TSTP Solution File: ITP021^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP021^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 13:23:51 EDT 2021
% Result : Timeout 291.36s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP021^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n006.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 : Fri Mar 19 02:34:06 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
% 0.43/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a200>, <kernel.Type object at 0x1e8ad88>) of role type named u
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring u:Type
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a3f8>, <kernel.Type object at 0x2126fc8>) of role type named d
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring d:Type
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e80ef0>, <kernel.Type object at 0x1e8ad88>) of role type named du
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring du:Type
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a368>, <kernel.Type object at 0x2b9ee60b8f80>) of role type named mono_2Etyop_2Eextreal_2Eextreal
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring mono_2Etyop_2Eextreal_2Eextreal:Type
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a3f8>, <kernel.Constant object at 0x1e8a128>) of role type named tyop_2Eextreal_2Eextreal
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring tyop_2Eextreal_2Eextreal:d
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8ad88>, <kernel.Constant object at 0x2b9ee60b8b90>) of role type named tyop_2Emin_2Ebool
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring tyop_2Emin_2Ebool:d
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a128>, <kernel.DependentProduct object at 0x1e8a368>) of role type named tyop_2Emin_2Efun
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring tyop_2Emin_2Efun:(d->(d->d))
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a3f8>, <kernel.DependentProduct object at 0x2b9ee60b8b90>) of role type named s
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring s:(d->(u->du))
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a368>, <kernel.DependentProduct object at 0x2b9ee60b8b90>) of role type named app_2E2
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring app_2E2:(du->(du->u))
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a3f8>, <kernel.Constant object at 0x2b9ee60b8b00>) of role type named combin_i_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring combin_i_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a368>, <kernel.Constant object at 0x2b9ee60b8b00>) of role type named combin_k_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring combin_k_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e8a368>, <kernel.Constant object at 0x2b9ee60b8c68>) of role type named combin_s_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring combin_s_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b9ee60b8b90>, <kernel.Constant object at 0x1e63b90>) of role type named c_2Ebool_2E_21_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Ebool_2E_21_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b9ee60b8c68>, <kernel.DependentProduct object at 0x1e63c20>) of role type named c_2Ebool_2E_21_2E1
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Ebool_2E_21_2E1:(du->u)
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b9ee60b8b00>, <kernel.Constant object at 0x1e63c20>) of role type named c_2Ebool_2E_2F_5C_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Ebool_2E_2F_5C_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b9ee60b8c68>, <kernel.DependentProduct object at 0x1e63d88>) of role type named c_2Ebool_2E_2F_5C_2E2
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Ebool_2E_2F_5C_2E2:(du->(du->u))
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x2b9ee60b8c68>, <kernel.Constant object at 0x1e63d88>) of role type named c_2Emin_2E_3D_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Emin_2E_3D_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e63cb0>, <kernel.DependentProduct object at 0x1e63998>) of role type named c_2Emin_2E_3D_2E2
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Emin_2E_3D_2E2:(du->(du->u))
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e63cf8>, <kernel.Constant object at 0x1e63998>) of role type named c_2Emin_2E_3D_3D_3E_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Emin_2E_3D_3D_3E_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e63c20>, <kernel.DependentProduct object at 0x1e63d88>) of role type named c_2Emin_2E_3D_3D_3E_2E2
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u))
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e63908>, <kernel.Constant object at 0x1e63d88>) of role type named c_2Ebool_2E_3F_2E0
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Ebool_2E_3F_2E0:u
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e63cf8>, <kernel.DependentProduct object at 0x1e858c0>) of role type named c_2Ebool_2E_3F_2E1
% 0.43/0.62 Using role type
% 0.43/0.62 Declaring c_2Ebool_2E_3F_2E1:(du->u)
% 0.43/0.62 FOF formula (<kernel.Constant object at 0x1e63cb0>, <kernel.Constant object at 0x1e63908>) of role type named c_2Ebool_2ECOND_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2ECOND_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e63dd0>, <kernel.DependentProduct object at 0x1e857a0>) of role type named c_2Ebool_2ECOND_2E3
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2ECOND_2E3:(du->(du->(du->u)))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e63cf8>, <kernel.Constant object at 0x1e85710>) of role type named c_2Ebool_2EF_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2EF_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e63dd0>, <kernel.Constant object at 0x1e85950>) of role type named c_2Ebool_2ET_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2ET_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e63cf8>, <kernel.Constant object at 0x1e857e8>) of role type named c_2Ebool_2E_5C_2F_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2E_5C_2F_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e63908>, <kernel.DependentProduct object at 0x1e85950>) of role type named c_2Ebool_2E_5C_2F_2E2
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2E_5C_2F_2E2:(du->(du->u))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85998>, <kernel.Constant object at 0x1e857e8>) of role type named c_2Eextreal_2Eextreal__le_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Eextreal_2Eextreal__le_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85638>, <kernel.DependentProduct object at 0x1e85998>) of role type named c_2Eextreal_2Eextreal__le_2E2
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Eextreal_2Eextreal__le_2E2:(du->(du->u))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85488>, <kernel.Constant object at 0x1e857e8>) of role type named c_2Eextreal_2Eextreal__max_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Eextreal_2Eextreal__max_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85710>, <kernel.DependentProduct object at 0x1e85488>) of role type named c_2Eextreal_2Eextreal__max_2E2
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Eextreal_2Eextreal__max_2E2:(du->(du->u))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85290>, <kernel.Constant object at 0x1e85710>) of role type named c_2Ebool_2E_7E_2E0
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2E_7E_2E0:u
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85488>, <kernel.DependentProduct object at 0x1e85440>) of role type named c_2Ebool_2E_7E_2E1
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring c_2Ebool_2E_7E_2E1:(du->u)
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85560>, <kernel.DependentProduct object at 0x1e857e8>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85290>, <kernel.DependentProduct object at 0x1e852d8>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop)))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85488>, <kernel.DependentProduct object at 0x1e85200>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:((Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))->(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e85560>, <kernel.DependentProduct object at 0x1e85290>) of role type named mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool
% 0.43/0.63 Using role type
% 0.43/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool:((mono_2Etyop_2Eextreal_2Eextreal->Prop)->(mono_2Etyop_2Eextreal_2Eextreal->Prop))
% 0.43/0.63 FOF formula (<kernel.Constant object at 0x1e854d0>, <kernel.DependentProduct object at 0x1e85488>) of role type named mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal:((mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e852d8>, <kernel.DependentProduct object at 0x1e85560>) of role type named mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop)))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85050>, <kernel.DependentProduct object at 0x1e854d0>) of role type named mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e850e0>, <kernel.DependentProduct object at 0x1e85248>) of role type named mono_2Ec_2Ebool_2E_2F_5C
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e852d8>, <kernel.DependentProduct object at 0x1e85e60>) of role type named mono_2Ec_2Emin_2E_3D_3D_3E
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85050>, <kernel.DependentProduct object at 0x1e85248>) of role type named mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e850e0>, <kernel.Sort object at 0x2b9ee60b85a8>) of role type named mono_2Ec_2Ebool_2EF
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Ebool_2EF:Prop
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85290>, <kernel.Sort object at 0x2b9ee60b85a8>) of role type named mono_2Ec_2Ebool_2ET
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Ebool_2ET:Prop
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e852d8>, <kernel.DependentProduct object at 0x1e85518>) of role type named mono_2Ec_2Ebool_2E_5C_2F
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e852d8>, <kernel.DependentProduct object at 0x1e850e0>) of role type named mono_2Ec_2Eextreal_2Eextreal__le
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Eextreal_2Eextreal__le:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85f38>, <kernel.DependentProduct object at 0x1e85290>) of role type named mono_2Ec_2Eextreal_2Eextreal__max
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Eextreal_2Eextreal__max:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85b48>, <kernel.DependentProduct object at 0x1e85f80>) of role type named mono_2Ec_2Ebool_2E_7E
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Ec_2Ebool_2E_7E:(Prop->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85290>, <kernel.DependentProduct object at 0x1e85518>) of role type named i_mono_2Etyop_2Emin_2Ebool
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Ebool:(Prop->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85290>, <kernel.DependentProduct object at 0x1e85dd0>) of role type named i_mono_2Etyop_2Eextreal_2Eextreal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Eextreal_2Eextreal:(mono_2Etyop_2Eextreal_2Eextreal->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e852d8>, <kernel.DependentProduct object at 0x1e85fc8>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85dd0>, <kernel.DependentProduct object at 0x1e85320>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85f80>, <kernel.DependentProduct object at 0x1e85e18>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29:((Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e852d8>, <kernel.DependentProduct object at 0x1e85d88>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:((mono_2Etyop_2Eextreal_2Eextreal->Prop)->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85830>, <kernel.DependentProduct object at 0x1e85d88>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:((mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85e18>, <kernel.DependentProduct object at 0x1e85c68>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85878>, <kernel.DependentProduct object at 0x1e85518>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85d88>, <kernel.DependentProduct object at 0x1e85290>) of role type named j_mono_2Etyop_2Emin_2Ebool
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring j_mono_2Etyop_2Emin_2Ebool:(du->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85d88>, <kernel.DependentProduct object at 0x2b9ee60dadd0>) of role type named j_mono_2Etyop_2Eextreal_2Eextreal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring j_mono_2Etyop_2Eextreal_2Eextreal:(du->mono_2Etyop_2Eextreal_2Eextreal)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85c68>, <kernel.DependentProduct object at 0x2b9ee60dadd0>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1e85290>, <kernel.DependentProduct object at 0x2b9ee60dadd0>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1e85f38>, <kernel.DependentProduct object at 0x2b9ee60dacb0>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29:(du->(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b9ee60dadd0>, <kernel.DependentProduct object at 0x1e85f38>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b9ee60da680>, <kernel.DependentProduct object at 0x1e85878>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b9ee60dadd0>, <kernel.DependentProduct object at 0x1e856c8>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b9ee60da680>, <kernel.DependentProduct object at 0x1e85f38>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))
% 0.48/0.64 FOF formula (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((forall (V2x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))->(((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) of role axiom named reserved_2Eho_2Eeq__ext
% 0.48/0.64 A new axiom: (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((forall (V2x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))->(((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0))))
% 0.48/0.64 FOF formula (forall (A_27a:d) (V0x_2E0:u), (((eq du) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) combin_i_2E0)) ((s A_27a) V0x_2E0)))) ((s A_27a) V0x_2E0))) of role axiom named reserved_2Eho_2Ei__thm
% 0.48/0.64 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)))
% 0.48/0.64 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
% 0.48/0.64 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)))
% 0.51/0.66 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
% 0.51/0.66 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)))))))
% 0.51/0.66 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
% 0.51/0.66 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1)))
% 0.51/0.66 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
% 0.51/0.66 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1)))
% 0.51/0.66 FOF formula (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))) of role axiom named reserved_2Elogic_2E_7E
% 0.51/0.66 A new axiom: (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0)))
% 0.51/0.66 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
% 0.51/0.66 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1)))
% 0.51/0.66 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
% 0.51/0.66 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))))
% 0.51/0.66 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
% 0.51/0.66 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)))))))
% 0.51/0.66 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
% 0.51/0.66 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))))))))
% 0.51/0.66 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
% 0.51/0.66 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)))
% 0.51/0.66 FOF formula (forall (V0_2E0:u), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (j_mono_2Etyop_2Eextreal_2Eextreal ((s tyop_2Eextreal_2Eextreal) V0_2E0))))) ((s tyop_2Eextreal_2Eextreal) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Eextreal_2Eextreal
% 0.51/0.66 A new axiom: (forall (V0_2E0:u), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (j_mono_2Etyop_2Eextreal_2Eextreal ((s tyop_2Eextreal_2Eextreal) V0_2E0))))) ((s tyop_2Eextreal_2Eextreal) V0_2E0)))
% 0.51/0.66 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
% 0.51/0.66 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)))
% 0.51/0.66 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
% 0.51/0.66 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)))
% 0.51/0.66 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29
% 0.51/0.67 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) V0_2E0)))
% 0.51/0.67 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.51/0.67 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 0.51/0.67 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.51/0.67 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) V0_2E0)))
% 0.51/0.67 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29
% 0.51/0.67 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) V0_2E0)))
% 0.51/0.67 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.51/0.67 A new axiom: (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) V0_2E0)))
% 0.51/0.67 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
% 0.51/0.67 A new axiom: (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0))
% 0.51/0.67 FOF formula (forall (V0:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) (j_mono_2Etyop_2Eextreal_2Eextreal ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Eextreal_2Eextreal
% 0.51/0.67 A new axiom: (forall (V0:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) (j_mono_2Etyop_2Eextreal_2Eextreal ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V0)))) V0))
% 0.51/0.67 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
% 0.51/0.67 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))
% 0.51/0.68 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
% 0.51/0.68 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))
% 0.51/0.68 FOF formula (forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))), (((eq (Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29
% 0.51/0.68 A new axiom: (forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))), (((eq (Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0)))) V0))
% 0.51/0.68 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)), (((eq (mono_2Etyop_2Eextreal_2Eextreal->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.51/0.68 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)), (((eq (mono_2Etyop_2Eextreal_2Eextreal->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0)))) V0))
% 0.51/0.68 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)), (((eq (mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.51/0.68 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)), (((eq (mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0)))) V0))
% 0.51/0.68 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29
% 0.51/0.68 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0))
% 0.51/0.68 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.51/0.68 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0)))) V0))
% 0.51/0.68 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
% 0.51/0.68 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))))))
% 0.51/0.69 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a
% 0.51/0.69 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0))))))
% 0.51/0.69 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
% 0.51/0.69 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))))))
% 0.51/0.69 FOF formula (forall (A_27a:d) (X0:Prop) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))) ((s A_27a) X1_2E0)) ((s A_27a) X2_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27a)))) c_2Ebool_2ECOND_2E0)) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))))) ((s A_27a) X1_2E0)))) ((s A_27a) X2_2E0))))) of role axiom named arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a
% 0.51/0.69 A new axiom: (forall (A_27a:d) (X0:Prop) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))) ((s A_27a) X1_2E0)) ((s A_27a) X2_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27a)))) c_2Ebool_2ECOND_2E0)) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))))) ((s A_27a) X1_2E0)))) ((s A_27a) X2_2E0)))))
% 0.51/0.69 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
% 0.51/0.69 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))))))
% 0.51/0.69 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
% 0.51/0.70 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))))))
% 0.51/0.70 FOF formula (forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_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_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.51/0.70 A new axiom: (forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1))))))
% 0.51/0.70 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool
% 0.51/0.70 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))))))
% 0.51/0.70 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (V0 V1)))) ((s tyop_2Eextreal_2Eextreal) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal
% 0.51/0.70 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (V0 V1)))) ((s tyop_2Eextreal_2Eextreal) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))))))
% 0.51/0.70 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.51/0.70 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))))))
% 0.51/0.70 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.51/0.70 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))))))
% 0.51/0.71 FOF formula (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) c_2Ebool_2ECOND_2E0)) of role axiom named monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eextreal_2Eextreal
% 0.51/0.71 A new axiom: (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) c_2Ebool_2ECOND_2E0))
% 0.51/0.71 FOF formula (forall (V0:Prop) (V1:mono_2Etyop_2Eextreal_2Eextreal) (V2:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal V0) V1) V2)))) ((s tyop_2Eextreal_2Eextreal) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V2)))))) of role axiom named monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal
% 0.51/0.71 A new axiom: (forall (V0:Prop) (V1:mono_2Etyop_2Eextreal_2Eextreal) (V2:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal V0) V1) V2)))) ((s tyop_2Eextreal_2Eextreal) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V2))))))
% 0.51/0.71 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
% 0.51/0.71 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.51/0.71 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
% 0.51/0.71 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1)))
% 0.51/0.71 FOF formula (forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29
% 0.51/0.71 A new axiom: (forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V0 V1)) (V0 V1)))
% 0.51/0.71 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq Prop) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool
% 0.51/0.72 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.51/0.72 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal
% 0.51/0.72 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) (V0 V1)) (V0 V1)))
% 0.51/0.72 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq (mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29
% 0.51/0.72 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq (mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V0 V1)) (V0 V1)))
% 0.51/0.72 FOF formula (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq (mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29
% 0.51/0.72 A new axiom: (forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq (mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V0 V1)) (V0 V1)))
% 0.51/0.72 FOF formula mono_2Ec_2Ebool_2ET of role axiom named thm_2Ebool_2ETRUTH
% 0.51/0.72 A new axiom: mono_2Ec_2Ebool_2ET
% 0.51/0.72 FOF formula (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))) of role axiom named thm_2Ebool_2EIMP__ANTISYM__AX
% 0.51/0.72 A new axiom: (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2))))
% 0.51/0.72 FOF formula (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)) of role axiom named thm_2Ebool_2EFALSITY
% 0.51/0.72 A new axiom: (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 0.51/0.72 FOF formula (forall (V0t:Prop), ((or V0t) (not V0t))) of role axiom named thm_2Ebool_2EEXCLUDED__MIDDLE
% 0.51/0.72 A new axiom: (forall (V0t:Prop), ((or V0t) (not V0t)))
% 0.51/0.72 FOF formula (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t))) of role axiom named thm_2Ebool_2EIMP__F
% 0.51/0.72 A new axiom: (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 0.51/0.72 FOF formula (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Ebool_2EF__IMP
% 0.51/0.72 A new axiom: (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 0.51/0.72 FOF formula (forall (V0t:Prop), ((and ((and ((and ((and ((iff (mono_2Ec_2Ebool_2ET->V0t)) V0t)) ((iff (V0t->mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff (mono_2Ec_2Ebool_2EF->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->mono_2Ec_2Ebool_2EF)) (not V0t)))) of role axiom named thm_2Ebool_2EIMP__CLAUSES
% 0.51/0.72 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((and ((iff (mono_2Ec_2Ebool_2ET->V0t)) V0t)) ((iff (V0t->mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff (mono_2Ec_2Ebool_2EF->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->mono_2Ec_2Ebool_2EF)) (not V0t))))
% 0.51/0.72 FOF formula ((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)) of role axiom named thm_2Ebool_2ENOT__CLAUSES
% 0.51/0.72 A new axiom: ((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET))
% 0.51/0.72 FOF formula (forall (A_27a:d) (V0x_2E0:u) (V1y_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V1y_2E0))) (((eq du) ((s A_27a) V1y_2E0)) ((s A_27a) V0x_2E0)))) of role axiom named thm_2Ebool_2EEQ__SYM__EQ
% 0.58/0.73 A new axiom: (forall (A_27a:d) (V0x_2E0:u) (V1y_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V1y_2E0))) (((eq du) ((s A_27a) V1y_2E0)) ((s A_27a) V0x_2E0))))
% 0.58/0.73 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
% 0.58/0.73 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))))
% 0.58/0.73 FOF formula (forall (A_27a:d) (V0t1_2E0:u) (V1t2_2E0:u), ((and (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool mono_2Ec_2Ebool_2ET))) ((s A_27a) V0t1_2E0)) ((s A_27a) V1t2_2E0)))) ((s A_27a) V0t1_2E0))) (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool mono_2Ec_2Ebool_2EF))) ((s A_27a) V0t1_2E0)) ((s A_27a) V1t2_2E0)))) ((s A_27a) V1t2_2E0)))) of role axiom named thm_2Ebool_2ECOND__CLAUSES
% 0.58/0.73 A new axiom: (forall (A_27a:d) (V0t1_2E0:u) (V1t2_2E0:u), ((and (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool mono_2Ec_2Ebool_2ET))) ((s A_27a) V0t1_2E0)) ((s A_27a) V1t2_2E0)))) ((s A_27a) V0t1_2E0))) (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool mono_2Ec_2Ebool_2EF))) ((s A_27a) V0t1_2E0)) ((s A_27a) V1t2_2E0)))) ((s A_27a) V1t2_2E0))))
% 0.58/0.73 FOF formula (forall (V0A:Prop) (V1B:Prop) (V2C:Prop), ((iff ((or ((or V0A) V1B)) V2C)) ((or ((or V0A) V1B)) V2C))) of role axiom named thm_2Ebool_2EDISJ__ASSOC
% 0.58/0.73 A new axiom: (forall (V0A:Prop) (V1B:Prop) (V2C:Prop), ((iff ((or ((or V0A) V1B)) V2C)) ((or ((or V0A) V1B)) V2C)))
% 0.58/0.73 FOF formula (forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A))) of role axiom named thm_2Ebool_2EDISJ__SYM
% 0.58/0.73 A new axiom: (forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A)))
% 0.58/0.73 FOF formula (forall (V0A:Prop) (V1B:Prop), ((and ((iff (not ((and V0A) V1B))) ((or (not V0A)) (not V1B)))) ((iff (not ((or V0A) V1B))) ((and (not V0A)) (not V1B))))) of role axiom named thm_2Ebool_2EDE__MORGAN__THM
% 0.58/0.73 A new axiom: (forall (V0A:Prop) (V1B:Prop), ((and ((iff (not ((and V0A) V1B))) ((or (not V0A)) (not V1B)))) ((iff (not ((or V0A) V1B))) ((and (not V0A)) (not V1B)))))
% 0.58/0.73 FOF formula (forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal) (V2z:mono_2Etyop_2Eextreal_2Eextreal), (((and ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V2z))->((mono_2Ec_2Eextreal_2Eextreal__le V0x) V2z))) of role axiom named thm_2Eextreal_2Ele__trans
% 0.58/0.73 A new axiom: (forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal) (V2z:mono_2Etyop_2Eextreal_2Eextreal), (((and ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V2z))->((mono_2Ec_2Eextreal_2Eextreal__le V0x) V2z)))
% 0.58/0.73 FOF formula (forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal), ((or ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0x))) of role axiom named thm_2Eextreal_2Ele__total
% 0.58/0.73 A new axiom: (forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal), ((or ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0x)))
% 0.58/0.73 FOF formula (forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) ((mono_2Ec_2Eextreal_2Eextreal__max V0x) V1y)) (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) V1y) V0x))) of role axiom named thm_2Eextreal_2Eextreal__max__def
% 0.58/0.75 A new axiom: (forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) ((mono_2Ec_2Eextreal_2Eextreal__max V0x) V1y)) (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) V1y) V0x)))
% 0.58/0.75 FOF formula (forall (V0t:Prop), ((iff (not (not V0t))) V0t)) of role axiom named thm_2Esat_2ENOT__NOT
% 0.58/0.75 A new axiom: (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 0.58/0.75 FOF formula (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Esat_2EAND__INV__IMP
% 0.58/0.75 A new axiom: (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 0.58/0.75 FOF formula (forall (V0B:Prop) (V1A:Prop), ((iff ((not ((or V1A) V0B))->mono_2Ec_2Ebool_2EF)) ((V1A->mono_2Ec_2Ebool_2EF)->((not V0B)->mono_2Ec_2Ebool_2EF)))) of role axiom named thm_2Esat_2EOR__DUAL2
% 0.58/0.75 A new axiom: (forall (V0B:Prop) (V1A:Prop), ((iff ((not ((or V1A) V0B))->mono_2Ec_2Ebool_2EF)) ((V1A->mono_2Ec_2Ebool_2EF)->((not V0B)->mono_2Ec_2Ebool_2EF))))
% 0.58/0.75 FOF formula (forall (V0B:Prop) (V1A:Prop), ((iff ((not ((or (not V1A)) V0B))->mono_2Ec_2Ebool_2EF)) (V1A->((not V0B)->mono_2Ec_2Ebool_2EF)))) of role axiom named thm_2Esat_2EOR__DUAL3
% 0.58/0.75 A new axiom: (forall (V0B:Prop) (V1A:Prop), ((iff ((not ((or (not V1A)) V0B))->mono_2Ec_2Ebool_2EF)) (V1A->((not V0B)->mono_2Ec_2Ebool_2EF))))
% 0.58/0.75 FOF formula (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Esat_2EAND__INV2
% 0.58/0.75 A new axiom: (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 0.58/0.75 FOF formula (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) (((eq Prop) V1q) V0r))) ((and ((and ((and ((or ((or V2p) V1q)) V0r)) ((or ((or V2p) (not V0r))) (not V1q)))) ((or ((or V1q) (not V0r))) (not V2p)))) ((or ((or V0r) (not V1q))) (not V2p))))) of role axiom named thm_2Esat_2Edc__eq
% 0.58/0.75 A new axiom: (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) (((eq Prop) V1q) V0r))) ((and ((and ((and ((or ((or V2p) V1q)) V0r)) ((or ((or V2p) (not V0r))) (not V1q)))) ((or ((or V1q) (not V0r))) (not V2p)))) ((or ((or V0r) (not V1q))) (not V2p)))))
% 0.58/0.75 FOF formula (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) ((and V1q) V0r))) ((and ((and ((or ((or V2p) (not V1q))) (not V0r))) ((or V1q) (not V2p)))) ((or V0r) (not V2p))))) of role axiom named thm_2Esat_2Edc__conj
% 0.58/0.75 A new axiom: (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) ((and V1q) V0r))) ((and ((and ((or ((or V2p) (not V1q))) (not V0r))) ((or V1q) (not V2p)))) ((or V0r) (not V2p)))))
% 0.58/0.75 FOF formula (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) ((or V1q) V0r))) ((and ((and ((or V2p) (not V1q))) ((or V2p) (not V0r)))) ((or ((or V1q) V0r)) (not V2p))))) of role axiom named thm_2Esat_2Edc__disj
% 0.58/0.75 A new axiom: (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) ((or V1q) V0r))) ((and ((and ((or V2p) (not V1q))) ((or V2p) (not V0r)))) ((or ((or V1q) V0r)) (not V2p)))))
% 0.58/0.75 FOF formula (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) (V1q->V0r))) ((and ((and ((or V2p) V1q)) ((or V2p) (not V0r)))) ((or ((or (not V1q)) V0r)) (not V2p))))) of role axiom named thm_2Esat_2Edc__imp
% 0.58/0.75 A new axiom: (forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) (V1q->V0r))) ((and ((and ((or V2p) V1q)) ((or V2p) (not V0r)))) ((or ((or (not V1q)) V0r)) (not V2p)))))
% 0.58/0.75 FOF formula (forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p))))) of role axiom named thm_2Esat_2Edc__neg
% 0.58/0.75 A new axiom: (forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p)))))
% 0.58/0.75 FOF formula (forall (V0z:mono_2Etyop_2Eextreal_2Eextreal) (V1x:mono_2Etyop_2Eextreal_2Eextreal) (V2y:mono_2Etyop_2Eextreal_2Eextreal), ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) of role conjecture named thm_2Eextreal_2Emax__le
% 0.58/0.75 Conjecture to prove = (forall (V0z:mono_2Etyop_2Eextreal_2Eextreal) (V1x:mono_2Etyop_2Eextreal_2Eextreal) (V2y:mono_2Etyop_2Eextreal_2Eextreal), ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 0.58/0.75 Parameter du_DUMMY:du.
% 0.58/0.75 Parameter mono_2Etyop_2Eextreal_2Eextreal_DUMMY:mono_2Etyop_2Eextreal_2Eextreal.
% 0.58/0.75 We need to prove ['(forall (V0z:mono_2Etyop_2Eextreal_2Eextreal) (V1x:mono_2Etyop_2Eextreal_2Eextreal) (V2y:mono_2Etyop_2Eextreal_2Eextreal), ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))']
% 0.58/0.75 Parameter u:Type.
% 0.58/0.75 Parameter d:Type.
% 0.58/0.75 Parameter du:Type.
% 0.58/0.75 Parameter mono_2Etyop_2Eextreal_2Eextreal:Type.
% 0.58/0.75 Parameter tyop_2Eextreal_2Eextreal:d.
% 0.58/0.75 Parameter tyop_2Emin_2Ebool:d.
% 0.58/0.75 Parameter tyop_2Emin_2Efun:(d->(d->d)).
% 0.58/0.75 Parameter s:(d->(u->du)).
% 0.58/0.75 Parameter app_2E2:(du->(du->u)).
% 0.58/0.75 Parameter combin_i_2E0:u.
% 0.58/0.75 Parameter combin_k_2E0:u.
% 0.58/0.75 Parameter combin_s_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_21_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_21_2E1:(du->u).
% 0.58/0.75 Parameter c_2Ebool_2E_2F_5C_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_2F_5C_2E2:(du->(du->u)).
% 0.58/0.75 Parameter c_2Emin_2E_3D_2E0:u.
% 0.58/0.75 Parameter c_2Emin_2E_3D_2E2:(du->(du->u)).
% 0.58/0.75 Parameter c_2Emin_2E_3D_3D_3E_2E0:u.
% 0.58/0.75 Parameter c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u)).
% 0.58/0.75 Parameter c_2Ebool_2E_3F_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_3F_2E1:(du->u).
% 0.58/0.75 Parameter c_2Ebool_2ECOND_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2ECOND_2E3:(du->(du->(du->u))).
% 0.58/0.75 Parameter c_2Ebool_2EF_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2ET_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_5C_2F_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_5C_2F_2E2:(du->(du->u)).
% 0.58/0.75 Parameter c_2Eextreal_2Eextreal__le_2E0:u.
% 0.58/0.75 Parameter c_2Eextreal_2Eextreal__le_2E2:(du->(du->u)).
% 0.58/0.75 Parameter c_2Eextreal_2Eextreal__max_2E0:u.
% 0.58/0.75 Parameter c_2Eextreal_2Eextreal__max_2E2:(du->(du->u)).
% 0.58/0.75 Parameter c_2Ebool_2E_7E_2E0:u.
% 0.58/0.75 Parameter c_2Ebool_2E_7E_2E1:(du->u).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop)).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:((Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))->(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool:((mono_2Etyop_2Eextreal_2Eextreal->Prop)->(mono_2Etyop_2Eextreal_2Eextreal->Prop)).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal:((mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))).
% 0.58/0.75 Parameter mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))).
% 0.58/0.75 Parameter mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop)).
% 0.58/0.75 Parameter mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop)).
% 0.58/0.75 Parameter mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))).
% 0.58/0.75 Parameter mono_2Ec_2Ebool_2EF:Prop.
% 0.58/0.75 Parameter mono_2Ec_2Ebool_2ET:Prop.
% 0.58/0.75 Parameter mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop)).
% 0.58/0.75 Parameter mono_2Ec_2Eextreal_2Eextreal__le:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop)).
% 0.58/0.75 Parameter mono_2Ec_2Eextreal_2Eextreal__max:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)).
% 0.58/0.75 Parameter mono_2Ec_2Ebool_2E_7E:(Prop->Prop).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Ebool:(Prop->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Eextreal_2Eextreal:(mono_2Etyop_2Eextreal_2Eextreal->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29:((Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:((mono_2Etyop_2Eextreal_2Eextreal->Prop)->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:((mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))->u).
% 0.58/0.75 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:((mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))->u).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Ebool:(du->Prop).
% 0.58/0.75 Parameter j_mono_2Etyop_2Eextreal_2Eextreal:(du->mono_2Etyop_2Eextreal_2Eextreal).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop)).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop))).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29:(du->(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->Prop)).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))).
% 0.58/0.75 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(du->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))).
% 0.58/0.75 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)))).
% 0.58/0.75 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))).
% 0.58/0.75 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))).
% 0.58/0.75 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))))))).
% 0.58/0.75 Axiom reserved_2Elogic_2E_2F_5C:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))).
% 0.58/0.75 Axiom reserved_2Elogic_2E_5C_2F:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))).
% 0.58/0.75 Axiom reserved_2Elogic_2E_7E:(forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))).
% 0.58/0.75 Axiom reserved_2Elogic_2E_3D_3D_3E:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))).
% 0.58/0.75 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)))).
% 0.58/0.75 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))))))).
% 0.58/0.75 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)))))))).
% 0.58/0.75 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))).
% 0.58/0.75 Axiom ij_2Emono_2Etyop_2Eextreal_2Eextreal:(forall (V0_2E0:u), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (j_mono_2Etyop_2Eextreal_2Eextreal ((s tyop_2Eextreal_2Eextreal) V0_2E0))))) ((s tyop_2Eextreal_2Eextreal) V0_2E0))).
% 0.58/0.75 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))).
% 0.58/0.75 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))).
% 0.58/0.75 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) V0_2E0))).
% 0.58/0.75 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))).
% 0.58/0.75 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) V0_2E0))).
% 0.58/0.75 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) V0_2E0))).
% 0.58/0.75 Axiom ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) V0_2E0))).
% 0.58/0.75 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)).
% 0.58/0.75 Axiom ji_2Emono_2Etyop_2Eextreal_2Eextreal:(forall (V0:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) (j_mono_2Etyop_2Eextreal_2Eextreal ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V0)))) V0)).
% 0.58/0.75 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)).
% 0.58/0.75 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)).
% 0.58/0.75 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29:(forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))), (((eq (Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0)))) V0)).
% 0.58/0.75 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)), (((eq (mono_2Etyop_2Eextreal_2Eextreal->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0)))) V0)).
% 0.58/0.75 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)), (((eq (mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0)))) V0)).
% 0.58/0.75 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0)).
% 0.58/0.75 Axiom ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0)))) V0)).
% 0.58/0.75 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)))))).
% 0.58/0.75 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)))))).
% 0.58/0.75 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)))))).
% 0.58/0.75 Axiom arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a:(forall (A_27a:d) (X0:Prop) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))) ((s A_27a) X1_2E0)) ((s A_27a) X2_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) A_27a)))) c_2Ebool_2ECOND_2E0)) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))))) ((s A_27a) X1_2E0)))) ((s A_27a) X2_2E0))))).
% 0.58/0.75 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)))))).
% 0.58/0.75 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)))))).
% 0.58/0.75 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))).
% 0.58/0.75 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))).
% 0.58/0.75 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (V0 V1)))) ((s tyop_2Eextreal_2Eextreal) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))).
% 0.58/0.75 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))).
% 0.58/0.75 Axiom monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1)))))).
% 0.58/0.75 Axiom monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eextreal_2Eextreal:(((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Eextreal_2Eextreal)))) c_2Ebool_2ECOND_2E0)).
% 0.58/0.75 Axiom monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal:(forall (V0:Prop) (V1:mono_2Etyop_2Eextreal_2Eextreal) (V2:mono_2Etyop_2Eextreal_2Eextreal), (((eq du) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal V0) V1) V2)))) ((s tyop_2Eextreal_2Eextreal) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V1))) ((s tyop_2Eextreal_2Eextreal) (i_mono_2Etyop_2Eextreal_2Eextreal V2)))))).
% 0.58/0.75 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))).
% 0.58/0.75 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))).
% 0.58/0.75 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V0 V1)) (V0 V1))).
% 0.58/0.75 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq Prop) (V0 V1)) (V0 V1))).
% 0.58/0.75 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) (V0 V1)) (V0 V1))).
% 0.58/0.75 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->Prop))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq (mono_2Etyop_2Eextreal_2Eextreal->Prop)) (V0 V1)) (V0 V1))).
% 0.58/0.75 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29:(forall (V0:(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V1:mono_2Etyop_2Eextreal_2Eextreal), (((eq (mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)) (V0 V1)) (V0 V1))).
% 0.58/0.75 Axiom thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET.
% 0.58/0.75 Axiom thm_2Ebool_2EIMP__ANTISYM__AX:(forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))).
% 0.58/0.75 Axiom thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)).
% 0.58/0.75 Axiom thm_2Ebool_2EEXCLUDED__MIDDLE:(forall (V0t:Prop), ((or V0t) (not V0t))).
% 0.58/0.75 Axiom thm_2Ebool_2EIMP__F:(forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t))).
% 0.58/0.75 Axiom thm_2Ebool_2EF__IMP:(forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF))).
% 0.58/0.75 Axiom thm_2Ebool_2EIMP__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((and ((iff (mono_2Ec_2Ebool_2ET->V0t)) V0t)) ((iff (V0t->mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff (mono_2Ec_2Ebool_2EF->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->mono_2Ec_2Ebool_2EF)) (not V0t)))).
% 0.58/0.75 Axiom thm_2Ebool_2ENOT__CLAUSES:((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)).
% 0.58/0.75 Axiom thm_2Ebool_2EEQ__SYM__EQ:(forall (A_27a:d) (V0x_2E0:u) (V1y_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V1y_2E0))) (((eq du) ((s A_27a) V1y_2E0)) ((s A_27a) V0x_2E0)))).
% 0.58/0.75 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)))).
% 0.58/0.75 Axiom thm_2Ebool_2ECOND__CLAUSES:(forall (A_27a:d) (V0t1_2E0:u) (V1t2_2E0:u), ((and (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool mono_2Ec_2Ebool_2ET))) ((s A_27a) V0t1_2E0)) ((s A_27a) V1t2_2E0)))) ((s A_27a) V0t1_2E0))) (((eq du) ((s A_27a) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool mono_2Ec_2Ebool_2EF))) ((s A_27a) V0t1_2E0)) ((s A_27a) V1t2_2E0)))) ((s A_27a) V1t2_2E0)))).
% 0.58/0.75 Axiom thm_2Ebool_2EDISJ__ASSOC:(forall (V0A:Prop) (V1B:Prop) (V2C:Prop), ((iff ((or ((or V0A) V1B)) V2C)) ((or ((or V0A) V1B)) V2C))).
% 33.08/33.24 Axiom thm_2Ebool_2EDISJ__SYM:(forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A))).
% 33.08/33.24 Axiom thm_2Ebool_2EDE__MORGAN__THM:(forall (V0A:Prop) (V1B:Prop), ((and ((iff (not ((and V0A) V1B))) ((or (not V0A)) (not V1B)))) ((iff (not ((or V0A) V1B))) ((and (not V0A)) (not V1B))))).
% 33.08/33.24 Axiom thm_2Eextreal_2Ele__trans:(forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal) (V2z:mono_2Etyop_2Eextreal_2Eextreal), (((and ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V2z))->((mono_2Ec_2Eextreal_2Eextreal__le V0x) V2z))).
% 33.08/33.24 Axiom thm_2Eextreal_2Ele__total:(forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal), ((or ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0x))).
% 33.08/33.24 Axiom thm_2Eextreal_2Eextreal__max__def:(forall (V0x:mono_2Etyop_2Eextreal_2Eextreal) (V1y:mono_2Etyop_2Eextreal_2Eextreal), (((eq mono_2Etyop_2Eextreal_2Eextreal) ((mono_2Ec_2Eextreal_2Eextreal__max V0x) V1y)) (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal ((mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) V1y) V0x))).
% 33.08/33.24 Axiom thm_2Esat_2ENOT__NOT:(forall (V0t:Prop), ((iff (not (not V0t))) V0t)).
% 33.08/33.24 Axiom thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF))).
% 33.08/33.24 Axiom thm_2Esat_2EOR__DUAL2:(forall (V0B:Prop) (V1A:Prop), ((iff ((not ((or V1A) V0B))->mono_2Ec_2Ebool_2EF)) ((V1A->mono_2Ec_2Ebool_2EF)->((not V0B)->mono_2Ec_2Ebool_2EF)))).
% 33.08/33.24 Axiom thm_2Esat_2EOR__DUAL3:(forall (V0B:Prop) (V1A:Prop), ((iff ((not ((or (not V1A)) V0B))->mono_2Ec_2Ebool_2EF)) (V1A->((not V0B)->mono_2Ec_2Ebool_2EF)))).
% 33.08/33.24 Axiom thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF))).
% 33.08/33.24 Axiom thm_2Esat_2Edc__eq:(forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) (((eq Prop) V1q) V0r))) ((and ((and ((and ((or ((or V2p) V1q)) V0r)) ((or ((or V2p) (not V0r))) (not V1q)))) ((or ((or V1q) (not V0r))) (not V2p)))) ((or ((or V0r) (not V1q))) (not V2p))))).
% 33.08/33.24 Axiom thm_2Esat_2Edc__conj:(forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) ((and V1q) V0r))) ((and ((and ((or ((or V2p) (not V1q))) (not V0r))) ((or V1q) (not V2p)))) ((or V0r) (not V2p))))).
% 33.08/33.24 Axiom thm_2Esat_2Edc__disj:(forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) ((or V1q) V0r))) ((and ((and ((or V2p) (not V1q))) ((or V2p) (not V0r)))) ((or ((or V1q) V0r)) (not V2p))))).
% 33.08/33.24 Axiom thm_2Esat_2Edc__imp:(forall (V0r:Prop) (V1q:Prop) (V2p:Prop), ((iff ((iff V2p) (V1q->V0r))) ((and ((and ((or V2p) V1q)) ((or V2p) (not V0r)))) ((or ((or (not V1q)) V0r)) (not V2p))))).
% 33.08/33.24 Axiom thm_2Esat_2Edc__neg:(forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p))))).
% 33.08/33.24 Trying to prove (forall (V0z:mono_2Etyop_2Eextreal_2Eextreal) (V1x:mono_2Etyop_2Eextreal_2Eextreal) (V2y:mono_2Etyop_2Eextreal_2Eextreal), ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 33.08/33.24 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 33.08/33.24 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 33.08/33.24 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False) as proof of False
% 33.08/33.24 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of False
% 33.08/33.24 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 33.08/33.24 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)
% 65.20/65.42 Instantiate: V1y:=V2y:mono_2Etyop_2Eextreal_2Eextreal
% 65.20/65.42 Found x1 as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 65.20/65.42 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 65.20/65.42 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False) as proof of False
% 65.20/65.42 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of False
% 65.20/65.42 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 65.20/65.42 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 65.20/65.42 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False) as proof of False
% 65.20/65.42 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of False
% 65.20/65.42 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 65.20/65.42 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 65.20/65.42 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False) as proof of False
% 65.20/65.42 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of False
% 65.20/65.42 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 65.20/65.42 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 65.20/65.42 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 65.20/65.42 Found x30:V0t
% 65.20/65.42 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 65.20/65.42 Found x30 as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 65.20/65.42 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 65.20/65.42 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29:(forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V0 V1)) (V0 V1)))
% 86.15/86.35 Instantiate: V0t:=(forall (V0:(Prop->(mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal)))) (V1:Prop), (((eq (mono_2Etyop_2Eextreal_2Eextreal->(mono_2Etyop_2Eextreal_2Eextreal->mono_2Etyop_2Eextreal_2Eextreal))) (V0 V1)) (V0 V1))):Prop
% 86.15/86.35 Found monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 as proof of V0t
% 86.15/86.35 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found x30:V0t
% 86.15/86.35 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 86.15/86.35 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 86.15/86.35 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((V0t->(not (not V0t)))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 86.15/86.35 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)
% 86.15/86.35 Instantiate: V1y:=V1x:mono_2Etyop_2Eextreal_2Eextreal
% 86.15/86.35 Found x0 as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 86.15/86.35 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 86.15/86.35 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 86.15/86.35 Found x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)
% 86.15/86.35 Instantiate: V1y:=V2y:mono_2Etyop_2Eextreal_2Eextreal
% 86.15/86.35 Found (fun (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 92.09/92.32 Found (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1) as proof of (((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z))
% 92.09/92.32 Found (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1) as proof of (((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)->(((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)))
% 92.09/92.32 Found (and_rect00 (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 92.09/92.32 Found ((and_rect0 ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)) (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 92.09/92.32 Found (((fun (P:Type) (x0:(((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)->(((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->P)))=> (((((and_rect ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)) P) x0) x)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)) (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 92.09/92.32 Found (((fun (P:Type) (x0:(((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)->(((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->P)))=> (((((and_rect ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)) P) x0) x)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)) (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 92.09/92.32 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found x60:=(fun (x7:mono_2Ec_2Ebool_2EF)=> ((x6 x7) thm_2Ebool_2ETRUTH)):(mono_2Ec_2Ebool_2EF->False)
% 92.09/92.32 Found (fun (x7:mono_2Ec_2Ebool_2EF)=> ((x6 x7) thm_2Ebool_2ETRUTH)) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (fun (x7:mono_2Ec_2Ebool_2EF)=> ((x6 x7) thm_2Ebool_2ETRUTH)) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 92.09/92.32 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 92.09/92.32 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 92.09/92.32 Found x30:=(x3 x40):V0t
% 92.09/92.32 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 92.09/92.32 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 92.09/92.32 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 92.09/92.32 Found x40:=(fun (x6:mono_2Ec_2Ebool_2EF)=> ((x4 x6) thm_2Ebool_2ETRUTH)):(mono_2Ec_2Ebool_2EF->False)
% 112.71/112.93 Found (fun (x6:mono_2Ec_2Ebool_2EF)=> ((x4 x6) thm_2Ebool_2ETRUTH)) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (fun (x6:mono_2Ec_2Ebool_2EF)=> ((x4 x6) thm_2Ebool_2ETRUTH)) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 112.71/112.93 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 112.71/112.93 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x20:=(x2 x10):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x20:=(x2 x10):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 112.71/112.93 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 112.71/112.93 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 112.71/112.93 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 112.71/112.93 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 112.71/112.93 Found (x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) as proof of (not (not V0t))
% 112.71/112.93 Found (x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) as proof of (not (not V0t))
% 112.71/112.93 Found x60:=(x6 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x6 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x6 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 112.71/112.93 Found x30:=(x3 x40):V0t
% 112.71/112.93 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 112.71/112.93 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 128.91/129.15 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 128.91/129.15 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 128.91/129.15 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 128.91/129.15 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False) as proof of False
% 128.91/129.15 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of False
% 128.91/129.15 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 128.91/129.15 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 128.91/129.15 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False) as proof of False
% 128.91/129.15 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of False
% 128.91/129.15 Found (fun (x2:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x2)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 128.91/129.15 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 128.91/129.15 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False) as proof of False
% 128.91/129.15 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of False
% 128.91/129.15 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 128.91/129.15 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 128.91/129.15 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 128.91/129.15 Found (x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) as proof of False
% 128.91/129.15 Found (fun (x4:(not V0t))=> (x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29)) as proof of False
% 128.91/129.15 Found (fun (x4:(not V0t))=> (x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29)) as proof of (not (not V0t))
% 128.91/129.15 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 128.91/129.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 131.84/132.06 Found False_rect00:=(False_rect0 ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 131.84/132.06 Found (False_rect0 ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 131.84/132.06 Found ((fun (P:Type)=> ((False_rect P) x400)) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 131.84/132.06 Found ((fun (P:Type)=> ((False_rect P) (x40 thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 131.84/132.06 Found ((fun (P:Type)=> ((False_rect P) ((x4 x30) thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 131.84/132.06 Found ((fun (P:Type)=> ((False_rect P) ((x4 x30) thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 131.84/132.06 Found thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 131.84/132.06 Found thm_2Esat_2EAND__INV2 as proof of (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 131.84/132.06 Found and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 131.84/132.06 Found and_comm_i as proof of (forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 131.84/132.06 Found thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 131.84/132.06 Found thm_2Esat_2EAND__INV__IMP as proof of (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 131.84/132.06 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 131.84/132.06 Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 131.84/132.06 Found x3:((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 131.84/132.06 Found x3 as proof of ((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 131.84/132.06 Found x4:(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 143.63/143.87 Found x4 as proof of (mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 143.63/143.87 Found x:((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 143.63/143.87 Found x as proof of ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 143.63/143.87 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 143.63/143.87 Found conj as proof of (forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 143.63/143.87 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 143.63/143.87 Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 143.63/143.87 Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 143.63/143.87 Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% 143.63/143.87 Found thm_2Ebool_2EIMP__F:(forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 143.63/143.87 Found thm_2Ebool_2EIMP__F as proof of (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 143.63/143.87 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 143.63/143.87 Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% 143.63/143.87 Found x2:((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found x2 as proof of ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 143.63/143.87 Found thm_2Ebool_2EFALSITY as proof of (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 143.63/143.87 Found x1:(forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 143.63/143.87 Found x1 as proof of (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 143.63/143.87 Found thm_2Ebool_2EF__IMP:(forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 143.63/143.87 Found thm_2Ebool_2EF__IMP as proof of (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 143.63/143.87 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 143.63/143.87 Found proj1 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->A))
% 143.63/143.87 Found proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 143.63/143.87 Found proj2 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->B))
% 143.63/143.87 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 143.63/143.87 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 143.63/143.87 Found x0:((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 143.63/143.87 Found x0 as proof of ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 143.63/143.87 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found x40:(not (not V0t))
% 143.63/143.87 Found x40 as proof of (not (not V0t))
% 143.63/143.87 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 143.63/143.87 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 143.63/143.87 Found (x3 x40) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 143.63/143.87 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 143.63/143.87 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 143.63/143.87 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False) as proof of False
% 143.63/143.87 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of False
% 143.63/143.87 Found (fun (x4:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x4)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 143.63/143.87 Found False_rect00:=(False_rect0 ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 145.41/145.64 Found (False_rect0 ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 145.41/145.64 Found ((fun (P:Type)=> ((False_rect P) x400)) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 145.41/145.64 Found ((fun (P:Type)=> ((False_rect P) (x40 thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 145.41/145.64 Found ((fun (P:Type)=> ((False_rect P) ((x4 x30) thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 145.41/145.64 Found (fun (x4:(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET)))=> ((fun (P:Type)=> ((False_rect P) ((x4 x30) thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 145.41/145.64 Found (fun (x4:(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET)))=> ((fun (P:Type)=> ((False_rect P) ((x4 x30) thm_2Ebool_2ETRUTH))) ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))) as proof of ((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 145.41/145.64 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 145.41/145.64 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 145.41/145.64 Found x1:(forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 145.41/145.64 Found x1 as proof of (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 145.41/145.64 Found thm_2Ebool_2EIMP__F:(forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 145.41/145.64 Found thm_2Ebool_2EIMP__F as proof of (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 145.41/145.64 Found thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 145.41/145.64 Found thm_2Esat_2EAND__INV2 as proof of (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 145.41/145.64 Found x2:((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 145.41/145.64 Found x2 as proof of ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 149.16/149.43 Found thm_2Ebool_2EF__IMP:(forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 149.16/149.43 Found thm_2Ebool_2EF__IMP as proof of (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 149.16/149.43 Found x0:((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 149.16/149.43 Found x0 as proof of ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 149.16/149.43 Found x3:((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 149.16/149.43 Found x3 as proof of ((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 149.16/149.43 Found and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 149.16/149.43 Found and_comm_i as proof of (forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 149.16/149.43 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 149.16/149.43 Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 149.16/149.43 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 149.16/149.43 Found conj as proof of (forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 149.16/149.43 Found thm_2Ebool_2EIMP__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((and ((iff (mono_2Ec_2Ebool_2ET->V0t)) V0t)) ((iff (V0t->mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff (mono_2Ec_2Ebool_2EF->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->mono_2Ec_2Ebool_2EF)) (not V0t))))
% 149.16/149.43 Found thm_2Ebool_2EIMP__CLAUSES as proof of (forall (V0t:Prop), ((and ((and ((and ((and ((iff (mono_2Ec_2Ebool_2ET->V0t)) V0t)) ((iff (V0t->mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff (mono_2Ec_2Ebool_2EF->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->V0t)) mono_2Ec_2Ebool_2ET))) ((iff (V0t->mono_2Ec_2Ebool_2EF)) (not V0t))))
% 149.16/149.43 Found x:((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 149.16/149.43 Found x as proof of ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 149.16/149.43 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 149.16/149.43 Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% 149.16/149.43 Found thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 149.16/149.43 Found thm_2Ebool_2EFALSITY as proof of (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 149.16/149.43 Found proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 149.16/149.43 Found proj2 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->B))
% 149.16/149.43 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 149.16/149.43 Found proj1 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->A))
% 149.16/149.43 Found thm_2Ebool_2ENOT__CLAUSES:((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET))
% 149.16/149.43 Found thm_2Ebool_2ENOT__CLAUSES as proof of ((and ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))) ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET))
% 149.16/149.43 Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 149.16/149.43 Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% 149.16/149.43 Found thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 149.16/149.43 Found thm_2Esat_2EAND__INV__IMP as proof of (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 149.16/149.43 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 149.16/149.43 Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 149.16/149.43 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 149.16/149.43 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 174.19/174.61 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 174.19/174.61 Found functional_extensionality_dep as proof of V0t
% 174.19/174.61 Found x30:V0t
% 174.19/174.61 Instantiate: V0t:=(((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)->((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))):Prop
% 174.19/174.61 Found x30 as proof of (((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)->((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))))
% 174.19/174.61 Found x5:mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 174.19/174.61 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 174.19/174.61 Found functional_extensionality_dep as proof of V0t
% 174.19/174.61 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found x30:V0t
% 174.19/174.61 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 174.19/174.61 Found x30 as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 174.19/174.61 Found x7:mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found x7 as proof of mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found x7:mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found x7 as proof of mono_2Ec_2Ebool_2ET
% 174.19/174.61 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 174.19/174.61 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 196.03/196.41 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 196.03/196.41 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 196.03/196.41 Found (x5 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) as proof of False
% 196.03/196.41 Found (fun (x5:(not V0t))=> (x5 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29)) as proof of False
% 196.03/196.41 Found (fun (x5:(not V0t))=> (x5 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29)) as proof of (not (not V0t))
% 196.03/196.41 Found x2:((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 196.03/196.42 Found x2 as proof of ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 196.03/196.42 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 196.03/196.42 Found conj as proof of (forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 196.03/196.42 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 196.03/196.42 Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 196.03/196.42 Found x:((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 196.03/196.42 Found x as proof of ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 196.03/196.42 Found and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 196.03/196.42 Found and_comm_i as proof of (forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 196.03/196.42 Found x1:(forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 196.03/196.42 Found x1 as proof of (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 196.03/196.42 Found x3:((not (not V0t))->V0t)
% 196.03/196.42 Found x3 as proof of ((not (not V0t))->V0t)
% 196.03/196.42 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 196.03/196.42 Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 196.03/196.42 Found x5:(not V0t)
% 196.03/196.42 Found x5 as proof of (not V0t)
% 196.03/196.42 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 196.03/196.42 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 196.03/196.42 Found x0:((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 196.03/196.42 Found x0 as proof of ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 196.03/196.42 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 196.03/196.42 Found proj1 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->A))
% 196.03/196.42 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 196.03/196.42 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 196.03/196.42 Found thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 196.03/196.42 Found thm_2Ebool_2EFALSITY as proof of (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 196.03/196.42 Found x4:(V0t->(not (not V0t)))
% 196.03/196.42 Found x4 as proof of (V0t->(not (not V0t)))
% 196.03/196.42 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 196.03/196.42 Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% 196.03/196.42 Found proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 196.03/196.42 Found proj2 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->B))
% 196.03/196.42 Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 196.03/196.42 Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% 196.03/196.42 Found x30:=(x3 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x3 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x3 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found x5:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x30:=(x3 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x3 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x3 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found x5:((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Instantiate: V0t:=((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF):Prop
% 213.75/214.18 Found x5 as proof of V0t
% 213.75/214.18 Found x30:V0t
% 213.75/214.18 Instantiate: V0t:=((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 213.75/214.18 Found x30 as proof of ((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 213.75/214.18 Found x5:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x30:V0t
% 213.75/214.18 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 213.75/214.18 Found x30 as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 213.75/214.18 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 213.75/214.18 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 213.75/214.18 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 213.75/214.18 Found x5:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found x5:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 213.75/214.18 Found x5:mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x5 as proof of mono_2Ec_2Ebool_2ET
% 213.75/214.18 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 221.84/222.28 Found x30:V0t
% 221.84/222.28 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 221.84/222.28 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 221.84/222.28 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((V0t->(not (not V0t)))->((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)))
% 221.84/222.28 Found x30:V0t
% 221.84/222.28 Instantiate: V0t:=(((not mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2ET)->((mono_2Ec_2Ebool_2ET->(not mono_2Ec_2Ebool_2EF))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))):Prop
% 221.84/222.28 Found x30 as proof of (((not mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2ET)->((mono_2Ec_2Ebool_2ET->(not mono_2Ec_2Ebool_2EF))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))))
% 221.84/222.28 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 221.84/222.28 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 221.84/222.28 Found functional_extensionality_dep as proof of V0t
% 221.84/222.28 Found x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)
% 221.84/222.28 Instantiate: V1y:=V2y:mono_2Etyop_2Eextreal_2Eextreal
% 221.84/222.28 Found (fun (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 221.84/222.28 Found (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1) as proof of (((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z))
% 221.84/222.28 Found (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1) as proof of (((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)->(((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)))
% 221.84/222.28 Found (and_rect00 (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 221.84/222.28 Found ((and_rect0 ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)) (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 221.84/222.28 Found (((fun (P:Type) (x0:(((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)->(((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->P)))=> (((((and_rect ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)) P) x0) x)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)) (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 236.35/236.78 Found (((fun (P:Type) (x0:(((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)->(((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)->P)))=> (((((and_rect ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)) P) x0) x)) ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)) (fun (x0:((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) (x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))=> x1)) as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 236.35/236.78 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 236.35/236.78 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 236.35/236.78 Found functional_extensionality_dep as proof of V0t
% 236.35/236.78 Found x50:V0t
% 236.35/236.78 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 236.35/236.78 Found x50 as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 236.35/236.78 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 236.35/236.78 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 236.35/236.78 Found x5:(not V0t)
% 236.35/236.78 Found x5 as proof of (not V0t)
% 236.35/236.78 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 236.35/236.78 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 236.35/236.78 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 236.35/236.78 Found ((x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) x5) as proof of False
% 236.35/236.78 Found (fun (x5:(not V0t))=> ((x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) x5)) as proof of False
% 236.35/236.78 Found (fun (x5:(not V0t))=> ((x4 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29) x5)) as proof of (not (not V0t))
% 236.35/236.78 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 236.35/236.78 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 236.35/236.78 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x3)) False) as proof of False
% 236.35/236.78 Found (fun (x3:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x3)) False)) as proof of False
% 236.35/236.78 Found (fun (x3:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x3)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 236.35/236.78 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 236.35/236.78 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 236.35/236.78 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 236.35/236.78 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 238.80/239.24 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 238.80/239.24 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 238.80/239.24 Found x30:V0t
% 238.80/239.24 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 238.80/239.24 Found x30 as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 238.80/239.24 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 238.80/239.24 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 238.80/239.24 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 238.80/239.24 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29:(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0)))
% 238.80/239.24 Instantiate: V0t:=(forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Eextreal_2Eextreal) tyop_2Emin_2Ebool)) V0_2E0))):Prop
% 238.80/239.24 Found ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 as proof of V0t
% 238.80/239.24 Found x30:V0t
% 238.80/239.24 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 238.80/239.24 Found x30 as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 238.80/239.24 Found x30:=(x3 x40):V0t
% 238.80/239.24 Instantiate: V0t:=(((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)->((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))):Prop
% 238.80/239.24 Found (x3 x40) as proof of (((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)->((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))))
% 252.55/252.97 Found (x3 x40) as proof of (((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)->((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))))
% 252.55/252.97 Found x7:mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found x7 as proof of mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found x7:mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found x7 as proof of mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found thm_2Ebool_2EFALSITY00:=(thm_2Ebool_2EFALSITY0 False):False
% 252.55/252.97 Found (thm_2Ebool_2EFALSITY0 False) as proof of False
% 252.55/252.97 Found ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x3)) False) as proof of False
% 252.55/252.97 Found (fun (x3:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x3)) False)) as proof of False
% 252.55/252.97 Found (fun (x3:mono_2Ec_2Ebool_2EF)=> ((fun (V0t:Prop)=> ((thm_2Ebool_2EFALSITY V0t) x3)) False)) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found x30:V0t
% 252.55/252.97 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 252.55/252.97 Found x30 as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 252.55/252.97 Found x6:(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 252.55/252.97 Instantiate: V0t:=(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET)):Prop
% 252.55/252.97 Found x6 as proof of V0t
% 252.55/252.97 Found x50:V0t
% 252.55/252.97 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 252.55/252.97 Found (fun (x6:(V0t->(not (not V0t))))=> x50) as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 252.55/252.97 Found (fun (x6:(V0t->(not (not V0t))))=> x50) as proof of ((V0t->(not (not V0t)))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 252.55/252.97 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 252.55/252.97 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 252.55/252.97 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found x30:=(x3 x40):V0t
% 259.74/260.15 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 259.74/260.15 Found (x3 x40) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 259.74/260.15 Found (x3 x40) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 259.74/260.15 Found x30:V0t
% 259.74/260.15 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 259.74/260.15 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 259.74/260.15 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((V0t->(not (not V0t)))->((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)))
% 259.74/260.15 Found x30:V0t
% 259.74/260.15 Instantiate: V0t:=((mono_2Ec_2Ebool_2ET->(not mono_2Ec_2Ebool_2EF))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 259.74/260.15 Found x30 as proof of ((mono_2Ec_2Ebool_2ET->(not mono_2Ec_2Ebool_2EF))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 259.74/260.15 Found x5:((not mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2ET)
% 259.74/260.15 Instantiate: V0t:=((not mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2ET):Prop
% 259.74/260.15 Found x5 as proof of V0t
% 259.74/260.15 Found x30:V0t
% 259.74/260.15 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 259.74/260.15 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 259.74/260.15 Found (fun (x4:(V0t->(not (not V0t))))=> x30) as proof of ((V0t->(not (not V0t)))->((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)))
% 259.74/260.15 Found x20:=(x2 x10):(not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 259.74/260.15 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 259.74/260.15 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 259.74/260.15 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found x20:=(x2 x10):(not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 274.87/275.32 Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 274.87/275.32 Found proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 274.87/275.32 Found proj2 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->B))
% 274.87/275.32 Found thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 274.87/275.32 Found thm_2Esat_2EAND__INV2 as proof of (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 274.87/275.32 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 274.87/275.32 Found proj1 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->A))
% 274.87/275.32 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 274.87/275.32 Found iff_refl as proof of (forall (P:Prop), ((iff P) P))
% 274.87/275.32 Found x:((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 274.87/275.32 Found x as proof of ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 274.87/275.32 Found thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 274.87/275.32 Found thm_2Ebool_2EFALSITY as proof of (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 274.87/275.32 Found x7:(not V0t)
% 274.87/275.32 Found x7 as proof of (not V0t)
% 274.87/275.32 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 274.87/275.32 Found conj as proof of (forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 274.87/275.32 Found x3:((not (not V0t))->V0t)
% 274.87/275.32 Found x3 as proof of ((not (not V0t))->V0t)
% 274.87/275.32 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 274.87/275.32 Found and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 274.87/275.32 Found and_comm_i as proof of (forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 274.87/275.32 Found x5:((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found x5 as proof of ((not mono_2Ec_2Ebool_2ET)->mono_2Ec_2Ebool_2EF)
% 274.87/275.32 Found thm_2Ebool_2EF__IMP:(forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 274.87/275.32 Found thm_2Ebool_2EF__IMP as proof of (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 274.87/275.32 Found thm_2Ebool_2EIMP__F:(forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 274.87/275.32 Found thm_2Ebool_2EIMP__F as proof of (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 274.87/275.32 Found x0:((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 274.87/275.32 Found x0 as proof of ((iff (not mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2ET)
% 274.87/275.32 Found x6:(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 274.87/275.32 Found x6 as proof of (mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 274.87/275.32 Found x4:(V0t->(not (not V0t)))
% 274.87/275.32 Found x4 as proof of (V0t->(not (not V0t)))
% 274.87/275.32 Found thm_2Esat_2ENOT__NOT:(forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 274.87/275.32 Found thm_2Esat_2ENOT__NOT as proof of (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 274.87/275.32 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 277.72/278.12 Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 277.72/278.12 Found x2:((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found x2 as proof of ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 277.72/278.12 Found thm_2Esat_2EAND__INV__IMP as proof of (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 277.72/278.12 Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 277.72/278.12 Found NNPP as proof of (forall (P:Prop), ((not (not P))->P))
% 277.72/278.12 Found x30:=(x3 x40):V0t
% 277.72/278.12 Instantiate: V0t:=((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 277.72/278.12 Found (x3 x40) as proof of ((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 277.72/278.12 Found (x3 x40) as proof of ((mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))->((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))
% 277.72/278.12 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 277.72/278.12 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 277.72/278.12 Found functional_extensionality_dep as proof of V0t
% 277.72/278.12 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 277.72/278.12 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 277.72/278.12 Found functional_extensionality_dep as proof of V0t
% 277.72/278.12 Found x30:V0t
% 277.72/278.12 Instantiate: V0t:=(((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)):Prop
% 277.72/278.12 Found x30 as proof of (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 277.72/278.12 Found x30:V0t
% 277.72/278.12 Instantiate: V0t:=(((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))):Prop
% 277.72/278.12 Found x30 as proof of (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 277.72/278.12 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 277.72/278.12 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 277.72/278.12 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 277.72/278.12 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found x1:((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)
% 291.36/291.83 Instantiate: V1y:=V2y:mono_2Etyop_2Eextreal_2Eextreal
% 291.36/291.83 Found x1 as proof of ((mono_2Ec_2Eextreal_2Eextreal__le V1y) V0z)
% 291.36/291.83 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found x20:=(x2 x10):(not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found x20:=(x2 x10):(not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 x10) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 291.36/291.83 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 291.36/291.83 Found functional_extensionality_dep as proof of V0t
% 291.36/291.83 Found x50:V0t
% 291.36/291.83 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 291.36/291.83 Found x50 as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 291.36/291.83 Found x50:V0t
% 291.36/291.83 Instantiate: V0t:=((and (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))) (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))):Prop
% 291.36/291.83 Found x50 as proof of ((iff ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)) ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))
% 291.36/291.83 Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 291.36/291.83 Instantiate: V0t:=(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g))):Prop
% 291.36/291.83 Found functional_extensionality_dep as proof of V0t
% 291.36/291.83 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 291.36/291.83 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 291.36/291.83 Found x30:=(x3 x40):V0t
% 291.36/291.83 Instantiate: V0t:=((and (((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))->((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))) (((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z)->((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z)))):Prop
% 291.36/291.83 Found (x3 x40) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 291.36/291.83 Found (x3 x40) as proof of ((iff ((and ((mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z)) ((mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))) ((mono_2Ec_2Eextreal_2Eextreal__le ((mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z))
% 298.35/298.77 Found x20:=(x2 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found (x2 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 298.35/298.77 Found iff_trans as proof of (forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 298.35/298.77 Found and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 298.35/298.77 Found and_comm_i as proof of (forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 298.35/298.77 Found x:((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 298.35/298.77 Found x as proof of ((and (forall (V0t:Prop), ((iff (not (not V0t))) V0t))) ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF))
% 298.35/298.77 Found x7:(not V0t)
% 298.35/298.77 Found x7 as proof of (not V0t)
% 298.35/298.77 Found thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET
% 298.35/298.77 Found thm_2Ebool_2ETRUTH as proof of mono_2Ec_2Ebool_2ET
% 298.35/298.77 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 298.35/298.77 Found proj1 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->A))
% 298.35/298.77 Found thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 298.35/298.77 Found thm_2Esat_2EAND__INV__IMP as proof of (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 298.35/298.77 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 298.35/298.77 Found conj as proof of (forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 298.35/298.77 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 298.35/298.77 Found iff_sym as proof of (forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 298.35/298.77 Found thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 298.35/298.77 Found thm_2Esat_2EAND__INV2 as proof of (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 298.35/298.77 Found thm_2Ebool_2EF__IMP:(forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 298.35/298.77 Found thm_2Ebool_2EF__IMP as proof of (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 298.35/298.77 Found thm_2Esat_2ENOT__NOT:(forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 298.35/298.77 Found thm_2Esat_2ENOT__NOT as proof of (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 298.35/298.77 Found x40:=(x4 thm_2Ebool_2ETRUTH):(not mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found (x4 thm_2Ebool_2ETRUTH) as proof of (not mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 298.35/298.77 Found proj2 as proof of (forall (A:Prop) (B:Prop), (((and A) B)->B))
% 298.35/298.77 Found x4:(V0t->(not (not V0t)))
% 298.35/298.77 Found x4 as proof of (V0t->(not (not V0t)))
% 298.35/298.77 Found x6:(mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 298.35/298.77 Found x6 as proof of (mono_2Ec_2Ebool_2EF->(not mono_2Ec_2Ebool_2ET))
% 298.35/298.77 Found thm_2Ebool_2EIMP__F:(forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 298.35/298.77 Found thm_2Ebool_2EIMP__F as proof of (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 298.35/298.77 Found x2:((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found x2 as proof of ((iff (not mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2EF)
% 298.35/298.77 Found thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 298.35/298.77 Found thm_2Ebool_2EFALSITY as proof of (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 298.35/298.77 Found NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Pr
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