TSTP Solution File: ITP007^1 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP007^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 13:23:34 EDT 2021
% Result : Timeout 300.08s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP007^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Thu Mar 18 21:16:37 EDT 2021
% 0.13/0.34 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 0.38/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77d40>, <kernel.Type object at 0x1e77c68>) of role type named u
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring u:Type
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9d0e0>, <kernel.Type object at 0x1e77998>) of role type named d
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring d:Type
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e779e0>, <kernel.Type object at 0x1e77a28>) of role type named du
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring du:Type
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77c68>, <kernel.Constant object at 0x1e77cb0>) of role type named tyop_2Emin_2Ebool
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring tyop_2Emin_2Ebool:d
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77bd8>, <kernel.DependentProduct object at 0x1e779e0>) of role type named tyop_2Emin_2Efun
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring tyop_2Emin_2Efun:(d->(d->d))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77f38>, <kernel.DependentProduct object at 0x1e9c128>) of role type named tyop_2Eoption_2Eoption
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring tyop_2Eoption_2Eoption:(d->d)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77ea8>, <kernel.DependentProduct object at 0x1e77cb0>) of role type named s
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring s:(d->(u->du))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77bd8>, <kernel.DependentProduct object at 0x1e9c1b8>) of role type named app_2E2
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring app_2E2:(du->(du->u))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77f38>, <kernel.Constant object at 0x1e9cef0>) of role type named combin_i_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring combin_i_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77bd8>, <kernel.Constant object at 0x1e9c128>) of role type named combin_k_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring combin_k_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77f38>, <kernel.Constant object at 0x1e9cc68>) of role type named combin_s_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring combin_s_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77cb0>, <kernel.Constant object at 0x1e9cc68>) of role type named c_2Ebool_2E_21_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_21_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e77cb0>, <kernel.DependentProduct object at 0x1e9c2d8>) of role type named c_2Ebool_2E_21_2E1
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_21_2E1:(du->u)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9cc20>, <kernel.Constant object at 0x1e9c2d8>) of role type named c_2Ebool_2E_2F_5C_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_2F_5C_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c290>, <kernel.DependentProduct object at 0x1e9cc68>) of role type named c_2Ebool_2E_2F_5C_2E2
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_2F_5C_2E2:(du->(du->u))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c368>, <kernel.Constant object at 0x1e9cc68>) of role type named c_2Emin_2E_3D_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Emin_2E_3D_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9cc20>, <kernel.DependentProduct object at 0x1e9c2d8>) of role type named c_2Emin_2E_3D_2E2
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Emin_2E_3D_2E2:(du->(du->u))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c1b8>, <kernel.Constant object at 0x1e9c2d8>) of role type named c_2Emin_2E_3D_3D_3E_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Emin_2E_3D_3D_3E_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c368>, <kernel.DependentProduct object at 0x1e9cc68>) of role type named c_2Emin_2E_3D_3D_3E_2E2
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c6c8>, <kernel.Constant object at 0x1e9cc68>) of role type named c_2Ebool_2E_3F_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_3F_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c1b8>, <kernel.DependentProduct object at 0x2b77f1d16200>) of role type named c_2Ebool_2E_3F_2E1
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_3F_2E1:(du->u)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c998>, <kernel.Constant object at 0x1e9c6c8>) of role type named c_2Emin_2E_40_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Emin_2E_40_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9cc68>, <kernel.DependentProduct object at 0x2b77f1d16560>) of role type named c_2Emin_2E_40_2E1
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Emin_2E_40_2E1:(du->u)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c6c8>, <kernel.Constant object at 0x1e9c998>) of role type named c_2Ebool_2ECOND_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2ECOND_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c1b8>, <kernel.DependentProduct object at 0x2b77f1d163b0>) of role type named c_2Ebool_2ECOND_2E3
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2ECOND_2E3:(du->(du->(du->u)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c998>, <kernel.Constant object at 0x2b77f1d16c20>) of role type named c_2Ebool_2EF_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2EF_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1e9c1b8>, <kernel.Constant object at 0x2b77f1d16560>) of role type named c_2Eoption_2ENONE_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2ENONE_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16368>, <kernel.Constant object at 0x2b77f1d16518>) of role type named c_2Eoption_2EOPTION__MAP_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2EOPTION__MAP_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16c20>, <kernel.DependentProduct object at 0x2b77f1d16a28>) of role type named c_2Eoption_2EOPTION__MAP_2E2
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2EOPTION__MAP_2E2:(du->(du->u))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16128>, <kernel.Constant object at 0x2b77f1d16c20>) of role type named c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16a28>, <kernel.DependentProduct object at 0x2b77f1d16368>) of role type named c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3:(du->(du->(du->u)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16488>, <kernel.DependentProduct object at 0x2b77f1d167e8>) of role type named c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4:(du->(du->(du->(du->u))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16c20>, <kernel.Constant object at 0x2b77f1d167e8>) of role type named c_2EpatternMatches_2EPMATCH__ROW_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__ROW_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16a28>, <kernel.DependentProduct object at 0x2b77f1d16368>) of role type named c_2EpatternMatches_2EPMATCH__ROW_2E3
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__ROW_2E3:(du->(du->(du->u)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16320>, <kernel.DependentProduct object at 0x2b77f1d16488>) of role type named c_2EpatternMatches_2EPMATCH__ROW_2E4
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__ROW_2E4:(du->(du->(du->(du->u))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1cf8a70>, <kernel.Constant object at 0x2b77f1d16320>) of role type named c_2EpatternMatches_2EPMATCH__ROW__COND_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__ROW__COND_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1cf8a70>, <kernel.DependentProduct object at 0x2b77f1d16a28>) of role type named c_2EpatternMatches_2EPMATCH__ROW__COND_2E4
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2EpatternMatches_2EPMATCH__ROW__COND_2E4:(du->(du->(du->(du->u))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16368>, <kernel.Constant object at 0x2b77f1d16a28>) of role type named c_2Eoption_2ESOME_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2ESOME_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d167e8>, <kernel.DependentProduct object at 0x2b77f1d16560>) of role type named c_2Eoption_2ESOME_2E1
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2ESOME_2E1:(du->u)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16cf8>, <kernel.Constant object at 0x2b77f1d16560>) of role type named c_2Ebool_2ET_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2ET_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d16368>, <kernel.Constant object at 0x2b77f1d16560>) of role type named c_2Ebool_2E_5C_2F_2E0
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_5C_2F_2E0:u
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2b77f1d167e8>, <kernel.DependentProduct object at 0x2b77f1d164d0>) of role type named c_2Ebool_2E_5C_2F_2E2
% 0.38/0.63 Using role type
% 0.38/0.63 Declaring c_2Ebool_2E_5C_2F_2E2:(du->(du->u))
% 0.38/0.63 FOF formula (<kernel.Constant object at 0x2b77f1d167e8>, <kernel.Constant object at 0x2b77f1d16a70>) of role type named c_2Eoption_2Eoption__CASE_2E0
% 0.38/0.63 Using role type
% 0.38/0.63 Declaring c_2Eoption_2Eoption__CASE_2E0:u
% 0.38/0.63 FOF formula (<kernel.Constant object at 0x2b77f1d167e8>, <kernel.DependentProduct object at 0x2b77f1cf9518>) of role type named c_2Eoption_2Eoption__CASE_2E3
% 0.38/0.63 Using role type
% 0.38/0.63 Declaring c_2Eoption_2Eoption__CASE_2E3:(du->(du->(du->u)))
% 0.38/0.63 FOF formula (<kernel.Constant object at 0x2b77f1d16320>, <kernel.Constant object at 0x2b77f1d16368>) of role type named c_2Eoption_2Esome_2E0
% 0.38/0.63 Using role type
% 0.38/0.63 Declaring c_2Eoption_2Esome_2E0:u
% 0.38/0.63 FOF formula (<kernel.Constant object at 0x2b77f1d16a70>, <kernel.DependentProduct object at 0x1e99d88>) of role type named c_2Eoption_2Esome_2E1
% 0.38/0.63 Using role type
% 0.38/0.63 Declaring c_2Eoption_2Esome_2E1:(du->u)
% 0.38/0.63 FOF formula (<kernel.Constant object at 0x2b77f1cf94d0>, <kernel.Constant object at 0x2b77f1d16320>) of role type named c_2Ebool_2E_7E_2E0
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ebool_2E_7E_2E0:u
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b77f1cf95a8>, <kernel.DependentProduct object at 0x1e99368>) of role type named c_2Ebool_2E_7E_2E1
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ebool_2E_7E_2E1:(du->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b77f1cf9248>, <kernel.DependentProduct object at 0x1e991b8>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b77f1cf9248>, <kernel.DependentProduct object at 0x1e991b8>) of role type named mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop)))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b77f1d16320>, <kernel.DependentProduct object at 0x1e99368>) 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 0x2b77f1d16cf8>, <kernel.DependentProduct object at 0x1e99098>) 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 0x2b77f1d16320>, <kernel.Sort object at 0x2b77f1cf1638>) 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 0x2b77f1d16cf8>, <kernel.Sort object at 0x2b77f1cf1638>) 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 0x2b77f1d16cf8>, <kernel.DependentProduct object at 0x1e99128>) 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 0x1e99e18>, <kernel.DependentProduct object at 0x1e99908>) 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 0x1e991b8>, <kernel.DependentProduct object at 0x1e99488>) 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 0x1e99098>, <kernel.DependentProduct object at 0x1e996c8>) 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 0x1e99e18>, <kernel.DependentProduct object at 0x1e99fc8>) 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)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1e991b8>, <kernel.DependentProduct object at 0x1e99128>) of role type named j_mono_2Etyop_2Emin_2Ebool
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Ebool:(du->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1e99b48>, <kernel.DependentProduct object at 0x1e99ab8>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1e99fc8>, <kernel.DependentProduct object at 0x1e99e18>) 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 (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)))
% 0.48/0.64 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (V0f_2E0:u) (V1g_2E0:u) (V2x_2E0:u), (((eq du) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c)))) combin_s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) ((s A_27a) V2x_2E0)))) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0))))))) of role axiom named reserved_2Eho_2Es__thm
% 0.48/0.64 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (V0f_2E0:u) (V1g_2E0:u) (V2x_2E0:u), (((eq du) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun A_27a) A_27c)))) combin_s_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) ((s A_27a) V2x_2E0)))) ((s A_27c) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)) ((s A_27a) V2x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) ((s A_27a) V2x_2E0)))))))
% 0.48/0.65 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))) of role axiom named reserved_2Elogic_2E_2F_5C
% 0.48/0.65 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1)))
% 0.48/0.65 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))) of role axiom named reserved_2Elogic_2E_5C_2F
% 0.48/0.65 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1)))
% 0.48/0.65 FOF formula (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))) of role axiom named reserved_2Elogic_2E_7E
% 0.48/0.65 A new axiom: (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0)))
% 0.48/0.65 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))) of role axiom named reserved_2Elogic_2E_3D_3D_3E
% 0.48/0.65 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1)))
% 0.48/0.65 FOF formula (forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0)))) of role axiom named reserved_2Elogic_2E_3D
% 0.48/0.65 A new axiom: (forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))
% 0.48/0.65 FOF formula (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))) of role axiom named reserved_2Equant_2E_21
% 0.48/0.65 A new axiom: (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))
% 0.48/0.65 FOF formula (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))) of role axiom named reserved_2Equant_2E_3F
% 0.48/0.65 A new axiom: (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))))
% 0.48/0.65 FOF formula (forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Ebool
% 0.48/0.65 A new axiom: (forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0)))
% 0.48/0.65 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.66 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)))
% 0.48/0.66 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
% 0.48/0.66 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)))
% 0.48/0.66 FOF formula (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Ebool
% 0.48/0.66 A new axiom: (forall (V0:Prop), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V0)))) V0))
% 0.48/0.66 FOF formula (forall (V0:(Prop->Prop)), (((eq (Prop->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.66 A new axiom: (forall (V0:(Prop->Prop)), (((eq (Prop->Prop)) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0)))) V0))
% 0.48/0.66 FOF formula (forall (V0:(Prop->(Prop->Prop))), (((eq (Prop->(Prop->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0)) of role axiom named ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.66 A new axiom: (forall (V0:(Prop->(Prop->Prop))), (((eq (Prop->(Prop->Prop))) (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0)))) V0))
% 0.48/0.66 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_21_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))) of role axiom named arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a
% 0.48/0.67 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_21_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))))
% 0.48/0.67 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a
% 0.48/0.67 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))))))
% 0.48/0.67 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
% 0.48/0.67 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))))))
% 0.48/0.67 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) A_27a)) c_2Emin_2E_40_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a
% 0.48/0.67 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) A_27a)) c_2Emin_2E_40_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))
% 0.48/0.67 FOF formula (forall (A_27a:d) (X0:Prop) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a))))) c_2Ebool_2ECOND_2E0)) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0))))) of role axiom named arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29
% 0.48/0.69 A new axiom: (forall (A_27a:d) (X0:Prop) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a))))) c_2Ebool_2ECOND_2E0)) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0)))))
% 0.48/0.69 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0))))) of role axiom named arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b
% 0.48/0.69 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))))
% 0.48/0.69 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) (tyop_2Eoption_2Eoption A_27a)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) X1_2E0))))) of role axiom named arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a
% 0.48/0.69 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) (tyop_2Eoption_2Eoption A_27a)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) X1_2E0)))))
% 0.48/0.69 FOF formula (forall (A_27a:d) (A_27b:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) X2_2E0))))) of role axiom named arityeq3_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b
% 0.55/0.70 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) X2_2E0)))))
% 0.55/0.70 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) X2_2E0)) ((s A_27c) X3_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))))) c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) X2_2E0)))) ((s A_27c) X3_2E0))))) of role axiom named arityeq4_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c
% 0.55/0.70 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) X2_2E0)) ((s A_27c) X3_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))))) c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) X2_2E0)))) ((s A_27c) X3_2E0)))))
% 0.55/0.70 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__ROW_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)) ((s A_27c) X3_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)))) ((s A_27c) X3_2E0))))) of role axiom named arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c
% 0.55/0.70 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__ROW_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)) ((s A_27c) X3_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)))) ((s A_27c) X3_2E0)))))
% 0.55/0.72 FOF formula (forall (A_27a:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0))))) of role axiom named arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a
% 0.55/0.72 A new axiom: (forall (A_27a:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))))
% 0.55/0.72 FOF formula (forall (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0))))) of role axiom named arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b
% 0.55/0.73 A new axiom: (forall (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))))
% 0.55/0.73 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)) ((s A_27b) X2_2E0)) ((s A_27a) X3_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_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))))) c_2EpatternMatches_2EPMATCH__ROW__COND_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))) ((s A_27b) X2_2E0)))) ((s A_27a) X3_2E0)))))) of role axiom named arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27a_20mono_2EA_27b
% 0.55/0.73 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)) ((s A_27b) X2_2E0)) ((s A_27a) X3_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_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))))) c_2EpatternMatches_2EPMATCH__ROW__COND_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))) ((s A_27b) X2_2E0)))) ((s A_27a) X3_2E0))))))
% 0.55/0.73 FOF formula (forall (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s A_27c) X2_2E0)) ((s A_27b) X3_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) c_2EpatternMatches_2EPMATCH__ROW__COND_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s A_27c) X2_2E0)))) ((s A_27b) X3_2E0)))))) of role axiom named arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27b_20mono_2EA_27c
% 0.55/0.74 A new axiom: (forall (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s A_27c) X2_2E0)) ((s A_27b) X3_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) c_2EpatternMatches_2EPMATCH__ROW__COND_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s A_27c) X2_2E0)))) ((s A_27b) X3_2E0))))))
% 0.55/0.74 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)) ((s A_27a) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a
% 0.55/0.74 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)) ((s A_27a) X0_2E0)))))
% 0.55/0.74 FOF formula (forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2ESOME_2E0)) ((s A_27b) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b
% 0.55/0.74 A new axiom: (forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2ESOME_2E0)) ((s A_27b) X0_2E0)))))
% 0.55/0.74 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s A_27b) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27b) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0))))) of role axiom named arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b
% 0.55/0.74 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s A_27b) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27b) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))))
% 0.55/0.75 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) X2_2E0))))) of role axiom named arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29
% 0.55/0.75 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))))
% 0.55/0.75 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2Esome_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a
% 0.55/0.75 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2Esome_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))))
% 0.55/0.75 FOF formula (forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2Esome_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0))))) of role axiom named arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27b
% 0.55/0.76 A new axiom: (forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2Esome_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))))
% 0.55/0.76 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
% 0.55/0.76 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))))))
% 0.55/0.76 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
% 0.55/0.76 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))))))
% 0.55/0.76 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
% 0.55/0.76 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.55/0.76 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
% 0.55/0.76 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1)))
% 0.55/0.76 FOF formula (forall (V0t:Prop), ((or (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) (((eq Prop) V0t) mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Ebool_2EBOOL__CASES__AX
% 0.55/0.76 A new axiom: (forall (V0t:Prop), ((or (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) (((eq Prop) V0t) mono_2Ec_2Ebool_2EF)))
% 0.55/0.76 FOF formula mono_2Ec_2Ebool_2ET of role axiom named thm_2Ebool_2ETRUTH
% 0.55/0.76 A new axiom: mono_2Ec_2Ebool_2ET
% 0.55/0.76 FOF formula (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))) of role axiom named thm_2Ebool_2EIMP__ANTISYM__AX
% 0.55/0.76 A new axiom: (forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2))))
% 0.55/0.76 FOF formula (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)) of role axiom named thm_2Ebool_2EFALSITY
% 0.55/0.76 A new axiom: (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 0.55/0.76 FOF formula (forall (V0t:Prop), ((or V0t) (not V0t))) of role axiom named thm_2Ebool_2EEXCLUDED__MIDDLE
% 0.55/0.76 A new axiom: (forall (V0t:Prop), ((or V0t) (not V0t)))
% 0.55/0.76 FOF formula (d->(forall (V0t:Prop), ((iff (u->V0t)) V0t))) of role axiom named thm_2Ebool_2EFORALL__SIMP
% 0.62/0.77 A new axiom: (d->(forall (V0t:Prop), ((iff (u->V0t)) V0t)))
% 0.62/0.77 FOF formula (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t))) of role axiom named thm_2Ebool_2EIMP__F
% 0.62/0.77 A new axiom: (forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t)))
% 0.62/0.77 FOF formula (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Ebool_2EF__IMP
% 0.62/0.77 A new axiom: (forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF)))
% 0.62/0.77 FOF formula (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((and mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff ((and V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff ((and mono_2Ec_2Ebool_2EF) V0t)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) V0t)) V0t))) of role axiom named thm_2Ebool_2EAND__CLAUSES
% 0.62/0.77 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((and mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff ((and V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff ((and mono_2Ec_2Ebool_2EF) V0t)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) V0t)) V0t)))
% 0.62/0.77 FOF formula (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((or mono_2Ec_2Ebool_2ET) V0t)) mono_2Ec_2Ebool_2ET)) ((iff ((or V0t) mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff ((or mono_2Ec_2Ebool_2EF) V0t)) V0t))) ((iff ((or V0t) mono_2Ec_2Ebool_2EF)) V0t))) ((iff ((or V0t) V0t)) V0t))) of role axiom named thm_2Ebool_2EOR__CLAUSES
% 0.62/0.77 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((and ((iff ((or mono_2Ec_2Ebool_2ET) V0t)) mono_2Ec_2Ebool_2ET)) ((iff ((or V0t) mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff ((or mono_2Ec_2Ebool_2EF) V0t)) V0t))) ((iff ((or V0t) mono_2Ec_2Ebool_2EF)) V0t))) ((iff ((or V0t) V0t)) V0t)))
% 0.62/0.77 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
% 0.62/0.77 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))))
% 0.62/0.77 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
% 0.62/0.77 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))
% 0.62/0.77 FOF formula (forall (A_27a:d) (V0x_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V0x_2E0))) mono_2Ec_2Ebool_2ET)) of role axiom named thm_2Ebool_2EREFL__CLAUSE
% 0.62/0.77 A new axiom: (forall (A_27a:d) (V0x_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V0x_2E0))) mono_2Ec_2Ebool_2ET))
% 0.62/0.77 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
% 0.62/0.77 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))))
% 0.62/0.77 FOF formula (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((iff (((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0))) (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))))))) of role axiom named thm_2Ebool_2EFUN__EQ__THM
% 0.62/0.77 A new axiom: (forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((iff (((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0))) (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)))))))
% 0.62/0.78 FOF formula (forall (V0t:Prop), ((and ((and ((and ((iff (((eq Prop) mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff (((eq Prop) mono_2Ec_2Ebool_2EF) V0t)) (not V0t)))) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2EF)) (not V0t)))) of role axiom named thm_2Ebool_2EEQ__CLAUSES
% 0.62/0.78 A new axiom: (forall (V0t:Prop), ((and ((and ((and ((iff (((eq Prop) mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff (((eq Prop) mono_2Ec_2Ebool_2EF) V0t)) (not V0t)))) ((iff (((eq Prop) V0t) mono_2Ec_2Ebool_2EF)) (not V0t))))
% 0.62/0.78 FOF formula (forall (A_27a:d) (V0P_2E0:u) (V1Q_2E0:u), (((and ((ex u) (fun (V2x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))) (forall (V3x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V3x_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1Q_2E0)) ((s A_27a) V3x_2E0)))))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1Q_2E0)) ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))))))) of role axiom named thm_2Ebool_2ESELECT__ELIM__THM
% 0.62/0.78 A new axiom: (forall (A_27a:d) (V0P_2E0:u) (V1Q_2E0:u), (((and ((ex u) (fun (V2x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))) (forall (V3x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V3x_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1Q_2E0)) ((s A_27a) V3x_2E0)))))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1Q_2E0)) ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0))))))))
% 0.62/0.78 FOF formula (forall (A_27a:d) (V0P_2E0:u), ((iff (not (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V1x_2E0))))))) ((ex u) (fun (V2x_2E0:u)=> (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))))) of role axiom named thm_2Ebool_2ENOT__FORALL__THM
% 0.62/0.78 A new axiom: (forall (A_27a:d) (V0P_2E0:u), ((iff (not (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V1x_2E0))))))) ((ex u) (fun (V2x_2E0:u)=> (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0)))))))))
% 0.62/0.78 FOF formula (forall (A_27a:d) (V0P_2E0:u), ((iff (not ((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)) V0P_2E0)) ((s A_27a) V1x_2E0)))))))) (forall (V2x_2E0:u), (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0)))))))) of role axiom named thm_2Ebool_2ENOT__EXISTS__THM
% 0.62/0.78 A new axiom: (forall (A_27a:d) (V0P_2E0:u), ((iff (not ((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)) V0P_2E0)) ((s A_27a) V1x_2E0)))))))) (forall (V2x_2E0:u), (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))))
% 0.65/0.80 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
% 0.65/0.80 A new axiom: (forall (V0A:Prop) (V1B:Prop) (V2C:Prop), ((iff ((or ((or V0A) V1B)) V2C)) ((or ((or V0A) V1B)) V2C)))
% 0.65/0.80 FOF formula (forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A))) of role axiom named thm_2Ebool_2EDISJ__SYM
% 0.65/0.80 A new axiom: (forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A)))
% 0.65/0.80 FOF formula (forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A))) of role axiom named thm_2Ebool_2EDISJ__COMM
% 0.65/0.80 A new axiom: (forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A)))
% 0.65/0.80 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
% 0.65/0.80 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)))))
% 0.65/0.80 FOF formula (forall (V0A:Prop) (V1B:Prop), ((iff (V0A->V1B)) ((or (not V0A)) V1B))) of role axiom named thm_2Ebool_2EIMP__DISJ__THM
% 0.65/0.80 A new axiom: (forall (V0A:Prop) (V1B:Prop), ((iff (V0A->V1B)) ((or (not V0A)) V1B)))
% 0.65/0.80 FOF formula (forall (V0t1:Prop) (V1t2:Prop) (V2t3:Prop), ((iff (V0t1->(V1t2->V2t3))) (((and V0t1) V1t2)->V2t3))) of role axiom named thm_2Ebool_2EAND__IMP__INTRO
% 0.65/0.80 A new axiom: (forall (V0t1:Prop) (V1t2:Prop) (V2t3:Prop), ((iff (V0t1->(V1t2->V2t3))) (((and V0t1) V1t2)->V2t3)))
% 0.65/0.80 FOF formula (forall (V0x:Prop) (V1x_27:Prop) (V2y:Prop) (V3y_27:Prop), (((and (((eq Prop) V0x) V1x_27)) (V1x_27->(((eq Prop) V2y) V3y_27)))->((iff (V0x->V2y)) (V1x_27->V3y_27)))) of role axiom named thm_2Ebool_2EIMP__CONG
% 0.65/0.80 A new axiom: (forall (V0x:Prop) (V1x_27:Prop) (V2y:Prop) (V3y_27:Prop), (((and (((eq Prop) V0x) V1x_27)) (V1x_27->(((eq Prop) V2y) V3y_27)))->((iff (V0x->V2y)) (V1x_27->V3y_27))))
% 0.65/0.80 FOF formula (forall (V0P:Prop) (V1P_27:Prop) (V2Q:Prop) (V3Q_27:Prop), (((and (V2Q->(((eq Prop) V0P) V1P_27))) (V1P_27->(((eq Prop) V2Q) V3Q_27)))->((iff ((and V0P) V2Q)) ((and V1P_27) V3Q_27)))) of role axiom named thm_2Ebool_2EAND__CONG
% 0.65/0.80 A new axiom: (forall (V0P:Prop) (V1P_27:Prop) (V2Q:Prop) (V3Q_27:Prop), (((and (V2Q->(((eq Prop) V0P) V1P_27))) (V1P_27->(((eq Prop) V2Q) V3Q_27)))->((iff ((and V0P) V2Q)) ((and V1P_27) V3Q_27))))
% 0.65/0.80 FOF formula (forall (A_27a:d) (V0f_2E0:u) (V1v_2E0:u), ((iff (forall (V2x_2E0:u), ((((eq du) ((s A_27a) V2x_2E0)) ((s A_27a) V1v_2E0))->(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) V2x_2E0))))))) (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) V1v_2E0)))))) of role axiom named thm_2Ebool_2EUNWIND__FORALL__THM2
% 0.65/0.80 A new axiom: (forall (A_27a:d) (V0f_2E0:u) (V1v_2E0:u), ((iff (forall (V2x_2E0:u), ((((eq du) ((s A_27a) V2x_2E0)) ((s A_27a) V1v_2E0))->(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) V2x_2E0))))))) (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) V1v_2E0))))))
% 0.65/0.80 FOF formula (forall (A_27a:d) (V0opt_2E0:u), ((or (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V0opt_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) ((ex u) (fun (V1x_2E0:u)=> (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V0opt_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))))) of role axiom named thm_2Eoption_2Eoption__nchotomy
% 0.65/0.80 A new axiom: (forall (A_27a:d) (V0opt_2E0:u), ((or (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V0opt_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) ((ex u) (fun (V1x_2E0:u)=> (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V0opt_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0))))))))
% 0.65/0.82 FOF formula (forall (A_27a:d) (A_27b:d), ((and (forall (V0v_2E0:u) (V1f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s A_27b) V0v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1f_2E0)))) ((s A_27b) V0v_2E0)))) (forall (V2x_2E0:u) (V3v_2E0:u) (V4f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V2x_2E0)))) ((s A_27b) V3v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V4f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V4f_2E0)) ((s A_27a) V2x_2E0))))))) of role axiom named thm_2Eoption_2Eoption__case__def
% 0.65/0.82 A new axiom: (forall (A_27a:d) (A_27b:d), ((and (forall (V0v_2E0:u) (V1f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s A_27b) V0v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1f_2E0)))) ((s A_27b) V0v_2E0)))) (forall (V2x_2E0:u) (V3v_2E0:u) (V4f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V2x_2E0)))) ((s A_27b) V3v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V4f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V4f_2E0)) ((s A_27a) V2x_2E0)))))))
% 0.65/0.82 FOF formula (forall (A_27a:d) (V0x_2E0:u) (V1y_2E0:u), ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1y_2E0))))) (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V1y_2E0)))) of role axiom named thm_2Eoption_2ESOME__11
% 0.65/0.82 A new axiom: (forall (A_27a:d) (V0x_2E0:u) (V1y_2E0:u), ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1y_2E0))))) (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V1y_2E0))))
% 0.65/0.82 FOF formula (forall (A_27a:d) (A_27b:d), ((and (forall (V0f_2E0:u) (V1x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))) (forall (V2f_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V2f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))) of role axiom named thm_2Eoption_2EOPTION__MAP__DEF
% 0.65/0.82 A new axiom: (forall (A_27a:d) (A_27b:d), ((and (forall (V0f_2E0:u) (V1x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))) (forall (V2f_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V2f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))))
% 0.65/0.82 FOF formula (forall (A_27a:d) (V0y_2E0:u) (V1x_2E0:u) (V2P:Prop), ((and ((and ((and ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (not V2P))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) V2P))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))) ((and V2P) (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V0y_2E0)))))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))) ((and (not V2P)) (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V0y_2E0)))))) of role axiom named thm_2Eoption_2EIF__EQUALS__OPTION
% 0.65/0.82 A new axiom: (forall (A_27a:d) (V0y_2E0:u) (V1x_2E0:u) (V2P:Prop), ((and ((and ((and ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (not V2P))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) V2P))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))) ((and V2P) (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V0y_2E0)))))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))) ((and (not V2P)) (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V0y_2E0))))))
% 0.65/0.82 FOF formula (forall (A_27a:d) (A_27b:d) (V0x_2E0:u) (V1f_2E0:u), ((and ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V1f_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V1f_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))) of role axiom named thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways
% 0.65/0.82 A new axiom: (forall (A_27a:d) (A_27b:d) (V0x_2E0:u) (V1f_2E0:u), ((and ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V1f_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V1f_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))))
% 0.68/0.83 FOF formula (forall (A_27a:d) (F0_2E0:u) (F1_2E0:u), ((forall (V0P_2E0:u), ((iff (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)) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_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)) V0P_2E0)) ((s A_27a) V1x_2E0))))))))->((forall (V0P_2E0:u) (V2x_2E0:u), (((eq Prop) (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 ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s A_27a) V2x_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))->(forall (V0P_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))))) of role axiom named thm_2Eoption_2Esome__def
% 0.68/0.83 A new axiom: (forall (A_27a:d) (F0_2E0:u) (F1_2E0:u), ((forall (V0P_2E0:u), ((iff (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)) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_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)) V0P_2E0)) ((s A_27a) V1x_2E0))))))))->((forall (V0P_2E0:u) (V2x_2E0:u), (((eq Prop) (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 ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s A_27a) V2x_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))->(forall (V0P_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))))))))
% 0.68/0.83 FOF formula (forall (A_27a:d) (A_27b:d) (V0pat_2E0:u) (V1guard_2E0:u) (V2inp_2E0:u) (V3v_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27b) V2inp_2E0)) ((s A_27a) V3v_2E0))))) ((and (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0pat_2E0)) ((s A_27a) V3v_2E0)))) ((s A_27b) V2inp_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27a) V3v_2E0))))))) of role axiom named thm_2EpatternMatches_2EPMATCH__ROW__COND__def
% 0.68/0.85 A new axiom: (forall (A_27a:d) (A_27b:d) (V0pat_2E0:u) (V1guard_2E0:u) (V2inp_2E0:u) (V3v_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27b) V2inp_2E0)) ((s A_27a) V3v_2E0))))) ((and (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0pat_2E0)) ((s A_27a) V3v_2E0)))) ((s A_27b) V2inp_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27a) V3v_2E0)))))))
% 0.68/0.85 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (F0_2E0:u), ((forall (V0pat_2E0:u) (V1guard_2E0:u) (V3i_2E0:u) (V4v_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)))) ((s A_27c) V3i_2E0)))) ((s A_27b) V4v_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27c) V3i_2E0)) ((s A_27b) V4v_2E0))))))->(forall (V0pat_2E0:u) (V1guard_2E0:u) (V2rhs_2E0:u) (V3i_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__ROW_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rhs_2E0)) ((s A_27c) V3i_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rhs_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)))) ((s A_27c) V3i_2E0))))))))))) of role axiom named thm_2EpatternMatches_2EPMATCH__ROW__def
% 0.68/0.85 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (F0_2E0:u), ((forall (V0pat_2E0:u) (V1guard_2E0:u) (V3i_2E0:u) (V4v_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)))) ((s A_27c) V3i_2E0)))) ((s A_27b) V4v_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27c) V3i_2E0)) ((s A_27b) V4v_2E0))))))->(forall (V0pat_2E0:u) (V1guard_2E0:u) (V2rhs_2E0:u) (V3i_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__ROW_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rhs_2E0)) ((s A_27c) V3i_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rhs_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)))) ((s A_27c) V3i_2E0)))))))))))
% 0.68/0.87 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (F1_2E0:u) (F0_2E0:u), ((forall (V2row_2E0:u) (V5x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)))) ((s A_27b) V5x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)) ((s A_27b) V5x_2E0)))) ((s A_27b) V5x_2E0)))))->((forall (V0p_2E0:u) (V1g_2E0:u) (V3v_2E0:u) (V4x_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)))) ((s A_27c) V3v_2E0)))) ((s A_27b) V4x_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)) ((s A_27c) V3v_2E0)) ((s A_27b) V4x_2E0))))))->(forall (V0p_2E0:u) (V1g_2E0:u) (V2row_2E0:u) (V3v_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)) ((s A_27c) V3v_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)))) ((s A_27c) V3v_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)))))))))) of role axiom named thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def
% 0.68/0.87 A new axiom: (forall (A_27a:d) (A_27b:d) (A_27c:d) (F1_2E0:u) (F0_2E0:u), ((forall (V2row_2E0:u) (V5x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)))) ((s A_27b) V5x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)) ((s A_27b) V5x_2E0)))) ((s A_27b) V5x_2E0)))))->((forall (V0p_2E0:u) (V1g_2E0:u) (V3v_2E0:u) (V4x_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)))) ((s A_27c) V3v_2E0)))) ((s A_27b) V4x_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)) ((s A_27c) V3v_2E0)) ((s A_27b) V4x_2E0))))))->(forall (V0p_2E0:u) (V1g_2E0:u) (V2row_2E0:u) (V3v_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)) ((s A_27c) V3v_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)))) ((s A_27c) V3v_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0))))))))))
% 0.68/0.91 FOF formula (forall (V0t:Prop), ((iff (not (not V0t))) V0t)) of role axiom named thm_2Esat_2ENOT__NOT
% 0.68/0.91 A new axiom: (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 0.68/0.91 FOF formula (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Esat_2EAND__INV__IMP
% 0.68/0.91 A new axiom: (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 0.68/0.91 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
% 0.68/0.91 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))))
% 0.68/0.91 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
% 0.68/0.91 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))))
% 0.68/0.91 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
% 0.68/0.91 A new axiom: (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 0.68/0.91 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
% 0.68/0.91 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)))))
% 0.68/0.91 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
% 0.68/0.91 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)))))
% 0.68/0.91 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
% 0.68/0.91 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)))))
% 0.68/0.91 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
% 0.68/0.91 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)))))
% 0.68/0.91 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
% 0.68/0.91 A new axiom: (forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p)))))
% 0.68/0.91 FOF formula (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (F0_2E0:u) (F3_2E0:u) (F2_2E0:u) (F1_2E0:u), ((forall (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u) (V7x_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) V7x_2E0)))))))->((forall (V6r_27_2E0:u) (V4p_27_2E0:u) (V10x_2E0:u), (((eq du) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V10x_2E0)))) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V10x_2E0)))))) ((s A_27c) V10x_2E0)))))->((forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s A_27c) V9x_2E0))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0)))))) ((s A_27c) V9x_2E0)))))))->((forall (V0p_2E0:u) (V4p_27_2E0:u) (V8x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V8x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V8x_2E0)))))))->(forall (V0p_2E0:u), ((forall (V1x1_2E0:u) (V2x2_2E0:u), ((((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V1x1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V2x2_2E0))))->(((eq du) ((s A_27a) V1x1_2E0)) ((s A_27a) V2x2_2E0))))->(forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))))))))))))) of role conjecture named thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW
% 0.68/0.92 Conjecture to prove = (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (F0_2E0:u) (F3_2E0:u) (F2_2E0:u) (F1_2E0:u), ((forall (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u) (V7x_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) V7x_2E0)))))))->((forall (V6r_27_2E0:u) (V4p_27_2E0:u) (V10x_2E0:u), (((eq du) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V10x_2E0)))) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V10x_2E0)))))) ((s A_27c) V10x_2E0)))))->((forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s A_27c) V9x_2E0))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0)))))) ((s A_27c) V9x_2E0)))))))->((forall (V0p_2E0:u) (V4p_27_2E0:u) (V8x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V8x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V8x_2E0)))))))->(forall (V0p_2E0:u), ((forall (V1x1_2E0:u) (V2x2_2E0:u), ((((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V1x1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V2x2_2E0))))->(((eq du) ((s A_27a) V1x1_2E0)) ((s A_27a) V2x2_2E0))))->(forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))))))))))))):Prop
% 0.68/0.92 Parameter du_DUMMY:du.
% 0.68/0.92 We need to prove ['(forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (F0_2E0:u) (F3_2E0:u) (F2_2E0:u) (F1_2E0:u), ((forall (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u) (V7x_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) V7x_2E0)))))))->((forall (V6r_27_2E0:u) (V4p_27_2E0:u) (V10x_2E0:u), (((eq du) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V10x_2E0)))) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V10x_2E0)))))) ((s A_27c) V10x_2E0)))))->((forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s A_27c) V9x_2E0))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0)))))) ((s A_27c) V9x_2E0)))))))->((forall (V0p_2E0:u) (V4p_27_2E0:u) (V8x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V8x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V8x_2E0)))))))->(forall (V0p_2E0:u), ((forall (V1x1_2E0:u) (V2x2_2E0:u), ((((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V1x1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V2x2_2E0))))->(((eq du) ((s A_27a) V1x1_2E0)) ((s A_27a) V2x2_2E0))))->(forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0))))))))))))))']
% 0.68/0.92 Parameter u:Type.
% 0.68/0.92 Parameter d:Type.
% 0.68/0.92 Parameter du:Type.
% 0.68/0.92 Parameter tyop_2Emin_2Ebool:d.
% 0.68/0.92 Parameter tyop_2Emin_2Efun:(d->(d->d)).
% 0.68/0.92 Parameter tyop_2Eoption_2Eoption:(d->d).
% 0.68/0.92 Parameter s:(d->(u->du)).
% 0.68/0.92 Parameter app_2E2:(du->(du->u)).
% 0.68/0.92 Parameter combin_i_2E0:u.
% 0.68/0.92 Parameter combin_k_2E0:u.
% 0.68/0.92 Parameter combin_s_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_21_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_21_2E1:(du->u).
% 0.68/0.92 Parameter c_2Ebool_2E_2F_5C_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_2F_5C_2E2:(du->(du->u)).
% 0.68/0.92 Parameter c_2Emin_2E_3D_2E0:u.
% 0.68/0.92 Parameter c_2Emin_2E_3D_2E2:(du->(du->u)).
% 0.68/0.92 Parameter c_2Emin_2E_3D_3D_3E_2E0:u.
% 0.68/0.92 Parameter c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u)).
% 0.68/0.92 Parameter c_2Ebool_2E_3F_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_3F_2E1:(du->u).
% 0.68/0.92 Parameter c_2Emin_2E_40_2E0:u.
% 0.68/0.92 Parameter c_2Emin_2E_40_2E1:(du->u).
% 0.68/0.92 Parameter c_2Ebool_2ECOND_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2ECOND_2E3:(du->(du->(du->u))).
% 0.68/0.92 Parameter c_2Ebool_2EF_2E0:u.
% 0.68/0.92 Parameter c_2Eoption_2ENONE_2E0:u.
% 0.68/0.92 Parameter c_2Eoption_2EOPTION__MAP_2E0:u.
% 0.68/0.92 Parameter c_2Eoption_2EOPTION__MAP_2E2:(du->(du->u)).
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0:u.
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3:(du->(du->(du->u))).
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4:(du->(du->(du->(du->u)))).
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__ROW_2E0:u.
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__ROW_2E3:(du->(du->(du->u))).
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__ROW_2E4:(du->(du->(du->(du->u)))).
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__ROW__COND_2E0:u.
% 0.68/0.92 Parameter c_2EpatternMatches_2EPMATCH__ROW__COND_2E4:(du->(du->(du->(du->u)))).
% 0.68/0.92 Parameter c_2Eoption_2ESOME_2E0:u.
% 0.68/0.92 Parameter c_2Eoption_2ESOME_2E1:(du->u).
% 0.68/0.92 Parameter c_2Ebool_2ET_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_5C_2F_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_5C_2F_2E2:(du->(du->u)).
% 0.68/0.92 Parameter c_2Eoption_2Eoption__CASE_2E0:u.
% 0.68/0.92 Parameter c_2Eoption_2Eoption__CASE_2E3:(du->(du->(du->u))).
% 0.68/0.92 Parameter c_2Eoption_2Esome_2E0:u.
% 0.68/0.92 Parameter c_2Eoption_2Esome_2E1:(du->u).
% 0.68/0.92 Parameter c_2Ebool_2E_7E_2E0:u.
% 0.68/0.92 Parameter c_2Ebool_2E_7E_2E1:(du->u).
% 0.68/0.92 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop)).
% 0.68/0.92 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))).
% 0.68/0.92 Parameter mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop)).
% 0.68/0.92 Parameter mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop)).
% 0.68/0.92 Parameter mono_2Ec_2Ebool_2EF:Prop.
% 0.68/0.92 Parameter mono_2Ec_2Ebool_2ET:Prop.
% 0.68/0.92 Parameter mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop)).
% 0.68/0.92 Parameter mono_2Ec_2Ebool_2E_7E:(Prop->Prop).
% 0.68/0.92 Parameter i_mono_2Etyop_2Emin_2Ebool:(Prop->u).
% 0.68/0.92 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u).
% 0.68/0.92 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u).
% 0.68/0.92 Parameter j_mono_2Etyop_2Emin_2Ebool:(du->Prop).
% 0.68/0.92 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop)).
% 0.68/0.92 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop))).
% 0.68/0.92 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)))).
% 0.68/0.92 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))).
% 0.68/0.92 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))).
% 0.68/0.92 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))))))).
% 0.68/0.92 Axiom reserved_2Elogic_2E_2F_5C:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))).
% 0.68/0.92 Axiom reserved_2Elogic_2E_5C_2F:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))).
% 0.68/0.92 Axiom reserved_2Elogic_2E_7E:(forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))).
% 0.68/0.92 Axiom reserved_2Elogic_2E_3D_3D_3E:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))).
% 0.68/0.92 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)))).
% 0.68/0.92 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))))))).
% 0.68/0.92 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)))))))).
% 0.68/0.92 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))).
% 0.68/0.92 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))).
% 0.68/0.92 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))).
% 0.68/0.92 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)).
% 0.68/0.92 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)).
% 0.68/0.92 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)).
% 0.68/0.92 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)))))).
% 0.68/0.92 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)))))).
% 0.68/0.92 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)))))).
% 0.68/0.92 Axiom arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) A_27a)) c_2Emin_2E_40_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))).
% 0.68/0.92 Axiom arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29:(forall (A_27a:d) (X0:Prop) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27a))))) c_2Ebool_2ECOND_2E0)) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool X0))))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X2_2E0))))).
% 0.68/0.92 Axiom arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) (tyop_2Eoption_2Eoption A_27b)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0))))).
% 0.68/0.92 Axiom arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X1_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) (tyop_2Eoption_2Eoption A_27a)))) c_2Eoption_2EOPTION__MAP_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) X1_2E0))))).
% 0.68/0.92 Axiom arityeq3_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) X2_2E0))))).
% 0.68/0.92 Axiom arityeq4_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c:(forall (A_27a:d) (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) X2_2E0)) ((s A_27c) X3_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))))) c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) X2_2E0)))) ((s A_27c) X3_2E0))))).
% 0.68/0.93 Axiom arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c:(forall (A_27a:d) (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__ROW_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)) ((s A_27c) X3_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27a)) ((tyop_2Emin_2Efun A_27c) (tyop_2Eoption_2Eoption A_27a)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) X2_2E0)))) ((s A_27c) X3_2E0))))).
% 0.68/0.93 Axiom arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a:(forall (A_27a:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0))))).
% 0.68/0.93 Axiom arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b:(forall (A_27b:d) (A_27c:d) (A_27d:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27d)) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d)))))) c_2EpatternMatches_2EPMATCH__ROW_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) X2_2E0))))).
% 0.68/0.93 Axiom arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)) ((s A_27b) X2_2E0)) ((s A_27a) X3_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_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))))) c_2EpatternMatches_2EPMATCH__ROW__COND_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))) ((s A_27b) X2_2E0)))) ((s A_27a) X3_2E0)))))).
% 0.68/0.93 Axiom arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27b_20mono_2EA_27c:(forall (A_27b:d) (A_27c:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u) (X3_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)) ((s A_27c) X2_2E0)) ((s A_27b) X3_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) c_2EpatternMatches_2EPMATCH__ROW__COND_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))) ((s A_27c) X2_2E0)))) ((s A_27b) X3_2E0)))))).
% 0.68/0.93 Axiom arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2ESOME_2E0)) ((s A_27a) X0_2E0))))).
% 0.68/0.93 Axiom arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b:(forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2ESOME_2E0)) ((s A_27b) X0_2E0))))).
% 0.68/0.93 Axiom arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)) ((s A_27b) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) A_27b)))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X0_2E0)))) ((s A_27b) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) X2_2E0))))).
% 0.68/0.93 Axiom arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u) (X2_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27b)) X0_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) X2_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a)))) ((app_2E2 ((s ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27b)) ((tyop_2Emin_2Efun (tyop_2Eoption_2Eoption A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) (tyop_2Eoption_2Eoption A_27a))))) c_2Eoption_2Eoption__CASE_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) X1_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) X2_2E0))))).
% 0.68/0.93 Axiom arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a:(forall (A_27a:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) (tyop_2Eoption_2Eoption A_27a))) c_2Eoption_2Esome_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))).
% 0.68/0.93 Axiom arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27b:(forall (A_27b:d) (X0_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) (tyop_2Eoption_2Eoption A_27b))) c_2Eoption_2Esome_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0))))).
% 0.68/0.93 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)))))).
% 0.68/0.93 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)))))).
% 0.68/0.93 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))).
% 0.68/0.93 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))).
% 0.68/0.93 Axiom thm_2Ebool_2EBOOL__CASES__AX:(forall (V0t:Prop), ((or (((eq Prop) V0t) mono_2Ec_2Ebool_2ET)) (((eq Prop) V0t) mono_2Ec_2Ebool_2EF))).
% 0.68/0.93 Axiom thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET.
% 0.68/0.93 Axiom thm_2Ebool_2EIMP__ANTISYM__AX:(forall (V0t1:Prop) (V1t2:Prop), ((V0t1->V1t2)->((V1t2->V0t1)->(((eq Prop) V0t1) V1t2)))).
% 0.68/0.93 Axiom thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)).
% 0.68/0.93 Axiom thm_2Ebool_2EEXCLUDED__MIDDLE:(forall (V0t:Prop), ((or V0t) (not V0t))).
% 0.68/0.93 Axiom thm_2Ebool_2EFORALL__SIMP:(d->(forall (V0t:Prop), ((iff (u->V0t)) V0t))).
% 0.68/0.93 Axiom thm_2Ebool_2EIMP__F:(forall (V0t:Prop), ((V0t->mono_2Ec_2Ebool_2EF)->(not V0t))).
% 0.68/0.93 Axiom thm_2Ebool_2EF__IMP:(forall (V0t:Prop), ((not V0t)->(V0t->mono_2Ec_2Ebool_2EF))).
% 0.68/0.93 Axiom thm_2Ebool_2EAND__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((and ((iff ((and mono_2Ec_2Ebool_2ET) V0t)) V0t)) ((iff ((and V0t) mono_2Ec_2Ebool_2ET)) V0t))) ((iff ((and mono_2Ec_2Ebool_2EF) V0t)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) mono_2Ec_2Ebool_2EF)) mono_2Ec_2Ebool_2EF))) ((iff ((and V0t) V0t)) V0t))).
% 0.68/0.93 Axiom thm_2Ebool_2EOR__CLAUSES:(forall (V0t:Prop), ((and ((and ((and ((and ((iff ((or mono_2Ec_2Ebool_2ET) V0t)) mono_2Ec_2Ebool_2ET)) ((iff ((or V0t) mono_2Ec_2Ebool_2ET)) mono_2Ec_2Ebool_2ET))) ((iff ((or mono_2Ec_2Ebool_2EF) V0t)) V0t))) ((iff ((or V0t) mono_2Ec_2Ebool_2EF)) V0t))) ((iff ((or V0t) V0t)) V0t))).
% 0.68/0.93 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)))).
% 0.68/0.93 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)).
% 0.68/0.93 Axiom thm_2Ebool_2EREFL__CLAUSE:(forall (A_27a:d) (V0x_2E0:u), ((iff (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V0x_2E0))) mono_2Ec_2Ebool_2ET)).
% 0.68/0.93 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)))).
% 0.68/0.93 Axiom thm_2Ebool_2EFUN__EQ__THM:(forall (A_27a:d) (A_27b:d) (V0f_2E0:u) (V1g_2E0:u), ((iff (((eq du) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0))) (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))))))).
% 0.68/0.93 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)))).
% 0.68/0.93 Axiom thm_2Ebool_2ESELECT__ELIM__THM:(forall (A_27a:d) (V0P_2E0:u) (V1Q_2E0:u), (((and ((ex u) (fun (V2x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))) (forall (V3x_2E0:u), ((j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V3x_2E0))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1Q_2E0)) ((s A_27a) V3x_2E0)))))))->(j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1Q_2E0)) ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))))))).
% 0.68/0.93 Axiom thm_2Ebool_2ENOT__FORALL__THM:(forall (A_27a:d) (V0P_2E0:u), ((iff (not (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V1x_2E0))))))) ((ex u) (fun (V2x_2E0:u)=> (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))))).
% 0.68/0.93 Axiom thm_2Ebool_2ENOT__EXISTS__THM:(forall (A_27a:d) (V0P_2E0:u), ((iff (not ((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)) V0P_2E0)) ((s A_27a) V1x_2E0)))))))) (forall (V2x_2E0:u), (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0)))))))).
% 0.78/0.93 Axiom thm_2Ebool_2EDISJ__ASSOC:(forall (V0A:Prop) (V1B:Prop) (V2C:Prop), ((iff ((or ((or V0A) V1B)) V2C)) ((or ((or V0A) V1B)) V2C))).
% 0.78/0.93 Axiom thm_2Ebool_2EDISJ__SYM:(forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A))).
% 0.78/0.93 Axiom thm_2Ebool_2EDISJ__COMM:(forall (V0A:Prop) (V1B:Prop), ((iff ((or V0A) V1B)) ((or V1B) V0A))).
% 0.78/0.93 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))))).
% 0.78/0.93 Axiom thm_2Ebool_2EIMP__DISJ__THM:(forall (V0A:Prop) (V1B:Prop), ((iff (V0A->V1B)) ((or (not V0A)) V1B))).
% 0.78/0.93 Axiom thm_2Ebool_2EAND__IMP__INTRO:(forall (V0t1:Prop) (V1t2:Prop) (V2t3:Prop), ((iff (V0t1->(V1t2->V2t3))) (((and V0t1) V1t2)->V2t3))).
% 0.78/0.93 Axiom thm_2Ebool_2EIMP__CONG:(forall (V0x:Prop) (V1x_27:Prop) (V2y:Prop) (V3y_27:Prop), (((and (((eq Prop) V0x) V1x_27)) (V1x_27->(((eq Prop) V2y) V3y_27)))->((iff (V0x->V2y)) (V1x_27->V3y_27)))).
% 0.78/0.93 Axiom thm_2Ebool_2EAND__CONG:(forall (V0P:Prop) (V1P_27:Prop) (V2Q:Prop) (V3Q_27:Prop), (((and (V2Q->(((eq Prop) V0P) V1P_27))) (V1P_27->(((eq Prop) V2Q) V3Q_27)))->((iff ((and V0P) V2Q)) ((and V1P_27) V3Q_27)))).
% 0.78/0.93 Axiom thm_2Ebool_2EUNWIND__FORALL__THM2:(forall (A_27a:d) (V0f_2E0:u) (V1v_2E0:u), ((iff (forall (V2x_2E0:u), ((((eq du) ((s A_27a) V2x_2E0)) ((s A_27a) V1v_2E0))->(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) V2x_2E0))))))) (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) V1v_2E0)))))).
% 0.78/0.93 Axiom thm_2Eoption_2Eoption__nchotomy:(forall (A_27a:d) (V0opt_2E0:u), ((or (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V0opt_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) ((ex u) (fun (V1x_2E0:u)=> (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) V0opt_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))))).
% 0.78/0.93 Axiom thm_2Eoption_2Eoption__case__def:(forall (A_27a:d) (A_27b:d), ((and (forall (V0v_2E0:u) (V1f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s A_27b) V0v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V1f_2E0)))) ((s A_27b) V0v_2E0)))) (forall (V2x_2E0:u) (V3v_2E0:u) (V4f_2E0:u), (((eq du) ((s A_27b) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V2x_2E0)))) ((s A_27b) V3v_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V4f_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V4f_2E0)) ((s A_27a) V2x_2E0))))))).
% 0.78/0.93 Axiom thm_2Eoption_2ESOME__11:(forall (A_27a:d) (V0x_2E0:u) (V1y_2E0:u), ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1y_2E0))))) (((eq du) ((s A_27a) V0x_2E0)) ((s A_27a) V1y_2E0)))).
% 0.78/0.93 Axiom thm_2Eoption_2EOPTION__MAP__DEF:(forall (A_27a:d) (A_27b:d), ((and (forall (V0f_2E0:u) (V1x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2ESOME_2E1 ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))) (forall (V2f_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V2f_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))).
% 0.78/0.93 Axiom thm_2Eoption_2EIF__EQUALS__OPTION:(forall (A_27a:d) (V0y_2E0:u) (V1x_2E0:u) (V2P:Prop), ((and ((and ((and ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (not V2P))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) V2P))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))) ((and V2P) (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V0y_2E0)))))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V2P))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V1x_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) V0y_2E0))))) ((and (not V2P)) (((eq du) ((s A_27a) V1x_2E0)) ((s A_27a) V0y_2E0)))))).
% 0.78/0.93 Axiom thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways:(forall (A_27a:d) (A_27b:d) (V0x_2E0:u) (V1f_2E0:u), ((and ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V1f_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0)))) ((iff (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V1f_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0))))) (((eq du) ((s (tyop_2Eoption_2Eoption A_27b)) V0x_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) c_2Eoption_2ENONE_2E0))))).
% 0.78/0.93 Axiom thm_2Eoption_2Esome__def:(forall (A_27a:d) (F0_2E0:u) (F1_2E0:u), ((forall (V0P_2E0:u), ((iff (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)) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_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)) V0P_2E0)) ((s A_27a) V1x_2E0))))))))->((forall (V0P_2E0:u) (V2x_2E0:u), (((eq Prop) (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 ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s A_27a) V2x_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)) ((s A_27a) V2x_2E0))))))->(forall (V0P_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Ebool_2ECOND_2E3 ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (c_2Eoption_2ESOME_2E1 ((s A_27a) (c_2Emin_2E_40_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0P_2E0)))))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)))))))).
% 0.78/0.93 Axiom thm_2EpatternMatches_2EPMATCH__ROW__COND__def:(forall (A_27a:d) (A_27b:d) (V0pat_2E0:u) (V1guard_2E0:u) (V2inp_2E0:u) (V3v_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27b) V2inp_2E0)) ((s A_27a) V3v_2E0))))) ((and (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0pat_2E0)) ((s A_27a) V3v_2E0)))) ((s A_27b) V2inp_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27a) V3v_2E0))))))).
% 0.78/0.93 Axiom thm_2EpatternMatches_2EPMATCH__ROW__def:(forall (A_27a:d) (A_27b:d) (A_27c:d) (F0_2E0:u), ((forall (V0pat_2E0:u) (V1guard_2E0:u) (V3i_2E0:u) (V4v_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)))) ((s A_27c) V3i_2E0)))) ((s A_27b) V4v_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s A_27c) V3i_2E0)) ((s A_27b) V4v_2E0))))))->(forall (V0pat_2E0:u) (V1guard_2E0:u) (V2rhs_2E0:u) (V3i_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__ROW_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rhs_2E0)) ((s A_27c) V3i_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((c_2Eoption_2EOPTION__MAP_2E2 ((s ((tyop_2Emin_2Efun A_27b) A_27a)) V2rhs_2E0)) ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0pat_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1guard_2E0)))) ((s A_27c) V3i_2E0))))))))))).
% 0.78/0.93 Axiom thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def:(forall (A_27a:d) (A_27b:d) (A_27c:d) (F1_2E0:u) (F0_2E0:u), ((forall (V2row_2E0:u) (V5x_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)))) ((s A_27b) V5x_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)) ((s A_27b) V5x_2E0)))) ((s A_27b) V5x_2E0)))))->((forall (V0p_2E0:u) (V1g_2E0:u) (V3v_2E0:u) (V4x_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)))) ((s A_27c) V3v_2E0)))) ((s A_27b) V4x_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((((c_2EpatternMatches_2EPMATCH__ROW__COND_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)) ((s A_27c) V3v_2E0)) ((s A_27b) V4x_2E0))))))->(forall (V0p_2E0:u) (V1g_2E0:u) (V2row_2E0:u) (V3v_2E0:u), (((eq du) ((s (tyop_2Eoption_2Eoption A_27a)) ((((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4 ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)) ((s A_27c) V3v_2E0)))) ((s (tyop_2Eoption_2Eoption A_27a)) (((c_2Eoption_2Eoption__CASE_2E3 ((s (tyop_2Eoption_2Eoption A_27b)) (c_2Eoption_2Esome_2E1 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) A_27c)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun A_27c) ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) A_27c)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1g_2E0)))) ((s A_27c) V3v_2E0)))))) ((s (tyop_2Eoption_2Eoption A_27a)) c_2Eoption_2ENONE_2E0)) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27b) ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27a)))) V2row_2E0)))))))))).
% 0.78/0.93 Axiom thm_2Esat_2ENOT__NOT:(forall (V0t:Prop), ((iff (not (not V0t))) V0t)).
% 0.78/0.93 Axiom thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF))).
% 0.78/0.93 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)))).
% 0.78/0.93 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)))).
% 0.78/0.93 Axiom thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF))).
% 0.78/0.93 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))))).
% 0.78/0.93 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))))).
% 0.78/0.93 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))))).
% 0.78/0.93 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))))).
% 0.78/0.93 Axiom thm_2Esat_2Edc__neg:(forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p))))).
% 0.78/0.95 Trying to prove (forall (A_27a:d) (A_27b:d) (A_27c:d) (A_27d:d) (F0_2E0:u) (F3_2E0:u) (F2_2E0:u) (F1_2E0:u), ((forall (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u) (V7x_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) V7x_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) V7x_2E0)))))))->((forall (V6r_27_2E0:u) (V4p_27_2E0:u) (V10x_2E0:u), (((eq du) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27d)))) F3_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V10x_2E0)))) ((s A_27d) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27d)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V10x_2E0)))))) ((s A_27c) V10x_2E0)))))->((forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V9x_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s A_27c) V9x_2E0))))) ((and (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0))))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V9x_2E0)))))) ((s A_27c) V9x_2E0)))))))->((forall (V0p_2E0:u) (V4p_27_2E0:u) (V8x_2E0:u), (((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s A_27c) V8x_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)) ((s A_27c) V8x_2E0)))))))->(forall (V0p_2E0:u), ((forall (V1x1_2E0:u) (V2x2_2E0:u), ((((eq du) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V1x1_2E0)))) ((s A_27b) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s A_27a) V2x2_2E0))))->(((eq du) ((s A_27a) V1x1_2E0)) ((s A_27a) V2x2_2E0))))->(forall (V3g_2E0:u) (V4p_27_2E0:u) (V5g_27_2E0:u) (V6r_27_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3 ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d)))))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) (tyop_2Eoption_2Eoption A_27d))))))) F0_2E0)) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) V5g_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) A_27d))) V6r_27_2E0)))))) ((s ((tyop_2Emin_2Efun A_27b) (tyop_2Eoption_2Eoption A_27d))) (((c_2EpatternMatches_2EPMATCH__ROW_2E3 ((s ((tyop_2Emin_2Efun A_27c) A_27b)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) A_27b)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun A_27c) A_27b)))) F1_2E0)) ((s ((tyop_2Emin_2Efun A_27a) A_27b)) V0p_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool)))) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27c) A_27a)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))) ((tyop_2Emin_2Efun A_27c) tyop_2Emin_2Ebool))))) F2_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V3g_2E0)))) ((s ((tyop_2Emin_2Efun A_27c) A_27a)) V4p_27_2E0)))) ((s ((tyop_2Emin_2Efun A_27
%------------------------------------------------------------------------------