TSTP Solution File: ITP004^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP004^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:23:30 EDT 2021
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP004^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Mar 18 20:02:38 EDT 2021
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 0.37/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd45128>, <kernel.Type object at 0x2abdcbd45bd8>) of role type named u
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring u:Type
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd45830>, <kernel.Type object at 0x2abdcbd48710>) of role type named d
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring d:Type
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd454d0>, <kernel.Type object at 0x2abdcbd48710>) of role type named du
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring du:Type
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd45bd8>, <kernel.Constant object at 0x2abdcbd45830>) of role type named tyop_2Emin_2Ebool
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring tyop_2Emin_2Ebool:d
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd453b0>, <kernel.DependentProduct object at 0x2abdcbd48440>) of role type named tyop_2Emin_2Efun
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring tyop_2Emin_2Efun:(d->(d->d))
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd45830>, <kernel.DependentProduct object at 0x2abdcbd48440>) of role type named s
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring s:(d->(u->du))
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd453b0>, <kernel.DependentProduct object at 0x2abdcbd48440>) of role type named app_2E2
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring app_2E2:(du->(du->u))
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd454d0>, <kernel.Constant object at 0x2abdcbd48440>) of role type named combin_i_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring combin_i_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd454d0>, <kernel.Constant object at 0x2abdcbd48758>) of role type named combin_k_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring combin_k_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd48a70>, <kernel.Constant object at 0x1212e18>) of role type named combin_s_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring combin_s_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd48758>, <kernel.Constant object at 0x1212b00>) of role type named c_2Ebool_2E_21_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Ebool_2E_21_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd48a70>, <kernel.DependentProduct object at 0x1212998>) of role type named c_2Ebool_2E_21_2E1
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Ebool_2E_21_2E1:(du->u)
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd48440>, <kernel.Constant object at 0x1212998>) of role type named c_2Ebool_2E_2F_5C_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Ebool_2E_2F_5C_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x2abdcbd48440>, <kernel.DependentProduct object at 0x12127e8>) of role type named c_2Ebool_2E_2F_5C_2E2
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Ebool_2E_2F_5C_2E2:(du->(du->u))
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x12127a0>, <kernel.Constant object at 0x12127e8>) of role type named c_2Emin_2E_3D_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Emin_2E_3D_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x1212b48>, <kernel.DependentProduct object at 0x1212998>) of role type named c_2Emin_2E_3D_2E2
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Emin_2E_3D_2E2:(du->(du->u))
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x12121b8>, <kernel.Constant object at 0x1212998>) of role type named c_2Emin_2E_3D_3D_3E_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Emin_2E_3D_3D_3E_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x12127a0>, <kernel.DependentProduct object at 0x12127e8>) of role type named c_2Emin_2E_3D_3D_3E_2E2
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u))
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x1212a28>, <kernel.Constant object at 0x12127e8>) of role type named c_2Ebool_2E_3F_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Ebool_2E_3F_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x12121b8>, <kernel.DependentProduct object at 0x1212b48>) of role type named c_2Ebool_2E_3F_2E1
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Ebool_2E_3F_2E1:(du->u)
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x1212d88>, <kernel.Constant object at 0x1212b48>) of role type named c_2Epred__set_2ECHOICE_2E0
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Epred__set_2ECHOICE_2E0:u
% 0.37/0.61 FOF formula (<kernel.Constant object at 0x1212a28>, <kernel.DependentProduct object at 0x12125a8>) of role type named c_2Epred__set_2ECHOICE_2E1
% 0.37/0.61 Using role type
% 0.37/0.61 Declaring c_2Epred__set_2ECHOICE_2E1:(du->u)
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212d40>, <kernel.Constant object at 0x12125a8>) of role type named c_2Epred__set_2EDELETE_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Epred__set_2EDELETE_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212d88>, <kernel.DependentProduct object at 0x1212b48>) of role type named c_2Epred__set_2EDELETE_2E2
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Epred__set_2EDELETE_2E2:(du->(du->u))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212a70>, <kernel.Constant object at 0x1212b48>) of role type named c_2Ebool_2EF_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2EF_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212d40>, <kernel.Constant object at 0x1212b48>) of role type named c_2Ebool_2EIN_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2EIN_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212d88>, <kernel.DependentProduct object at 0x12127e8>) of role type named c_2Ebool_2EIN_2E2
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2EIN_2E2:(du->(du->u))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x12123f8>, <kernel.Constant object at 0x12127e8>) of role type named c_2Epred__set_2EREST_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Epred__set_2EREST_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212d40>, <kernel.DependentProduct object at 0x1212a70>) of role type named c_2Epred__set_2EREST_2E1
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Epred__set_2EREST_2E1:(du->u)
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212b90>, <kernel.Constant object at 0x1212a70>) of role type named c_2Epred__set_2ESUBSET_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Epred__set_2ESUBSET_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x12123f8>, <kernel.DependentProduct object at 0x12127e8>) of role type named c_2Epred__set_2ESUBSET_2E2
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Epred__set_2ESUBSET_2E2:(du->(du->u))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212878>, <kernel.Constant object at 0x12127e8>) of role type named c_2Ebool_2ET_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2ET_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212b90>, <kernel.Constant object at 0x12127e8>) of role type named c_2Ebool_2E_5C_2F_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2E_5C_2F_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x12123f8>, <kernel.DependentProduct object at 0x1212b48>) of role type named c_2Ebool_2E_5C_2F_2E2
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2E_5C_2F_2E2:(du->(du->u))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212e60>, <kernel.Constant object at 0x1212b48>) of role type named c_2Ebool_2E_7E_2E0
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2E_7E_2E0:u
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212b90>, <kernel.DependentProduct object at 0x1212878>) of role type named c_2Ebool_2E_7E_2E1
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring c_2Ebool_2E_7E_2E1:(du->u)
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212ea8>, <kernel.DependentProduct object at 0x12127e8>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212e60>, <kernel.DependentProduct object at 0x12123f8>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop)))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212b90>, <kernel.DependentProduct object at 0x1212cb0>) of role type named mono_2Ec_2Ebool_2E_2F_5C
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212ea8>, <kernel.DependentProduct object at 0x1212fc8>) of role type named mono_2Ec_2Emin_2E_3D_3D_3E
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop))
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x1212e60>, <kernel.Sort object at 0x2abdcbd265a8>) of role type named mono_2Ec_2Ebool_2EF
% 0.37/0.62 Using role type
% 0.37/0.62 Declaring mono_2Ec_2Ebool_2EF:Prop
% 0.37/0.62 FOF formula (<kernel.Constant object at 0x12125f0>, <kernel.Sort object at 0x2abdcbd265a8>) of role type named mono_2Ec_2Ebool_2ET
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring mono_2Ec_2Ebool_2ET:Prop
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x1212b90>, <kernel.DependentProduct object at 0x12128c0>) of role type named mono_2Ec_2Ebool_2E_5C_2F
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop))
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x1212f80>, <kernel.DependentProduct object at 0x1212c68>) of role type named mono_2Ec_2Ebool_2E_7E
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring mono_2Ec_2Ebool_2E_7E:(Prop->Prop)
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x12125f0>, <kernel.DependentProduct object at 0x1212098>) of role type named i_mono_2Etyop_2Emin_2Ebool
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring i_mono_2Etyop_2Emin_2Ebool:(Prop->u)
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x1212b90>, <kernel.DependentProduct object at 0x1212f38>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u)
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x1212f80>, <kernel.DependentProduct object at 0x1212ef0>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u)
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x12125f0>, <kernel.DependentProduct object at 0x12128c0>) of role type named j_mono_2Etyop_2Emin_2Ebool
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring j_mono_2Etyop_2Emin_2Ebool:(du->Prop)
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x1212050>, <kernel.DependentProduct object at 0x1212518>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop))
% 0.37/0.63 FOF formula (<kernel.Constant object at 0x1212ef0>, <kernel.DependentProduct object at 0x1212f80>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.37/0.63 Using role type
% 0.37/0.63 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop)))
% 0.37/0.63 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
% 0.37/0.63 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))))
% 0.37/0.63 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
% 0.37/0.63 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)))
% 0.37/0.63 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
% 0.37/0.63 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
% 0.47/0.64 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)))))))
% 0.47/0.64 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
% 0.47/0.65 A new axiom: (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0))
% 0.47/0.65 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
% 0.47/0.65 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))
% 0.47/0.66 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
% 0.47/0.66 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))
% 0.47/0.66 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
% 0.47/0.66 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))))))
% 0.47/0.66 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
% 0.47/0.66 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))))))
% 0.47/0.66 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_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
% 0.47/0.66 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_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))))))
% 0.47/0.66 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Epred__set_2ECHOICE_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) A_27a)) c_2Epred__set_2ECHOICE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a
% 0.47/0.67 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Epred__set_2ECHOICE_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) A_27a)) c_2Epred__set_2ECHOICE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))
% 0.47/0.67 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s A_27a) X1_2E0)))) ((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))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)))) c_2Epred__set_2EDELETE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) X1_2E0))))) of role axiom named arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a
% 0.47/0.67 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s A_27a) X1_2E0)))) ((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))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)))) c_2Epred__set_2EDELETE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) X1_2E0)))))
% 0.47/0.67 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_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)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ebool_2EIN_2E0)) ((s A_27a) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a
% 0.47/0.67 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_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)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ebool_2EIN_2E0)) ((s A_27a) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0))))))
% 0.47/0.67 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Epred__set_2EREST_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a
% 0.47/0.67 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Epred__set_2EREST_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))
% 0.47/0.67 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_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)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Epred__set_2ESUBSET_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a
% 0.47/0.68 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_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)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Epred__set_2ESUBSET_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0))))))
% 0.47/0.68 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
% 0.47/0.68 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))))))
% 0.47/0.68 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
% 0.47/0.68 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))))))
% 0.47/0.68 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
% 0.47/0.68 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.47/0.68 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
% 0.47/0.68 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1)))
% 0.47/0.68 FOF formula (forall (A_27a:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1t_2E0))))) (forall (V2x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V2x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V2x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1t_2E0)))))))) of role axiom named thm_2Epred__set_2ESUBSET__DEF
% 0.47/0.69 A new axiom: (forall (A_27a:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1t_2E0))))) (forall (V2x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V2x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V2x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1t_2E0))))))))
% 0.47/0.69 FOF formula (forall (A_27a:d) (V0s_2E0:u) (V1x_2E0:u) (V2y_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V1x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2y_2E0))))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V1x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))) (not (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V2y_2E0)))))) of role axiom named thm_2Epred__set_2EIN__DELETE
% 0.47/0.69 A new axiom: (forall (A_27a:d) (V0s_2E0:u) (V1x_2E0:u) (V2y_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V1x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2y_2E0))))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V1x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))) (not (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V2y_2E0))))))
% 0.47/0.69 FOF formula (forall (A_27a:d) (V0s_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) (c_2Epred__set_2ECHOICE_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))))) of role axiom named thm_2Epred__set_2EREST__DEF
% 0.47/0.69 A new axiom: (forall (A_27a:d) (V0s_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) (c_2Epred__set_2ECHOICE_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))))))
% 0.47/0.69 FOF formula (forall (A_27a:d) (V0s_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))) of role conjecture named thm_2Epred__set_2EREST__SUBSET
% 0.47/0.69 Conjecture to prove = (forall (A_27a:d) (V0s_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))):Prop
% 0.47/0.69 Parameter du_DUMMY:du.
% 0.47/0.69 We need to prove ['(forall (A_27a:d) (V0s_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))))']
% 0.47/0.69 Parameter u:Type.
% 0.47/0.69 Parameter d:Type.
% 0.47/0.69 Parameter du:Type.
% 0.47/0.69 Parameter tyop_2Emin_2Ebool:d.
% 0.47/0.69 Parameter tyop_2Emin_2Efun:(d->(d->d)).
% 0.47/0.69 Parameter s:(d->(u->du)).
% 0.47/0.69 Parameter app_2E2:(du->(du->u)).
% 0.47/0.69 Parameter combin_i_2E0:u.
% 0.47/0.69 Parameter combin_k_2E0:u.
% 0.47/0.69 Parameter combin_s_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_21_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_21_2E1:(du->u).
% 0.47/0.69 Parameter c_2Ebool_2E_2F_5C_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_2F_5C_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Emin_2E_3D_2E0:u.
% 0.47/0.69 Parameter c_2Emin_2E_3D_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Emin_2E_3D_3D_3E_2E0:u.
% 0.47/0.69 Parameter c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Ebool_2E_3F_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_3F_2E1:(du->u).
% 0.47/0.69 Parameter c_2Epred__set_2ECHOICE_2E0:u.
% 0.47/0.69 Parameter c_2Epred__set_2ECHOICE_2E1:(du->u).
% 0.47/0.69 Parameter c_2Epred__set_2EDELETE_2E0:u.
% 0.47/0.69 Parameter c_2Epred__set_2EDELETE_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Ebool_2EF_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2EIN_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2EIN_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Epred__set_2EREST_2E0:u.
% 0.47/0.69 Parameter c_2Epred__set_2EREST_2E1:(du->u).
% 0.47/0.69 Parameter c_2Epred__set_2ESUBSET_2E0:u.
% 0.47/0.69 Parameter c_2Epred__set_2ESUBSET_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Ebool_2ET_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_5C_2F_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_5C_2F_2E2:(du->(du->u)).
% 0.47/0.69 Parameter c_2Ebool_2E_7E_2E0:u.
% 0.47/0.69 Parameter c_2Ebool_2E_7E_2E1:(du->u).
% 0.47/0.69 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop)).
% 0.47/0.69 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))).
% 0.47/0.69 Parameter mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop)).
% 0.47/0.69 Parameter mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop)).
% 0.47/0.69 Parameter mono_2Ec_2Ebool_2EF:Prop.
% 0.47/0.69 Parameter mono_2Ec_2Ebool_2ET:Prop.
% 0.47/0.69 Parameter mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop)).
% 0.47/0.69 Parameter mono_2Ec_2Ebool_2E_7E:(Prop->Prop).
% 0.47/0.69 Parameter i_mono_2Etyop_2Emin_2Ebool:(Prop->u).
% 0.47/0.69 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u).
% 0.47/0.69 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u).
% 0.47/0.69 Parameter j_mono_2Etyop_2Emin_2Ebool:(du->Prop).
% 0.47/0.69 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop)).
% 0.47/0.69 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop))).
% 0.47/0.69 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)))).
% 0.47/0.69 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))).
% 0.47/0.69 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))).
% 0.47/0.69 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))))))).
% 0.47/0.69 Axiom reserved_2Elogic_2E_2F_5C:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))).
% 0.47/0.69 Axiom reserved_2Elogic_2E_5C_2F:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))).
% 0.47/0.69 Axiom reserved_2Elogic_2E_7E:(forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))).
% 0.47/0.69 Axiom reserved_2Elogic_2E_3D_3D_3E:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))).
% 0.47/0.69 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)))).
% 0.47/0.69 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))))))).
% 0.47/0.69 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)))))))).
% 0.47/0.69 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))).
% 0.47/0.69 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))).
% 0.47/0.69 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))).
% 0.47/0.69 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)).
% 0.47/0.69 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)).
% 0.47/0.69 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)).
% 0.47/0.69 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)))))).
% 0.47/0.69 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)))))).
% 0.47/0.69 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)))))).
% 0.47/0.69 Axiom arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Epred__set_2ECHOICE_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) A_27a)) c_2Epred__set_2ECHOICE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))).
% 0.47/0.69 Axiom arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s A_27a) X1_2E0)))) ((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))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)))) c_2Epred__set_2EDELETE_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) X1_2E0))))).
% 0.47/0.69 Axiom arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_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)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ebool_2EIN_2E0)) ((s A_27a) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))))).
% 0.47/0.69 Axiom arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Epred__set_2EREST_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))).
% 0.47/0.69 Axiom arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_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)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Epred__set_2ESUBSET_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))))).
% 166.07/166.28 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)))))).
% 166.07/166.28 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)))))).
% 166.07/166.28 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))).
% 166.07/166.28 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))).
% 166.07/166.28 Axiom thm_2Epred__set_2ESUBSET__DEF:(forall (A_27a:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1t_2E0))))) (forall (V2x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V2x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V2x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1t_2E0)))))))).
% 166.07/166.28 Axiom thm_2Epred__set_2EIN__DELETE:(forall (A_27a:d) (V0s_2E0:u) (V1x_2E0:u) (V2y_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V1x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2y_2E0))))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ebool_2EIN_2E2 ((s A_27a) V1x_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))) (not (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V2y_2E0)))))).
% 166.07/166.28 Axiom thm_2Epred__set_2EREST__DEF:(forall (A_27a:d) (V0s_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((c_2Epred__set_2EDELETE_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) (c_2Epred__set_2ECHOICE_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))))).
% 166.07/166.28 Trying to prove (forall (A_27a:d) (V0s_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Epred__set_2ESUBSET_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (c_2Epred__set_2EREST_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))))
% 166.07/166.28 Found eq_ref00:=(eq_ref0 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))):(((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found (eq_ref0 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found (fun (V2x_2E0:u)=> ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0))))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found (fun (V2x_2E0:u)=> ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0))))) as proof of (forall (V2x_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0)))))
% 166.37/166.56 Found eq_ref00:=(eq_ref0 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))):(((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found (eq_ref0 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found (fun (V2x_2E0:u)=> ((eq_ref du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0))))) as proof of (((eq du) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s A_27a) V2x_2E0))))
% 166.37/166.56 Found (fun (V2x_2E0:u)=> ((eq_ref
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