TSTP Solution File: ITP011^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP011^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:23:39 EDT 2021
% Result : Timeout 300.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP011^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.08/0.14 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Thu Mar 18 22:46:07 EDT 2021
% 0.14/0.35 % CPUTime :
% 0.14/0.36 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.14/0.37 Python 2.7.5
% 0.48/0.65 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2899998>, <kernel.Type object at 0x28998c0>) of role type named u
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring u:Type
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x289dfc8>, <kernel.Type object at 0x28992d8>) of role type named d
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring d:Type
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x28994d0>, <kernel.Type object at 0x2899518>) of role type named du
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring du:Type
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x28998c0>, <kernel.Constant object at 0x2899098>) of role type named tyop_2Emin_2Ebool
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring tyop_2Emin_2Ebool:d
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2899908>, <kernel.DependentProduct object at 0x28994d0>) of role type named tyop_2Emin_2Efun
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring tyop_2Emin_2Efun:(d->(d->d))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2899098>, <kernel.DependentProduct object at 0x2afe5bcaad40>) of role type named tyop_2Eoption_2Eoption
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring tyop_2Eoption_2Eoption:(d->d)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x28998c0>, <kernel.DependentProduct object at 0x2afe5bcaa1b8>) of role type named s
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring s:(d->(u->du))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2899098>, <kernel.DependentProduct object at 0x2afe5bcaa200>) of role type named app_2E2
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring app_2E2:(du->(du->u))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x28998c0>, <kernel.Constant object at 0x2afe5bcaa680>) of role type named combin_i_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring combin_i_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x28994d0>, <kernel.Constant object at 0x2afe5bcaa680>) of role type named combin_k_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring combin_k_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x28994d0>, <kernel.Constant object at 0x2afe5bcaa680>) of role type named combin_s_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring combin_s_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa998>, <kernel.Constant object at 0x2afe5bcaa680>) of role type named c_2Ebool_2E_21_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_21_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa128>, <kernel.DependentProduct object at 0x29fbef0>) of role type named c_2Ebool_2E_21_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_21_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa1b8>, <kernel.Constant object at 0x2afe5bcaa998>) of role type named c_2Ebool_2E_2F_5C_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_2F_5C_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaad40>, <kernel.DependentProduct object at 0x29fbf38>) of role type named c_2Ebool_2E_2F_5C_2E2
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_2F_5C_2E2:(du->(du->u))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa128>, <kernel.Constant object at 0x29fbe60>) of role type named c_2Emin_2E_3D_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Emin_2E_3D_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaad40>, <kernel.DependentProduct object at 0x29fbea8>) of role type named c_2Emin_2E_3D_2E2
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Emin_2E_3D_2E2:(du->(du->u))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa128>, <kernel.Constant object at 0x29fbef0>) of role type named c_2Emin_2E_3D_3D_3E_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Emin_2E_3D_3D_3E_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa998>, <kernel.DependentProduct object at 0x29fbea8>) of role type named c_2Emin_2E_3D_3D_3E_2E2
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2afe5bcaa998>, <kernel.Constant object at 0x29fbea8>) of role type named c_2Ebool_2E_3F_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_3F_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbf80>, <kernel.DependentProduct object at 0x29fbfc8>) of role type named c_2Ebool_2E_3F_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_3F_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbd40>, <kernel.Constant object at 0x29fbfc8>) of role type named c_2Ebool_2EF_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2EF_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbef0>, <kernel.Constant object at 0x29fbfc8>) of role type named c_2Eoption_2EIS__NONE_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EIS__NONE_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbf80>, <kernel.DependentProduct object at 0x29fbbd8>) of role type named c_2Eoption_2EIS__NONE_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EIS__NONE_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbdd0>, <kernel.Constant object at 0x29fbbd8>) of role type named c_2Eoption_2EIS__SOME_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EIS__SOME_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbef0>, <kernel.DependentProduct object at 0x29fbb48>) of role type named c_2Eoption_2EIS__SOME_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EIS__SOME_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbb90>, <kernel.Constant object at 0x29fbb48>) of role type named c_2Eoption_2ENONE_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2ENONE_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbb90>, <kernel.Constant object at 0x29fbb00>) of role type named c_2Eoption_2EOPTION__JOIN_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EOPTION__JOIN_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbfc8>, <kernel.DependentProduct object at 0x29fb950>) of role type named c_2Eoption_2EOPTION__JOIN_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EOPTION__JOIN_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbdd0>, <kernel.Constant object at 0x29fbb00>) of role type named c_2Eoption_2EOPTION__MAP_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EOPTION__MAP_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fba28>, <kernel.DependentProduct object at 0x29fbdd0>) of role type named c_2Eoption_2EOPTION__MAP_2E2
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EOPTION__MAP_2E2:(du->(du->u))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb998>, <kernel.Constant object at 0x29fba28>) of role type named c_2Eoption_2EOPTREL_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EOPTREL_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbdd0>, <kernel.DependentProduct object at 0x29fbb00>) of role type named c_2Eoption_2EOPTREL_2E3
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2EOPTREL_2E3:(du->(du->(du->u)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.Constant object at 0x29fbb00>) of role type named c_2Eoption_2ESOME_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2ESOME_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb998>, <kernel.DependentProduct object at 0x29fb5f0>) of role type named c_2Eoption_2ESOME_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2ESOME_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb680>, <kernel.Constant object at 0x29fb5f0>) of role type named c_2Ebool_2ET_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2ET_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.Constant object at 0x29fb5f0>) of role type named c_2Eoption_2ETHE_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2ETHE_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb998>, <kernel.DependentProduct object at 0x29fb638>) of role type named c_2Eoption_2ETHE_2E1
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2ETHE_2E1:(du->u)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fba28>, <kernel.Constant object at 0x29fb638>) of role type named c_2Ebool_2E_5C_2F_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_5C_2F_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.DependentProduct object at 0x29fb5f0>) of role type named c_2Ebool_2E_5C_2F_2E2
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_5C_2F_2E2:(du->(du->u))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.Constant object at 0x29fb638>) of role type named c_2Eoption_2Eoption__CASE_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2Eoption__CASE_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fbab8>, <kernel.DependentProduct object at 0x29fb8c0>) of role type named c_2Eoption_2Eoption__CASE_2E3
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Eoption_2Eoption__CASE_2E3:(du->(du->(du->u)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb4d0>, <kernel.Constant object at 0x29fbab8>) of role type named c_2Ebool_2E_7E_2E0
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_2Ebool_2E_7E_2E0:u
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.DependentProduct object at 0x29fb368>) of role type named c_2Ebool_2E_7E_2E1
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring c_2Ebool_2E_7E_2E1:(du->u)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb3f8>, <kernel.DependentProduct object at 0x29fb638>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb4d0>, <kernel.DependentProduct object at 0x29fb3b0>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop)))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.DependentProduct object at 0x29fb488>) of role type named mono_2Ec_2Ebool_2E_2F_5C
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb3f8>, <kernel.DependentProduct object at 0x29fb998>) of role type named mono_2Ec_2Emin_2E_3D_3D_3E
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb4d0>, <kernel.Sort object at 0x2afe5bc86638>) of role type named mono_2Ec_2Ebool_2EF
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Ec_2Ebool_2EF:Prop
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb320>, <kernel.Sort object at 0x2afe5bc86638>) of role type named mono_2Ec_2Ebool_2ET
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Ec_2Ebool_2ET:Prop
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.DependentProduct object at 0x29fb200>) of role type named mono_2Ec_2Ebool_2E_5C_2F
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb290>, <kernel.DependentProduct object at 0x29fb248>) of role type named mono_2Ec_2Ebool_2E_7E
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mono_2Ec_2Ebool_2E_7E:(Prop->Prop)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb320>, <kernel.DependentProduct object at 0x29fb1b8>) of role type named i_mono_2Etyop_2Emin_2Ebool
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring i_mono_2Etyop_2Emin_2Ebool:(Prop->u)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb8c0>, <kernel.DependentProduct object at 0x29fb098>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb290>, <kernel.DependentProduct object at 0x29fb0e0>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb320>, <kernel.DependentProduct object at 0x29fb200>) of role type named j_mono_2Etyop_2Emin_2Ebool
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring j_mono_2Etyop_2Emin_2Ebool:(du->Prop)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb050>, <kernel.DependentProduct object at 0x29fb128>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x29fb0e0>, <kernel.DependentProduct object at 0x29fb290>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop)))
% 0.48/0.66 FOF formula (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((forall (V2x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))->(((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) of role axiom named reserved_2Eho_2Eeq__ext
% 0.48/0.67 A new axiom: (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((forall (V2x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))->(((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0))))
% 0.48/0.67 FOF formula (forall (A_27a:d) (V0x_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) combin_i_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27a) V0x_2E0))) of role axiom named reserved_2Eho_2Ei__thm
% 0.48/0.67 A new axiom: (forall (A_27a:d) (V0x_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) combin_i_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27a) V0x_2E0)))
% 0.48/0.67 FOF formula (forall (A_27a:d) (A_27b:d) (V0x_2E0:u) (V1y_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27a))) combin_k_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27b) V1y_2E0)))) ((s A_27a) V0x_2E0))) of role axiom named reserved_2Eho_2Ek__thm
% 0.48/0.67 A new axiom: (forall (A_27a:d) (A_27b:d) (V0x_2E0:u) (V1y_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27a))) combin_k_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27b) V1y_2E0)))) ((s A_27a) V0x_2E0)))
% 0.48/0.67 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (V0f_2E0:u) (V1g_2E0:u) (V2x_2E0:u), (((eq du) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c)))) combin_s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) ((s A_27a) V2x_2E0)))) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0))))))) of role axiom named reserved_2Eho_2Es__thm
% 0.48/0.67 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (V0f_2E0:u) (V1g_2E0:u) (V2x_2E0:u), (((eq du) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c)))) combin_s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) ((s A_27a) V2x_2E0)))) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))))
% 0.48/0.67 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))) of role axiom named reserved_2Elogic_2E_2F_5C
% 0.48/0.67 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1)))
% 0.48/0.67 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))) of role axiom named reserved_2Elogic_2E_5C_2F
% 0.48/0.67 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1)))
% 0.48/0.67 FOF formula (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))) of role axiom named reserved_2Elogic_2E_7E
% 0.48/0.67 A new axiom: (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0)))
% 0.48/0.68 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))) of role axiom named reserved_2Elogic_2E_3D_3D_3E
% 0.48/0.68 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1)))
% 0.48/0.68 FOF formula (forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0)))) of role axiom named reserved_2Elogic_2E_3D
% 0.48/0.68 A new axiom: (forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))
% 0.48/0.68 FOF formula (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))) of role axiom named reserved_2Equant_2E_21
% 0.48/0.68 A new axiom: (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))
% 0.48/0.68 FOF formula (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))) of role axiom named reserved_2Equant_2E_3F
% 0.48/0.68 A new axiom: (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))))
% 0.48/0.68 FOF formula (forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Ebool
% 0.48/0.68 A new axiom: (forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0)))
% 0.48/0.68 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.68 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0)))
% 0.48/0.68 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.69 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) V0_2E0)))
% 0.48/0.69 FOF formula (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Ebool
% 0.48/0.69 A new axiom: (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0))
% 0.48/0.69 FOF formula (forall (V0:(Prop->Prop)), (((eq (Prop->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.69 A new axiom: (forall (V0:(Prop->Prop)), (((eq (Prop->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0)))) V0))
% 0.48/0.69 FOF formula (forall (V0:(Prop->(Prop->Prop))), (((eq (Prop->(Prop->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.69 A new axiom: (forall (V0:(Prop->(Prop->Prop))), (((eq (Prop->(Prop->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0))
% 0.48/0.69 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_21_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))) of role axiom named arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a
% 0.48/0.69 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_21_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))))
% 0.48/0.69 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a
% 0.48/0.69 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0))))))
% 0.54/0.70 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_3F_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))) of role axiom named arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a
% 0.54/0.70 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_3F_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))))
% 0.54/0.70 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) c_2Eoption_2EIS__NONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))))) of role axiom named arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a
% 0.54/0.70 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) c_2Eoption_2EIS__NONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))))
% 0.54/0.70 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) c_2Eoption_2EIS__SOME_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))))) of role axiom named arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a
% 0.54/0.70 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) c_2Eoption_2EIS__SOME_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))))
% 0.54/0.70 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2EOPTION__JOIN_2E0)) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a
% 0.54/0.70 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2EOPTION__JOIN_2E0)) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) X0_2E0)))))
% 0.54/0.70 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0))))) of role axiom named arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b
% 0.54/0.71 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))))
% 0.54/0.71 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)))) c_2Eoption_2EOPTREL_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0)))))) of role axiom named arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a
% 0.54/0.71 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)))) c_2Eoption_2EOPTREL_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0))))))
% 0.54/0.71 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool)))) c_2Eoption_2EOPTREL_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) X2_2E0)))))) of role axiom named arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b
% 0.54/0.72 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool)))) c_2Eoption_2EOPTREL_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) X2_2E0))))))
% 0.54/0.72 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)) ((s A_27a) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a
% 0.54/0.72 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)) ((s A_27a) X0_2E0)))))
% 0.54/0.72 FOF formula (forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2ESOME_2E0)) ((s A_27b) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b
% 0.54/0.72 A new axiom: (forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2ESOME_2E0)) ((s A_27b) X0_2E0)))))
% 0.54/0.72 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (c_2Eoption_2ESOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a)))) c_2Eoption_2ESOME_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29
% 0.54/0.72 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (c_2Eoption_2ESOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a)))) c_2Eoption_2ESOME_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))))
% 0.54/0.72 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) A_27a)) c_2Eoption_2ETHE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a
% 0.54/0.73 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) A_27a)) c_2Eoption_2ETHE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))))
% 0.54/0.73 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s A_27b) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27b) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0))))) of role axiom named arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b
% 0.54/0.73 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s A_27b) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27b) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))))
% 0.54/0.73 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) X2_2E0))))) of role axiom named arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29
% 0.54/0.73 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))))
% 0.54/0.74 FOF formula (forall (V0:(Prop->Prop)) (V1:Prop), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.54/0.74 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1))))))
% 0.54/0.74 FOF formula (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.54/0.74 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1))))))
% 0.54/0.74 FOF formula (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.54/0.74 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.54/0.74 FOF formula (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.54/0.74 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1)))
% 0.54/0.74 FOF formula mono_2Ec_2Ebool_2ET of role axiom named thm_2Ebool_2ETRUTH
% 0.54/0.74 A new axiom: mono_2Ec_2Ebool_2ET
% 0.54/0.74 FOF formula (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))) of role axiom named thm_2Ebool_2EIMP__ANTISYM__AX
% 0.54/0.74 A new axiom: (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2))))
% 0.54/0.74 FOF formula (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)) of role axiom named thm_2Ebool_2EFALSITY
% 0.54/0.74 A new axiom: (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 0.54/0.74 FOF formula (d->(forall (V0t:Prop), ((iff ((ex u) (fun (V1x_2E0:u)=> V0t))) V0t))) of role axiom named thm_2Ebool_2EEXISTS__SIMP
% 0.54/0.74 A new axiom: (d->(forall (V0t:Prop), ((iff ((ex u) (fun (V1x_2E0:u)=> V0t))) V0t)))
% 0.54/0.74 FOF formula (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((and mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff ((and V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff ((and mono_2Ec_2Ebool_2EF) V0t)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) V0t)) V0t))) of role axiom named thm_2Ebool_2EAND__CLAUSES
% 0.54/0.74 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((and mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff ((and V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff ((and mono_2Ec_2Ebool_2EF) V0t)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) V0t)) V0t)))
% 0.54/0.74 FOF formula (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((or mono_2Ec_2Ebool_2ET) V0t)) mono_2Ec_2Ebool_2ET)) ((iff ((or V0t) mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff ((or mono_2Ec_2Ebool_2EF) V0t)) V0t))) ((iff ((or V0t) mono_2Ec_2Ebool_2EF)) V0t))) ((iff ((or V0t) V0t)) V0t))) of role axiom named thm_2Ebool_2EOR__CLAUSES
% 0.60/0.78 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((or mono_2Ec_2Ebool_2ET) V0t)) mono_2Ec_2Ebool_2ET)) ((iff ((or V0t) mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff ((or mono_2Ec_2Ebool_2EF) V0t)) V0t))) ((iff ((or V0t) mono_2Ec_2Ebool_2EF)) V0t))) ((iff ((or V0t) V0t)) V0t)))
% 0.60/0.78 FOF formula ((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)) of role axiom named thm_2Ebool_2ENOT__CLAUSES
% 0.60/0.78 A new axiom: ((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET))
% 0.60/0.78 FOF formula (forall (A_27a:d) (V0x_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V0x_2E0))) mono_2Ec_2Ebool_2ET)) of role axiom named thm_2Ebool_2EREFL__CLAUSE
% 0.60/0.78 A new axiom: (forall (A_27a:d) (V0x_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V0x_2E0))) mono_2Ec_2Ebool_2ET))
% 0.60/0.78 FOF formula (forall (V0t:Prop), ((and ((and ((and ((iff (((eq Prop) mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff (((eq Prop) mono_2Ec_2Ebool_2EF) V0t)) (not V0t)))) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2EF)) (not V0t)))) of role axiom named thm_2Ebool_2EEQ__CLAUSES
% 0.60/0.78 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((iff (((eq Prop) mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff (((eq Prop) mono_2Ec_2Ebool_2EF) V0t)) (not V0t)))) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2EF)) (not V0t))))
% 0.60/0.78 FOF formula (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1e_2E0:u) (V2e_2E0:u), ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (V3x_2E0:u) (V4y_2E0:u), ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V3x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V4y_2E0))))) (((eq du) ((s A_27a) V3x_2E0)) ((s A_27a) V4y_2E0))))) (forall (V5x_2E0:u), (((eq du) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V5x_2E0)))))) ((s A_27a) V5x_2E0))))) (forall (V6x_2E0:u), (not (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V6x_2E0)))))))) (forall (V7x_2E0:u), (not (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V7x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V8x_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V8x_2E0))))))) mono_2Ec_2Ebool_2ET)))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2EF))) (forall (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V9x_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V9x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V10x_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V10x_2E0)))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V10x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V11x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0))))->(((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0)))))) (forall (V12x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V12x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V12x_2E0))))) (forall (V13x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0))))) (forall (V14x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V14x_2E0))))->(((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V14x_2E0)) ((s A_27b) V2e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)))) ((s A_27b) V2e_2E0)))))) (forall (V15x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0))))->(((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0)) ((s A_27b) V2e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0)))))))))) (forall (V16x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0))))->(((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V1e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0)))))) (forall (V17v_2E0:u) (V18f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s A_27b) V17v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V18f_2E0)))) ((s A_27b) V17v_2E0))))) (forall (V19x_2E0:u) (V20v_2E0:u) (V21f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V19x_2E0)))) ((s A_27b) V20v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0)) ((s A_27a) V19x_2E0))))))) (forall (V22f_2E0:u) (V23x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V23x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0)) ((s A_27a) V23x_2E0))))))))) (forall (V24f_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V24f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) (forall (V25x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (c_2Eoption_2ESOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V25x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) V25x_2E0))))) of role axiom named thm_2Eoption_2Eoption__CLAUSES
% 0.60/0.78 A new axiom: (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1e_2E0:u) (V2e_2E0:u), ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (V3x_2E0:u) (V4y_2E0:u), ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V3x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V4y_2E0))))) (((eq du) ((s A_27a) V3x_2E0)) ((s A_27a) V4y_2E0))))) (forall (V5x_2E0:u), (((eq du) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V5x_2E0)))))) ((s A_27a) V5x_2E0))))) (forall (V6x_2E0:u), (not (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V6x_2E0)))))))) (forall (V7x_2E0:u), (not (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V7x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V8x_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V8x_2E0))))))) mono_2Ec_2Ebool_2ET)))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2EF))) (forall (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V9x_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V9x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V10x_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V10x_2E0)))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V10x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V11x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0))))->(((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0)))))) (forall (V12x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V12x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V12x_2E0))))) (forall (V13x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0))))) (forall (V14x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V14x_2E0))))->(((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V14x_2E0)) ((s A_27b) V2e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)))) ((s A_27b) V2e_2E0)))))) (forall (V15x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0))))->(((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0)) ((s A_27b) V2e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0)))))))))) (forall (V16x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0))))->(((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V1e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0)))))) (forall (V17v_2E0:u) (V18f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s A_27b) V17v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V18f_2E0)))) ((s A_27b) V17v_2E0))))) (forall (V19x_2E0:u) (V20v_2E0:u) (V21f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V19x_2E0)))) ((s A_27b) V20v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0)) ((s A_27a) V19x_2E0))))))) (forall (V22f_2E0:u) (V23x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V23x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0)) ((s A_27a) V23x_2E0))))))))) (forall (V24f_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V24f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) (forall (V25x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (c_2Eoption_2ESOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V25x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) V25x_2E0)))))
% 0.60/0.79 FOF formula (forall (A_27a:d) (A_27b:d) (V0R_2E0:u) (V1x_2E0:u) (V2y_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V0R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0))))) ((or ((and (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))) ((ex u) (fun (V3x0_2E0:u)=> ((ex u) (fun (V4y0_2E0:u)=> ((and ((and (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V3x0_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) V4y0_2E0)))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V0R_2E0)) ((s A_27a) V3x0_2E0)))) ((s A_27b) V4y0_2E0)))))))))))) of role axiom named thm_2Eoption_2EOPTREL__def
% 0.60/0.79 A new axiom: (forall (A_27a:d) (A_27b:d) (V0R_2E0:u) (V1x_2E0:u) (V2y_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V0R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0))))) ((or ((and (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))) ((ex u) (fun (V3x0_2E0:u)=> ((ex u) (fun (V4y0_2E0:u)=> ((and ((and (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V3x0_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) V4y0_2E0)))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V0R_2E0)) ((s A_27a) V3x0_2E0)))) ((s A_27b) V4y0_2E0))))))))))))
% 0.64/0.80 FOF formula (forall (A_27a:d) (V0y_2E0:u) (V1x_2E0:u) (V2R_2E0:u), ((and ((and ((and (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2ET)) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2EF))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))))) mono_2Ec_2Ebool_2EF))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27a) V0y_2E0))))))) of role conjecture named thm_2Equotient__option_2EOPTION__REL__def
% 0.64/0.80 Conjecture to prove = (forall (A_27a:d) (V0y_2E0:u) (V1x_2E0:u) (V2R_2E0:u), ((and ((and ((and (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2ET)) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2EF))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))))) mono_2Ec_2Ebool_2EF))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27a) V0y_2E0))))))):Prop
% 0.64/0.80 Parameter du_DUMMY:du.
% 0.64/0.80 We need to prove ['(forall (A_27a:d) (V0y_2E0:u) (V1x_2E0:u) (V2R_2E0:u), ((and ((and ((and (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2ET)) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2EF))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))))) mono_2Ec_2Ebool_2EF))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V2R_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27a) V0y_2E0)))))))']
% 0.64/0.80 Parameter u:Type.
% 0.64/0.80 Parameter d:Type.
% 0.64/0.80 Parameter du:Type.
% 0.64/0.80 Parameter tyop_2Emin_2Ebool:d.
% 0.64/0.80 Parameter tyop_2Emin_2Efun:(d->(d->d)).
% 0.64/0.80 Parameter tyop_2Eoption_2Eoption:(d->d).
% 0.64/0.80 Parameter s:(d->(u->du)).
% 0.64/0.80 Parameter app_2E2:(du->(du->u)).
% 0.64/0.80 Parameter combin_i_2E0:u.
% 0.64/0.80 Parameter combin_k_2E0:u.
% 0.64/0.80 Parameter combin_s_2E0:u.
% 0.64/0.80 Parameter c_2Ebool_2E_21_2E0:u.
% 0.64/0.80 Parameter c_2Ebool_2E_21_2E1:(du->u).
% 0.64/0.80 Parameter c_2Ebool_2E_2F_5C_2E0:u.
% 0.64/0.80 Parameter c_2Ebool_2E_2F_5C_2E2:(du->(du->u)).
% 0.64/0.80 Parameter c_2Emin_2E_3D_2E0:u.
% 0.64/0.80 Parameter c_2Emin_2E_3D_2E2:(du->(du->u)).
% 0.64/0.80 Parameter c_2Emin_2E_3D_3D_3E_2E0:u.
% 0.64/0.80 Parameter c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u)).
% 0.64/0.80 Parameter c_2Ebool_2E_3F_2E0:u.
% 0.64/0.80 Parameter c_2Ebool_2E_3F_2E1:(du->u).
% 0.64/0.80 Parameter c_2Ebool_2EF_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EIS__NONE_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EIS__NONE_2E1:(du->u).
% 0.64/0.80 Parameter c_2Eoption_2EIS__SOME_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EIS__SOME_2E1:(du->u).
% 0.64/0.80 Parameter c_2Eoption_2ENONE_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EOPTION__JOIN_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EOPTION__JOIN_2E1:(du->u).
% 0.64/0.80 Parameter c_2Eoption_2EOPTION__MAP_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EOPTION__MAP_2E2:(du->(du->u)).
% 0.64/0.80 Parameter c_2Eoption_2EOPTREL_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2EOPTREL_2E3:(du->(du->(du->u))).
% 0.64/0.80 Parameter c_2Eoption_2ESOME_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2ESOME_2E1:(du->u).
% 0.64/0.80 Parameter c_2Ebool_2ET_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2ETHE_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2ETHE_2E1:(du->u).
% 0.64/0.80 Parameter c_2Ebool_2E_5C_2F_2E0:u.
% 0.64/0.80 Parameter c_2Ebool_2E_5C_2F_2E2:(du->(du->u)).
% 0.64/0.80 Parameter c_2Eoption_2Eoption__CASE_2E0:u.
% 0.64/0.80 Parameter c_2Eoption_2Eoption__CASE_2E3:(du->(du->(du->u))).
% 0.64/0.80 Parameter c_2Ebool_2E_7E_2E0:u.
% 0.64/0.80 Parameter c_2Ebool_2E_7E_2E1:(du->u).
% 0.64/0.80 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop)).
% 0.64/0.80 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))).
% 0.64/0.80 Parameter mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop)).
% 0.64/0.80 Parameter mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop)).
% 0.64/0.80 Parameter mono_2Ec_2Ebool_2EF:Prop.
% 0.64/0.80 Parameter mono_2Ec_2Ebool_2ET:Prop.
% 0.64/0.80 Parameter mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop)).
% 0.64/0.80 Parameter mono_2Ec_2Ebool_2E_7E:(Prop->Prop).
% 0.64/0.80 Parameter i_mono_2Etyop_2Emin_2Ebool:(Prop->u).
% 0.64/0.80 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u).
% 0.64/0.80 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u).
% 0.64/0.80 Parameter j_mono_2Etyop_2Emin_2Ebool:(du->Prop).
% 0.64/0.80 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop)).
% 0.64/0.80 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop))).
% 0.64/0.80 Axiom reserved_2Eho_2Eeq__ext:(forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((forall (V2x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))->(((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))).
% 0.64/0.80 Axiom reserved_2Eho_2Ei__thm:(forall (A_27a:d) (V0x_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) combin_i_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27a) V0x_2E0))).
% 0.64/0.80 Axiom reserved_2Eho_2Ek__thm:(forall (A_27a:d) (A_27b:d) (V0x_2E0:u) (V1y_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27a))) combin_k_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27b) V1y_2E0)))) ((s A_27a) V0x_2E0))).
% 0.64/0.80 Axiom reserved_2Eho_2Es__thm:(forall (A_27a:d) (A_27b:d) (A_27c:d) (V0f_2E0:u) (V1g_2E0:u) (V2x_2E0:u), (((eq du) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c)))) combin_s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) ((s A_27a) V2x_2E0)))) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0))))))).
% 0.64/0.80 Axiom reserved_2Elogic_2E_2F_5C:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))).
% 0.64/0.80 Axiom reserved_2Elogic_2E_5C_2F:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))).
% 0.64/0.80 Axiom reserved_2Elogic_2E_7E:(forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))).
% 0.64/0.80 Axiom reserved_2Elogic_2E_3D_3D_3E:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))).
% 0.64/0.80 Axiom reserved_2Elogic_2E_3D:(forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0)))).
% 0.64/0.80 Axiom reserved_2Equant_2E_21:(forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))).
% 0.64/0.80 Axiom reserved_2Equant_2E_3F:(forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))).
% 0.64/0.80 Axiom ij_2Emono_2Etyop_2Emin_2Ebool:(forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0))).
% 0.64/0.80 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))).
% 0.64/0.80 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) V0_2E0))).
% 0.64/0.80 Axiom ji_2Emono_2Etyop_2Emin_2Ebool:(forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0)).
% 0.64/0.80 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(forall (V0:(Prop->Prop)), (((eq (Prop->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0)))) V0)).
% 0.64/0.80 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(forall (V0:(Prop->(Prop->Prop))), (((eq (Prop->(Prop->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0)).
% 0.64/0.80 Axiom arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_21_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))).
% 0.64/0.80 Axiom arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0)))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_3F_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) c_2Eoption_2EIS__NONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) c_2Eoption_2EIS__SOME_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2EOPTION__JOIN_2E0)) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) X0_2E0))))).
% 0.64/0.80 Axiom arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0))))).
% 0.64/0.80 Axiom arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a:(forall (A_27a:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) tyop_2Emin_2Ebool)))) c_2Eoption_2EOPTREL_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0)))))).
% 0.64/0.80 Axiom arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) tyop_2Emin_2Ebool)))) c_2Eoption_2EOPTREL_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) X2_2E0)))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)) ((s A_27a) X0_2E0))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b:(forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2ESOME_2E0)) ((s A_27b) X0_2E0))))).
% 0.64/0.80 Axiom arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (c_2Eoption_2ESOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a)))) c_2Eoption_2ESOME_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))).
% 0.64/0.81 Axiom arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) A_27a)) c_2Eoption_2ETHE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0))))).
% 0.64/0.81 Axiom arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s A_27b) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27b) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0))))).
% 0.64/0.81 Axiom arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29:(forall (A_27a:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) X2_2E0))))).
% 0.64/0.81 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))).
% 0.64/0.81 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))).
% 0.64/0.81 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))).
% 0.64/0.81 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1))).
% 0.64/0.81 Axiom thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET.
% 0.64/0.81 Axiom thm_2Ebool_2EIMP__ANTISYM__AX:(forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))).
% 0.64/0.81 Axiom thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)).
% 0.64/0.81 Axiom thm_2Ebool_2EEXISTS__SIMP:(d->(forall (V0t:Prop), ((iff ((ex u) (fun (V1x_2E0:u)=> V0t))) V0t))).
% 0.64/0.81 Axiom thm_2Ebool_2EAND__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((and ((iff ((and mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff ((and V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff ((and mono_2Ec_2Ebool_2EF) V0t)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) V0t)) V0t))).
% 0.64/0.81 Axiom thm_2Ebool_2EOR__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((and ((iff ((or mono_2Ec_2Ebool_2ET) V0t)) mono_2Ec_2Ebool_2ET)) ((iff ((or V0t) mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff ((or mono_2Ec_2Ebool_2EF) V0t)) V0t))) ((iff ((or V0t) mono_2Ec_2Ebool_2EF)) V0t))) ((iff ((or V0t) V0t)) V0t))).
% 0.64/0.81 Axiom thm_2Ebool_2ENOT__CLAUSES:((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)).
% 0.64/0.81 Axiom thm_2Ebool_2EREFL__CLAUSE:(forall (A_27a:d) (V0x_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V0x_2E0))) mono_2Ec_2Ebool_2ET)).
% 0.64/0.81 Axiom thm_2Ebool_2EEQ__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((iff (((eq Prop) mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff (((eq Prop) mono_2Ec_2Ebool_2EF) V0t)) (not V0t)))) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2EF)) (not V0t)))).
% 0.64/0.81 Axiom thm_2Eoption_2Eoption__CLAUSES:(forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1e_2E0:u) (V2e_2E0:u), ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (V3x_2E0:u) (V4y_2E0:u), ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V3x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V4y_2E0))))) (((eq du) ((s A_27a) V3x_2E0)) ((s A_27a) V4y_2E0))))) (forall (V5x_2E0:u), (((eq du) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V5x_2E0)))))) ((s A_27a) V5x_2E0))))) (forall (V6x_2E0:u), (not (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V6x_2E0)))))))) (forall (V7x_2E0:u), (not (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V7x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V8x_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V8x_2E0))))))) mono_2Ec_2Ebool_2ET)))) (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))) mono_2Ec_2Ebool_2EF))) (forall (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V9x_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V9x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V10x_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V10x_2E0)))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V10x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))) (forall (V11x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0))))->(((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) V11x_2E0)))))) (forall (V12x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V12x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V12x_2E0))))) (forall (V13x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V13x_2E0))))) (forall (V14x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__NONE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V14x_2E0))))->(((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V14x_2E0)) ((s A_27b) V2e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)))) ((s A_27b) V2e_2E0)))))) (forall (V15x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0))))->(((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0)) ((s A_27b) V2e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) (c_2Eoption_2ETHE_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V15x_2E0)))))))))) (forall (V16x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Eoption_2EIS__SOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0))))->(((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V1e_2E0)) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) V16x_2E0)))))) (forall (V17v_2E0:u) (V18f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s A_27b) V17v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V18f_2E0)))) ((s A_27b) V17v_2E0))))) (forall (V19x_2E0:u) (V20v_2E0:u) (V21f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V19x_2E0)))) ((s A_27b) V20v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0)) ((s A_27a) V19x_2E0))))))) (forall (V22f_2E0:u) (V23x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V23x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0)) ((s A_27a) V23x_2E0))))))))) (forall (V24f_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V24f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) (forall (V25x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2EOPTION__JOIN_2E1 ((s (tyop_2Eoption_2Eoption (tyop_2Eoption_2Eoption A_27a))) (c_2Eoption_2ESOME_2E1 ((s (tyop_2Eoption_2Eoption A_27a)) V25x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) V25x_2E0))))).
% 0.64/0.81 Axiom thm_2Eoption_2EOPTREL__def:(forall (A_27a:d) (A_27b:d) (V0R_2E0:u) (V1x_2E0:u) (V2y_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Eoption_2EOPTREL_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V0R_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0))))) ((or ((and (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V1x_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V2y_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))) ((ex u) (fun (V3x0_2E0:u)=> ((ex u) (fun (V4y0_2E0:u)=>
%------------------------------------------------------------------------------