
thf(f1389,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK5 @ sK6))) @ (s @ sK5 @ sK3))))) = $true) | ~spl9_9),
  inference(backward_demodulation,[],[f1376,f1385])).
thf(f1390,plain,(
  ($true = $false) | (~spl9_7 | ~spl9_9)),
  inference(forward_demodulation,[],[f1389,f410])).
thf(f1391,plain,(
  $false | (~spl9_7 | ~spl9_9)),
  inference(trivial_inequality_removal,[],[f1390])).
thf(f1392,plain,(
  ~spl9_7 | ~spl9_9),
  inference(avatar_contradiction_clause,[],[f1391])).
thf(f1393,plain,(
  ($true = $false) | (~spl9_7 | ~spl9_10)),
  inference(forward_demodulation,[],[f423,f410])).
thf(f1394,plain,(
  $false | (~spl9_7 | ~spl9_10)),
  inference(trivial_inequality_removal,[],[f1393])).
thf(f1395,plain,(
  ~spl9_7 | ~spl9_10),
  inference(avatar_contradiction_clause,[],[f1394])).
thf(f1435,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Eoption_2Eoption @ sK5)) @ c_2Eoption_2ESOME_2E0))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Eoption_2Eoption @ sK5)) @ c_2Eoption_2ESOME_2E0)))))))) | ~spl9_10),
  inference(unit_resulting_resolution,[],[f192,f205,f200,f423])).
thf(f1473,plain,(
  (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Eoption_2Eoption @ sK5)) @ c_2Eoption_2ESOME_2E0) @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Eoption_2Eoption @ sK5)) @ c_2Eoption_2ESOME_2E0))))))) = $true) | ~spl9_10),
  inference(forward_demodulation,[],[f1435,f204])).
thf(f1509,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Eoption_2Eoption @ sK5)) @ c_2Eoption_2ESOME_2E0)))))))) | ~spl9_10),
  inference(forward_demodulation,[],[f1473,f196])).
thf(f1567,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Eoption_2Eoption @ sK5)) @ c_2Eoption_2ESOME_2E0) @ (s @ sK5 @ sK3)))))))) | ~spl9_10),
  inference(forward_demodulation,[],[f1509,f204])).
thf(f1622,plain,(
  ($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK6))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))) | ~spl9_10),
  inference(forward_demodulation,[],[f1567,f196])).
thf(f1650,plain,(
  ($true = $false) | (~spl9_8 | ~spl9_10)),
  inference(forward_demodulation,[],[f1622,f414])).
thf(f1651,plain,(
  $false | (~spl9_8 | ~spl9_10)),
  inference(trivial_inequality_removal,[],[f1650])).
thf(f1652,plain,(
  ~spl9_8 | ~spl9_10),
  inference(avatar_contradiction_clause,[],[f1651])).
thf(f1654,plain,(
  ($true = $false) | (~spl9_8 | ~spl9_9)),
  inference(forward_demodulation,[],[f419,f414])).
thf(f1655,plain,(
  $false | (~spl9_8 | ~spl9_9)),
  inference(trivial_inequality_removal,[],[f1654])).
thf(f1656,plain,(
  ~spl9_8 | ~spl9_9),
  inference(avatar_contradiction_clause,[],[f1655])).
cnf(s14, plain, ~spl9_4 | spl9_5 | spl9_6 | spl9_7 | spl9_8, inference(sat_conversion,[],[f415])).
cnf(s15, plain, ~spl9_4 | spl9_5 | spl9_6 | spl9_9 | spl9_10, inference(sat_conversion,[],[f424])).
cnf(s183, plain, spl9_4, inference(sat_conversion,[],[f1205])).
cnf(s202, plain, ~spl9_5, inference(sat_conversion,[],[f1300])).
cnf(s204, plain, ~spl9_6, inference(sat_conversion,[],[f1319])).
cnf(s206, plain, ~spl9_7 | ~spl9_9, inference(sat_conversion,[],[f1392])).
cnf(s207, plain, ~spl9_7 | ~spl9_10, inference(sat_conversion,[],[f1395])).
cnf(s247, plain, ~spl9_8 | ~spl9_10, inference(sat_conversion,[],[f1652])).
cnf(s249, plain, ~spl9_8 | ~spl9_9, inference(sat_conversion,[],[f1656])).
cnf(s251, plain, spl9_9 | spl9_10, inference(rat,[],[s15,s204,s202,s183])).
cnf(s252, plain, spl9_7 | spl9_8, inference(rat,[],[s14,s204,s202,s183])).
cnf(s253, plain, ~spl9_8, inference(rat,[],[s251,s247,s249])).
cnf(s254, plain, spl9_7, inference(rat,[],[s252,s253])).
cnf(s255, plain, ~spl9_10, inference(rat,[],[s207,s254])).
cnf(s256, plain, ~spl9_9, inference(rat,[],[s206,s254])).
cnf(s257, plain, $false, inference(rat,[],[s251,s255,s256])).
thf(f1657,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s257])).
% SZS output end Proof for theBenchmark