TSTP Solution File: ITP009^1 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP009^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 13:23:36 EDT 2021
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP009^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.04/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Thu Mar 18 22:09:14 EDT 2021
% 0.13/0.34 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 0.40/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c290>, <kernel.Type object at 0x287c6c8>) of role type named u
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring u:Type
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2880e18>, <kernel.Type object at 0x287c248>) of role type named d
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring d:Type
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c1b8>, <kernel.Type object at 0x287c2d8>) of role type named du
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring du:Type
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c6c8>, <kernel.Constant object at 0x287c878>) of role type named tyop_2Emin_2Ebool
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring tyop_2Emin_2Ebool:d
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c098>, <kernel.DependentProduct object at 0x2ba15534af80>) of role type named tyop_2Emin_2Efun
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring tyop_2Emin_2Efun:(d->(d->d))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2ba15534a830>, <kernel.DependentProduct object at 0x287c6c8>) of role type named s
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring s:(d->(u->du))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2ba15534a8c0>, <kernel.DependentProduct object at 0x287c758>) of role type named app_2E2
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring app_2E2:(du->(du->u))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2ba15534a8c0>, <kernel.Constant object at 0x287c758>) of role type named combin_i_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring combin_i_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c1b8>, <kernel.Constant object at 0x287c758>) of role type named combin_k_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring combin_k_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c6c8>, <kernel.Constant object at 0x287c758>) of role type named combin_s_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring combin_s_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c878>, <kernel.Constant object at 0x287c1b8>) of role type named c_2Ebool_2E_21_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Ebool_2E_21_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c6c8>, <kernel.DependentProduct object at 0x2ba14d89bfc8>) of role type named c_2Ebool_2E_21_2E1
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Ebool_2E_21_2E1:(du->u)
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c878>, <kernel.Constant object at 0x287c1b8>) of role type named c_2Equotient_2E_2D_2D_3E_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Equotient_2E_2D_2D_3E_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c878>, <kernel.DependentProduct object at 0x2ba14d89be60>) of role type named c_2Equotient_2E_2D_2D_3E_2E2
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Equotient_2E_2D_2D_3E_2E2:(du->(du->u))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c878>, <kernel.DependentProduct object at 0x2ba14d89bdd0>) of role type named c_2Equotient_2E_2D_2D_3E_2E3
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Equotient_2E_2D_2D_3E_2E3:(du->(du->(du->u)))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c758>, <kernel.Constant object at 0x2ba14d89be60>) of role type named c_2Ebool_2E_2F_5C_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Ebool_2E_2F_5C_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c878>, <kernel.DependentProduct object at 0x2ba14d89bf80>) of role type named c_2Ebool_2E_2F_5C_2E2
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Ebool_2E_2F_5C_2E2:(du->(du->u))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287c758>, <kernel.Constant object at 0x2ba14d89bcf8>) of role type named c_2Emin_2E_3D_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Emin_2E_3D_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x287cf38>, <kernel.DependentProduct object at 0x2ba14d89bf80>) of role type named c_2Emin_2E_3D_2E2
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Emin_2E_3D_2E2:(du->(du->u))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2ba14d89be60>, <kernel.Constant object at 0x2ba14d89bcf8>) of role type named c_2Equotient_2E_3D_3D_3D_3E_2E0
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Equotient_2E_3D_3D_3D_3E_2E0:u
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2ba14d89be18>, <kernel.DependentProduct object at 0x2ba14d89be60>) of role type named c_2Equotient_2E_3D_3D_3D_3E_2E2
% 0.40/0.61 Using role type
% 0.40/0.61 Declaring c_2Equotient_2E_3D_3D_3D_3E_2E2:(du->(du->u))
% 0.40/0.61 FOF formula (<kernel.Constant object at 0x2ba14d89bb48>, <kernel.DependentProduct object at 0x2ba14d89be18>) of role type named c_2Equotient_2E_3D_3D_3D_3E_2E4
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Equotient_2E_3D_3D_3D_3E_2E4:(du->(du->(du->(du->u))))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bd88>, <kernel.Constant object at 0x2ba14d89bb48>) of role type named c_2Emin_2E_3D_3D_3E_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Emin_2E_3D_3D_3E_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89be18>, <kernel.DependentProduct object at 0x2ba14d89be60>) of role type named c_2Emin_2E_3D_3D_3E_2E2
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b950>, <kernel.Constant object at 0x2ba14d89be60>) of role type named c_2Ebool_2E_3F_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2E_3F_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bd88>, <kernel.DependentProduct object at 0x2ba14d89b9e0>) of role type named c_2Ebool_2E_3F_2E1
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2E_3F_2E1:(du->u)
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bef0>, <kernel.Constant object at 0x2ba14d89b9e0>) of role type named c_2Ebool_2EF_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2EF_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b950>, <kernel.Constant object at 0x2ba14d89b9e0>) of role type named c_2Equotient_2EQUOTIENT_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Equotient_2EQUOTIENT_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bd88>, <kernel.DependentProduct object at 0x2ba14d89ba28>) of role type named c_2Equotient_2EQUOTIENT_2E3
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Equotient_2EQUOTIENT_2E3:(du->(du->(du->u)))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bb48>, <kernel.Constant object at 0x2ba14d89ba28>) of role type named c_2Ebool_2ET_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2ET_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b950>, <kernel.Constant object at 0x2ba14d89ba28>) of role type named c_2Ecombin_2EW_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ecombin_2EW_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bd88>, <kernel.DependentProduct object at 0x2ba14d89b7a0>) of role type named c_2Ecombin_2EW_2E2
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ecombin_2EW_2E2:(du->(du->u))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bef0>, <kernel.Constant object at 0x2ba14d89b7a0>) of role type named c_2Ebool_2E_5C_2F_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2E_5C_2F_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b950>, <kernel.DependentProduct object at 0x2ba14d89ba28>) of role type named c_2Ebool_2E_5C_2F_2E2
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2E_5C_2F_2E2:(du->(du->u))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b830>, <kernel.Constant object at 0x2ba14d89ba28>) of role type named c_2Equotient_2Erespects_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Equotient_2Erespects_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89bef0>, <kernel.DependentProduct object at 0x2ba14d89b7a0>) of role type named c_2Equotient_2Erespects_2E2
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Equotient_2Erespects_2E2:(du->(du->u))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b6c8>, <kernel.Constant object at 0x2ba14d89b7a0>) of role type named c_2Ebool_2E_7E_2E0
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2E_7E_2E0:u
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b830>, <kernel.DependentProduct object at 0x2ba14d89b950>) of role type named c_2Ebool_2E_7E_2E1
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring c_2Ebool_2E_7E_2E1:(du->u)
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b638>, <kernel.DependentProduct object at 0x2ba14d89ba28>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b6c8>, <kernel.DependentProduct object at 0x2ba14d89bef0>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop)))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2ba14d89b830>, <kernel.DependentProduct object at 0x2ba14d89b560>) of role type named mono_2Ec_2Ebool_2E_2F_5C
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop))
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b638>, <kernel.DependentProduct object at 0x2ba14d89b518>) of role type named mono_2Ec_2Emin_2E_3D_3D_3E
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop))
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b6c8>, <kernel.Sort object at 0x2ba15534a5a8>) of role type named mono_2Ec_2Ebool_2EF
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring mono_2Ec_2Ebool_2EF:Prop
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b4d0>, <kernel.Sort object at 0x2ba15534a5a8>) of role type named mono_2Ec_2Ebool_2ET
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring mono_2Ec_2Ebool_2ET:Prop
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b830>, <kernel.DependentProduct object at 0x2ba14d89b3b0>) of role type named mono_2Ec_2Ebool_2E_5C_2F
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop))
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b440>, <kernel.DependentProduct object at 0x2ba14d89b3f8>) of role type named mono_2Ec_2Ebool_2E_7E
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring mono_2Ec_2Ebool_2E_7E:(Prop->Prop)
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b4d0>, <kernel.DependentProduct object at 0x2ba14d89b368>) of role type named i_mono_2Etyop_2Emin_2Ebool
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring i_mono_2Etyop_2Emin_2Ebool:(Prop->u)
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b830>, <kernel.DependentProduct object at 0x2ba14d89b2d8>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u)
% 0.40/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b440>, <kernel.DependentProduct object at 0x2ba14d89b200>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b4d0>, <kernel.DependentProduct object at 0x2ba14d89b3b0>) of role type named j_mono_2Etyop_2Emin_2Ebool
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring j_mono_2Etyop_2Emin_2Ebool:(du->Prop)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b290>, <kernel.DependentProduct object at 0x2ba14d89b248>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ba14d89b200>, <kernel.DependentProduct object at 0x2ba14d89b440>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop)))
% 0.47/0.63 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
% 0.47/0.63 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))))
% 0.47/0.63 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
% 0.47/0.64 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)))
% 0.47/0.64 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
% 0.47/0.64 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)))
% 0.47/0.64 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
% 0.47/0.64 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)))))))
% 0.47/0.64 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
% 0.47/0.64 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1)))
% 0.47/0.64 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
% 0.47/0.64 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1)))
% 0.47/0.64 FOF formula (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))) of role axiom named reserved_2Elogic_2E_7E
% 0.47/0.64 A new axiom: (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0)))
% 0.47/0.64 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
% 0.47/0.64 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1)))
% 0.47/0.64 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
% 0.47/0.64 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))))
% 0.47/0.64 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
% 0.47/0.65 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)))))))
% 0.47/0.65 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
% 0.47/0.65 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))))))))
% 0.47/0.65 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
% 0.47/0.65 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)))
% 0.47/0.65 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
% 0.47/0.65 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)))
% 0.47/0.65 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
% 0.47/0.65 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)))
% 0.47/0.65 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
% 0.50/0.66 A new axiom: (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0))
% 0.50/0.66 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
% 0.50/0.66 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))
% 0.50/0.66 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
% 0.50/0.66 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))
% 0.50/0.66 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
% 0.50/0.66 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))))))
% 0.50/0.66 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X1_2E0))))) of role axiom named arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b
% 0.50/0.66 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X1_2E0)))))
% 0.50/0.67 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0))))) of role axiom named arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d
% 0.50/0.67 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))))
% 0.50/0.67 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0))))) of role axiom named arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d
% 0.50/0.67 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))))
% 0.50/0.68 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
% 0.50/0.68 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))))))
% 0.50/0.68 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) 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_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))))) c_2Equotient_2E_3D_3D_3D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0))))) of role axiom named arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b
% 0.50/0.68 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) 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_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))))) c_2Equotient_2E_3D_3D_3D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))))
% 0.50/0.69 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2Equotient_2E_3D_3D_3D_3E_2E4 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X3_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) 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_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))))) c_2Equotient_2E_3D_3D_3D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X3_2E0)))))) of role axiom named arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b
% 0.50/0.69 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2Equotient_2E_3D_3D_3D_3E_2E4 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X3_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) 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_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))))) c_2Equotient_2E_3D_3D_3D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X3_2E0))))))
% 0.50/0.69 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_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
% 0.50/0.69 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_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))))))
% 0.50/0.70 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_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) 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_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)))))) of role axiom named arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27b
% 0.50/0.70 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_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) 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_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0))))))
% 0.50/0.70 FOF formula (forall (A_27a:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) 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_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X2_2E0)))))) of role axiom named arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c
% 0.50/0.70 A new axiom: (forall (A_27a:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) 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_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X2_2E0))))))
% 0.50/0.72 FOF formula (forall (A_27b:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X2_2E0)))))) of role axiom named arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d
% 0.50/0.72 A new axiom: (forall (A_27b:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X2_2E0))))))
% 0.50/0.72 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) X1_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) X2_2E0)))))) of role axiom named arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29
% 0.56/0.73 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) X1_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) X2_2E0))))))
% 0.56/0.73 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s A_27b) ((c_2Ecombin_2EW_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) X0_2E0)) ((s A_27a) X1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Ecombin_2EW_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) X0_2E0)))) ((s A_27a) X1_2E0))))) of role axiom named arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b
% 0.56/0.73 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s A_27b) ((c_2Ecombin_2EW_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) X0_2E0)) ((s A_27a) X1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Ecombin_2EW_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) X0_2E0)))) ((s A_27a) X1_2E0)))))
% 0.56/0.73 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) c_2Equotient_2Erespects_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool
% 0.56/0.74 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) c_2Equotient_2Erespects_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0))))))
% 0.56/0.74 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
% 0.56/0.74 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))))))
% 0.56/0.74 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
% 0.56/0.74 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))))))
% 0.56/0.74 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
% 0.56/0.74 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.56/0.74 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
% 0.56/0.74 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1)))
% 0.56/0.74 FOF formula mono_2Ec_2Ebool_2ET of role axiom named thm_2Ebool_2ETRUTH
% 0.56/0.75 A new axiom: mono_2Ec_2Ebool_2ET
% 0.56/0.75 FOF formula (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))) of role axiom named thm_2Ebool_2EIMP__ANTISYM__AX
% 0.56/0.75 A new axiom: (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2))))
% 0.56/0.75 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
% 0.56/0.75 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)))
% 0.56/0.75 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
% 0.56/0.75 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))))
% 0.56/0.75 FOF formula (forall (V0t1:Prop) (V1t2:Prop) (V2t3:Prop), ((iff (V0t1->(V1t2->V2t3))) (((and V0t1) V1t2)->V2t3))) of role axiom named thm_2Ebool_2EAND__IMP__INTRO
% 0.56/0.75 A new axiom: (forall (V0t1:Prop) (V1t2:Prop) (V2t3:Prop), ((iff (V0t1->(V1t2->V2t3))) (((and V0t1) V1t2)->V2t3)))
% 0.56/0.75 FOF formula (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1x_2E0:u), (((eq du) ((s A_27b) ((c_2Ecombin_2EW_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) V0f_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) V0f_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27a) V1x_2E0))))) of role axiom named thm_2Ecombin_2EW__THM
% 0.56/0.75 A new axiom: (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1x_2E0:u), (((eq du) ((s A_27b) ((c_2Ecombin_2EW_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) V0f_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) V0f_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27a) V1x_2E0)))))
% 0.56/0.75 FOF formula (forall (A_27a:d) (A_27b:d) (V0R_2E0:u) (V1abs_2E0:u) (V2rep_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rep_2E0))))->(forall (V3r_2E0:u) (V4s_2E0:u), ((iff (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))) V0R_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27a) V4s_2E0))))) ((and ((and (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))) V0R_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27a) V3r_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))) V0R_2E0)) ((s A_27a) V4s_2E0)))) ((s A_27a) V4s_2E0)))))) (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s A_27a) V4s_2E0))))))))) of role axiom named thm_2Equotient_2EQUOTIENT__REL
% 0.56/0.75 A new axiom: (forall (A_27a:d) (A_27b:d) (V0R_2E0:u) (V1abs_2E0:u) (V2rep_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rep_2E0))))->(forall (V3r_2E0:u) (V4s_2E0:u), ((iff (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))) V0R_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27a) V4s_2E0))))) ((and ((and (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))) V0R_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27a) V3r_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))) V0R_2E0)) ((s A_27a) V4s_2E0)))) ((s A_27a) V4s_2E0)))))) (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s A_27a) V4s_2E0)))))))))
% 0.56/0.76 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (V0R1_2E0:u) (V1abs1_2E0:u) (V2rep1_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0))))->(forall (V3R2_2E0:u) (V4abs2_2E0:u) (V5rep2_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0)))))))))) of role axiom named thm_2Equotient_2EFUN__QUOTIENT
% 0.56/0.76 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (V0R1_2E0:u) (V1abs1_2E0:u) (V2rep1_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0))))->(forall (V3R2_2E0:u) (V4abs2_2E0:u) (V5rep2_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))))))))
% 0.60/0.78 FOF formula (forall (A_27a:d) (A_27b:d), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Equotient_2Erespects_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Ecombin_2EW_2E0))) of role axiom named thm_2Equotient_2Erespects__def
% 0.60/0.78 A new axiom: (forall (A_27a:d) (A_27b:d), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Equotient_2Erespects_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Ecombin_2EW_2E0)))
% 0.60/0.78 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (V0R1_2E0:u) (V1abs1_2E0:u) (V2rep1_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0))))->(forall (V3R2_2E0:u) (V4abs2_2E0:u) (V5rep2_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))->(forall (V6f_2E0:u) (V7g_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2Equotient_2E_3D_3D_3D_3E_2E4 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0))))) ((and ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0)))))) (((eq du) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0))))))))))) of role conjecture named thm_2Equotient_2EFUN__REL__EQ__REL
% 0.60/0.78 Conjecture to prove = (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (V0R1_2E0:u) (V1abs1_2E0:u) (V2rep1_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0))))->(forall (V3R2_2E0:u) (V4abs2_2E0:u) (V5rep2_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))->(forall (V6f_2E0:u) (V7g_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2Equotient_2E_3D_3D_3D_3E_2E4 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0))))) ((and ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0)))))) (((eq du) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0))))))))))):Prop
% 0.60/0.78 Parameter du_DUMMY:du.
% 0.60/0.78 We need to prove ['(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (V0R1_2E0:u) (V1abs1_2E0:u) (V2rep1_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0))))->(forall (V3R2_2E0:u) (V4abs2_2E0:u) (V5rep2_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))->(forall (V6f_2E0:u) (V7g_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2Equotient_2E_3D_3D_3D_3E_2E4 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0))))) ((and ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0)))))) (((eq du) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V6f_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V7g_2E0)))))))))))']
% 0.60/0.78 Parameter u:Type.
% 0.60/0.78 Parameter d:Type.
% 0.60/0.78 Parameter du:Type.
% 0.60/0.78 Parameter tyop_2Emin_2Ebool:d.
% 0.60/0.78 Parameter tyop_2Emin_2Efun:(d->(d->d)).
% 0.60/0.78 Parameter s:(d->(u->du)).
% 0.60/0.78 Parameter app_2E2:(du->(du->u)).
% 0.60/0.78 Parameter combin_i_2E0:u.
% 0.60/0.78 Parameter combin_k_2E0:u.
% 0.60/0.78 Parameter combin_s_2E0:u.
% 0.60/0.78 Parameter c_2Ebool_2E_21_2E0:u.
% 0.60/0.78 Parameter c_2Ebool_2E_21_2E1:(du->u).
% 0.60/0.78 Parameter c_2Equotient_2E_2D_2D_3E_2E0:u.
% 0.60/0.78 Parameter c_2Equotient_2E_2D_2D_3E_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Equotient_2E_2D_2D_3E_2E3:(du->(du->(du->u))).
% 0.60/0.78 Parameter c_2Ebool_2E_2F_5C_2E0:u.
% 0.60/0.78 Parameter c_2Ebool_2E_2F_5C_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Emin_2E_3D_2E0:u.
% 0.60/0.78 Parameter c_2Emin_2E_3D_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Equotient_2E_3D_3D_3D_3E_2E0:u.
% 0.60/0.78 Parameter c_2Equotient_2E_3D_3D_3D_3E_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Equotient_2E_3D_3D_3D_3E_2E4:(du->(du->(du->(du->u)))).
% 0.60/0.78 Parameter c_2Emin_2E_3D_3D_3E_2E0:u.
% 0.60/0.78 Parameter c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Ebool_2E_3F_2E0:u.
% 0.60/0.78 Parameter c_2Ebool_2E_3F_2E1:(du->u).
% 0.60/0.78 Parameter c_2Ebool_2EF_2E0:u.
% 0.60/0.78 Parameter c_2Equotient_2EQUOTIENT_2E0:u.
% 0.60/0.78 Parameter c_2Equotient_2EQUOTIENT_2E3:(du->(du->(du->u))).
% 0.60/0.78 Parameter c_2Ebool_2ET_2E0:u.
% 0.60/0.78 Parameter c_2Ecombin_2EW_2E0:u.
% 0.60/0.78 Parameter c_2Ecombin_2EW_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Ebool_2E_5C_2F_2E0:u.
% 0.60/0.78 Parameter c_2Ebool_2E_5C_2F_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Equotient_2Erespects_2E0:u.
% 0.60/0.78 Parameter c_2Equotient_2Erespects_2E2:(du->(du->u)).
% 0.60/0.78 Parameter c_2Ebool_2E_7E_2E0:u.
% 0.60/0.78 Parameter c_2Ebool_2E_7E_2E1:(du->u).
% 0.60/0.78 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop)).
% 0.60/0.78 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))).
% 0.60/0.78 Parameter mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop)).
% 0.60/0.78 Parameter mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop)).
% 0.60/0.78 Parameter mono_2Ec_2Ebool_2EF:Prop.
% 0.60/0.78 Parameter mono_2Ec_2Ebool_2ET:Prop.
% 0.60/0.78 Parameter mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop)).
% 0.60/0.78 Parameter mono_2Ec_2Ebool_2E_7E:(Prop->Prop).
% 0.60/0.78 Parameter i_mono_2Etyop_2Emin_2Ebool:(Prop->u).
% 0.60/0.78 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u).
% 0.60/0.78 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u).
% 0.60/0.78 Parameter j_mono_2Etyop_2Emin_2Ebool:(du->Prop).
% 0.60/0.78 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop)).
% 0.60/0.78 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop))).
% 0.60/0.78 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)))).
% 0.60/0.78 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))).
% 0.60/0.78 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))).
% 0.60/0.79 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))))))).
% 0.60/0.79 Axiom reserved_2Elogic_2E_2F_5C:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))).
% 0.60/0.79 Axiom reserved_2Elogic_2E_5C_2F:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))).
% 0.60/0.79 Axiom reserved_2Elogic_2E_7E:(forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))).
% 0.60/0.79 Axiom reserved_2Elogic_2E_3D_3D_3E:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))).
% 0.60/0.79 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)))).
% 0.60/0.79 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))))))).
% 0.60/0.79 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)))))))).
% 0.60/0.79 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))).
% 0.60/0.79 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))).
% 0.60/0.79 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))).
% 0.60/0.79 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)).
% 0.60/0.79 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)).
% 0.60/0.79 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)).
% 0.60/0.79 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)))))).
% 0.60/0.79 Axiom arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X1_2E0))))).
% 0.60/0.79 Axiom arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d:(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((c_2Equotient_2E_2D_2D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0))))).
% 0.60/0.79 Axiom arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d:(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) (((c_2Equotient_2E_2D_2D_3E_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))))) c_2Equotient_2E_2D_2D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0))))).
% 0.60/0.79 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)))))).
% 0.60/0.79 Axiom arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) 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_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))))) c_2Equotient_2E_3D_3D_3D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0))))).
% 0.60/0.79 Axiom arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2Equotient_2E_3D_3D_3D_3E_2E4 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X3_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) 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_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))))) c_2Equotient_2E_3D_3D_3D_3E_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X3_2E0)))))).
% 0.60/0.79 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)))))).
% 0.60/0.79 Axiom arityeq3_2Ec_2Equotient_2EQUOTIENT_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_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) 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_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)))))).
% 0.60/0.79 Axiom arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c:(forall (A_27a:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) 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_2Emin_2Efun A_27a) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X2_2E0)))))).
% 0.60/0.79 Axiom arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d:(forall (A_27b:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27d)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27d) A_27b)) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) X2_2E0)))))).
% 0.60/0.79 Axiom arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29:(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) X1_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) X2_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) tyop_2Emin_2Ebool)))) c_2Equotient_2EQUOTIENT_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27c) A_27d))) X1_2E0)))) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) A_27b))) X2_2E0)))))).
% 0.60/0.79 Axiom arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s A_27b) ((c_2Ecombin_2EW_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) X0_2E0)) ((s A_27a) X1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) ((tyop_2Emin_2Efun A_27a) A_27b))) c_2Ecombin_2EW_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) X0_2E0)))) ((s A_27a) X1_2E0))))).
% 0.60/0.79 Axiom arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Equotient_2Erespects_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) c_2Equotient_2Erespects_2E0)) ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X1_2E0)))))).
% 0.60/0.79 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)))))).
% 0.60/0.79 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)))))).
% 0.60/0.79 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))).
% 0.60/0.79 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))).
% 0.60/0.79 Axiom thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET.
% 0.60/0.79 Axiom thm_2Ebool_2EIMP__ANTISYM__AX:(forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))).
% 0.60/0.79 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))).
% 0.60/0.79 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)))).
% 0.60/0.79 Axiom thm_2Ebool_2EAND__IMP__INTRO:(forall (V0t1:Prop) (V1t2:Prop) (V2t3:Prop), ((iff (V0t1->(V1t2->V2t3))) (((and V0t1) V1t2)->V2t3))).
% 0.60/0.79 Axiom thm_2Ecombin_2EW__THM:(forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1x_2E0:u), (((eq du) ((s A_27b) ((c_2Ecombin_2EW_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) V0f_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27b))) V0f_2E0)) ((s A_27a) V1x_2E0)))) ((s A_27a) V1x_2E0))))).
% 0.60/0.79 Axiom thm_2Equotient_2EQUOTIENT__REL:(forall (A_27a:d) (A_27b:d) (V0R_2E0:u) (V1abs_2E0:u) (V2rep_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rep_2E0))))->(forall (V3r_2E0:u) (V4s_2E0:u), ((iff (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))) V0R_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27a) V4s_2E0))))) ((and ((and (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))) V0R_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27a) V3r_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))) V0R_2E0)) ((s A_27a) V4s_2E0)))) ((s A_27a) V4s_2E0)))))) (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s A_27a) V3r_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1abs_2E0)) ((s A_27a) V4s_2E0))))))))).
% 0.60/0.79 Axiom thm_2Equotient_2EFUN__QUOTIENT:(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (V0R1_2E0:u) (V1abs1_2E0:u) (V2rep1_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27c)) V1abs1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V2rep1_2E0))))->(forall (V3R2_2E0:u) (V4abs2_2E0:u) (V5rep2_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) V3R2_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27d)) V4abs2_2E0)) ((s ((tyop_2Emin_2Efun A_27d) A_27b)) V5rep2_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (((c_2Equotient_2EQUOTIENT_2E3 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) tyop_2Emin_2Ebool))) ((c_2Equotient_2E_3D_3D_3D_3E_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) V0R1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun
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