TSTP Solution File: ITP010^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP010^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 13:23:37 EDT 2021
% Result : Theorem 1.02s
% Output : Proof 1.02s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP010^1 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.08/0.13 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Mar 18 23:06:45 EDT 2021
% 0.13/0.35 % CPUTime :
% 0.13/0.36 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.36 Python 2.7.5
% 0.44/0.63 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f128>, <kernel.Type object at 0x1a6fbd8>) of role type named u
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring u:Type
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f758>, <kernel.Type object at 0x1a73d88>) of role type named d
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring d:Type
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f2d8>, <kernel.Type object at 0x2b5d566d8050>) of role type named du
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring du:Type
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6fbd8>, <kernel.Constant object at 0x1a6f758>) of role type named tyop_2Emin_2Ebool
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring tyop_2Emin_2Ebool:d
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6af38>, <kernel.DependentProduct object at 0x2b5d566d8ab8>) of role type named tyop_2Emin_2Efun
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring tyop_2Emin_2Efun:(d->(d->d))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f2d8>, <kernel.DependentProduct object at 0x2b5d566d8a28>) of role type named s
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring s:(d->(u->du))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6fbd8>, <kernel.DependentProduct object at 0x2b5d566d8a70>) of role type named app_2E2
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring app_2E2:(du->(du->u))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f2d8>, <kernel.Constant object at 0x2b5d566d87a0>) of role type named combin_i_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring combin_i_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f758>, <kernel.Constant object at 0x2b5d566d87a0>) of role type named combin_k_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring combin_k_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1a6f758>, <kernel.Constant object at 0x2b5d566d87a0>) of role type named combin_s_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring combin_s_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8830>, <kernel.Constant object at 0x2b5d566d87a0>) of role type named c_2Ebool_2E_21_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2E_21_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8170>, <kernel.DependentProduct object at 0x1bd7ef0>) of role type named c_2Ebool_2E_21_2E1
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2E_21_2E1:(du->u)
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8a28>, <kernel.Constant object at 0x2b5d566d8830>) of role type named c_2Ebool_2E_2F_5C_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2E_2F_5C_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8ab8>, <kernel.DependentProduct object at 0x1bd7f38>) of role type named c_2Ebool_2E_2F_5C_2E2
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2E_2F_5C_2E2:(du->(du->u))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8170>, <kernel.Constant object at 0x1bd7e60>) of role type named c_2Emin_2E_3D_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Emin_2E_3D_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8ab8>, <kernel.DependentProduct object at 0x1bd7ea8>) of role type named c_2Emin_2E_3D_2E2
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Emin_2E_3D_2E2:(du->(du->u))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8170>, <kernel.Constant object at 0x1bd7ef0>) of role type named c_2Emin_2E_3D_3D_3E_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Emin_2E_3D_3D_3E_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8830>, <kernel.DependentProduct object at 0x1bd7ea8>) of role type named c_2Emin_2E_3D_3D_3E_2E2
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u))
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x2b5d566d8830>, <kernel.Constant object at 0x1bd7ea8>) of role type named c_2Ebool_2E_3F_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2E_3F_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1bd7f80>, <kernel.DependentProduct object at 0x1bd7fc8>) of role type named c_2Ebool_2E_3F_2E1
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2E_3F_2E1:(du->u)
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1bd7d40>, <kernel.Constant object at 0x1bd7fc8>) of role type named c_2Ebool_2EF_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2EF_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1bd7ef0>, <kernel.Constant object at 0x1bd7fc8>) of role type named c_2Ebool_2ET_2E0
% 0.44/0.63 Using role type
% 0.44/0.63 Declaring c_2Ebool_2ET_2E0:u
% 0.44/0.63 FOF formula (<kernel.Constant object at 0x1bd7f80>, <kernel.Constant object at 0x1bd7fc8>) of role type named c_2Ebool_2E_5C_2F_2E0
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ebool_2E_5C_2F_2E0:u
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1bd7d40>, <kernel.DependentProduct object at 0x1bd7dd0>) of role type named c_2Ebool_2E_5C_2F_2E2
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ebool_2E_5C_2F_2E2:(du->(du->u))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1bd7c68>, <kernel.Constant object at 0x1bd7dd0>) of role type named c_2Ecardinal_2Ecardleq_2E0
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ecardinal_2Ecardleq_2E0:u
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1bd7f80>, <kernel.DependentProduct object at 0x1bd7fc8>) of role type named c_2Ecardinal_2Ecardleq_2E2
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ecardinal_2Ecardleq_2E2:(du->(du->u))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1bd7b90>, <kernel.Constant object at 0x1bd7fc8>) 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 0x1bd7c68>, <kernel.DependentProduct object at 0x1bd7d40>) 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 0x1bd7a70>, <kernel.DependentProduct object at 0x1bd7dd0>) 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 0x1bd7b90>, <kernel.DependentProduct object at 0x1bd7f80>) 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 0x1bd7c68>, <kernel.DependentProduct object at 0x1bd7ab8>) 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 0x1bd7a70>, <kernel.DependentProduct object at 0x1bd7950>) 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 0x1bd7b90>, <kernel.Sort object at 0x2b5d566b4638>) 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 0x1bd7a28>, <kernel.Sort object at 0x2b5d566b4638>) 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 0x1bd7c68>, <kernel.DependentProduct object at 0x1bd7908>) 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 0x1bd7998>, <kernel.DependentProduct object at 0x1bd7830>) 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 0x1bd7a28>, <kernel.DependentProduct object at 0x1bd7710>) 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 0x1bd7c68>, <kernel.DependentProduct object at 0x1bd7680>) 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 0x1bd7998>, <kernel.DependentProduct object at 0x1bd76c8>) of role type named i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1bd7a28>, <kernel.DependentProduct object at 0x1bd7908>) of role type named j_mono_2Etyop_2Emin_2Ebool
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring j_mono_2Etyop_2Emin_2Ebool:(du->Prop)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1bd7758>, <kernel.DependentProduct object at 0x1bd75f0>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1bd76c8>, <kernel.DependentProduct object at 0x1bd7998>) of role type named j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop)))
% 0.48/0.65 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
% 0.48/0.65 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))))
% 0.48/0.65 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
% 0.48/0.65 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)))
% 0.48/0.65 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
% 0.48/0.65 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)))
% 0.48/0.65 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
% 0.48/0.65 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)))))))
% 0.48/0.66 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))) of role axiom named reserved_2Elogic_2E_2F_5C
% 0.48/0.66 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1)))
% 0.48/0.66 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))) of role axiom named reserved_2Elogic_2E_5C_2F
% 0.48/0.66 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1)))
% 0.48/0.66 FOF formula (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))) of role axiom named reserved_2Elogic_2E_7E
% 0.48/0.66 A new axiom: (forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0)))
% 0.48/0.66 FOF formula (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))) of role axiom named reserved_2Elogic_2E_3D_3D_3E
% 0.48/0.66 A new axiom: (forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1)))
% 0.48/0.66 FOF formula (forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0)))) of role axiom named reserved_2Elogic_2E_3D
% 0.48/0.66 A new axiom: (forall (A_27a:d) (V0_2E0:u) (V1_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Emin_2E_3D_2E2 ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))) (((eq du) ((s A_27a) V0_2E0)) ((s A_27a) V1_2E0))))
% 0.48/0.66 FOF formula (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))) of role axiom named reserved_2Equant_2E_21
% 0.48/0.66 A new axiom: (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) (forall (V1x_2E0:u), (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))
% 0.48/0.66 FOF formula (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0)))))))) of role axiom named reserved_2Equant_2E_3F
% 0.48/0.66 A new axiom: (forall (A_27a:d) (V0f_2E0:u), ((iff (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_3F_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0))))) ((ex u) (fun (V1x_2E0:u)=> (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0f_2E0)) ((s A_27a) V1x_2E0))))))))
% 0.48/0.66 FOF formula (forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Ebool
% 0.48/0.66 A new axiom: (forall (V0_2E0:u), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) V0_2E0))))) ((s tyop_2Emin_2Ebool) V0_2E0)))
% 0.48/0.66 FOF formula (forall (V0_2E0:u), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) V0_2E0))) of role axiom named ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.66 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
% 0.48/0.68 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_21_2E1 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) c_2Ebool_2E_21_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0))))))
% 0.48/0.68 FOF formula (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a
% 0.48/0.68 A new axiom: (forall (A_27a:d) (X0_2E0:u) (X1_2E0:u), ((iff (((eq du) ((s A_27a) X0_2E0)) ((s A_27a) X1_2E0))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun A_27a) ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool))) c_2Emin_2E_3D_2E0)) ((s A_27a) X0_2E0)))) ((s A_27a) X1_2E0))))))
% 0.48/0.68 FOF formula (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_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
% 0.48/0.68 A new axiom: (forall (A_27a:d) (X0_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) (c_2Ebool_2E_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))))))
% 0.48/0.68 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ecardinal_2Ecardleq_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27b
% 0.48/0.68 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ecardinal_2Ecardleq_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0))))))
% 0.48/0.68 FOF formula (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ecardinal_2Ecardleq_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))))) of role axiom named arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27a
% 0.48/0.68 A new axiom: (forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ecardinal_2Ecardleq_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0))))))
% 0.48/0.68 FOF formula (forall (V0:(Prop->Prop)) (V1:Prop), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.48/0.68 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq du) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool (V0 V1)))) ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1))))))
% 0.48/0.68 FOF formula (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1)))))) of role axiom named monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.68 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq du) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (V0 V1)))) ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) ((tyop_2Emin_2Efun tyop_2Emin_2Ebool) tyop_2Emin_2Ebool))) (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) ((s tyop_2Emin_2Ebool) (i_mono_2Etyop_2Emin_2Ebool V1))))))
% 0.48/0.68 FOF formula (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 0.48/0.68 A new axiom: (forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1)))
% 0.48/0.68 FOF formula (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1))) of role axiom named monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29
% 0.48/0.68 A new axiom: (forall (V0:(Prop->(Prop->Prop))) (V1:Prop), (((eq (Prop->Prop)) (V0 V1)) (V0 V1)))
% 0.48/0.68 FOF formula mono_2Ec_2Ebool_2ET of role axiom named thm_2Ebool_2ETRUTH
% 0.48/0.68 A new axiom: mono_2Ec_2Ebool_2ET
% 0.48/0.68 FOF formula (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)) of role axiom named thm_2Ebool_2EFALSITY
% 0.48/0.68 A new axiom: (forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t))
% 0.48/0.69 FOF formula (d->(forall (V0t:Prop), ((iff (u->V0t)) V0t))) of role axiom named thm_2Ebool_2EFORALL__SIMP
% 0.48/0.69 A new axiom: (d->(forall (V0t:Prop), ((iff (u->V0t)) V0t)))
% 0.48/0.69 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
% 0.48/0.69 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))))
% 0.48/0.69 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
% 0.48/0.70 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))
% 0.48/0.70 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
% 0.48/0.70 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))
% 0.48/0.70 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
% 0.48/0.70 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))))
% 0.48/0.70 FOF formula (forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((or (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))))) of role axiom named thm_2Ecardinal_2ECARD__LE__TOTAL
% 0.48/0.70 A new axiom: (forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((or (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0))))))
% 0.48/0.70 FOF formula (forall (V0t:Prop), ((iff (not (not V0t))) V0t)) of role axiom named thm_2Esat_2ENOT__NOT
% 0.48/0.70 A new axiom: (forall (V0t:Prop), ((iff (not (not V0t))) V0t))
% 0.48/0.70 FOF formula (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF))) of role axiom named thm_2Esat_2EAND__INV__IMP
% 0.48/0.70 A new axiom: (forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF)))
% 0.48/0.70 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
% 0.48/0.70 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))))
% 0.48/0.70 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
% 0.48/0.70 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))))
% 0.55/0.70 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
% 0.55/0.70 A new axiom: (forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF)))
% 0.55/0.70 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
% 0.55/0.70 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)))))
% 0.55/0.70 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
% 0.55/0.70 A new axiom: (forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p)))))
% 0.55/0.70 FOF formula (forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))) of role conjecture named thm_2Ecardinal_2ECARD__NOT__LE
% 0.55/0.70 Conjecture to prove = (forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))):Prop
% 0.55/0.70 Parameter du_DUMMY:du.
% 0.55/0.70 We need to prove ['(forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))']
% 0.55/0.70 Parameter u:Type.
% 0.55/0.70 Parameter d:Type.
% 0.55/0.70 Parameter du:Type.
% 0.55/0.70 Parameter tyop_2Emin_2Ebool:d.
% 0.55/0.70 Parameter tyop_2Emin_2Efun:(d->(d->d)).
% 0.55/0.70 Parameter s:(d->(u->du)).
% 0.55/0.70 Parameter app_2E2:(du->(du->u)).
% 0.55/0.70 Parameter combin_i_2E0:u.
% 0.55/0.70 Parameter combin_k_2E0:u.
% 0.55/0.70 Parameter combin_s_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_21_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_21_2E1:(du->u).
% 0.55/0.70 Parameter c_2Ebool_2E_2F_5C_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_2F_5C_2E2:(du->(du->u)).
% 0.55/0.70 Parameter c_2Emin_2E_3D_2E0:u.
% 0.55/0.70 Parameter c_2Emin_2E_3D_2E2:(du->(du->u)).
% 0.55/0.70 Parameter c_2Emin_2E_3D_3D_3E_2E0:u.
% 0.55/0.70 Parameter c_2Emin_2E_3D_3D_3E_2E2:(du->(du->u)).
% 0.55/0.70 Parameter c_2Ebool_2E_3F_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_3F_2E1:(du->u).
% 0.55/0.70 Parameter c_2Ebool_2EF_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2ET_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_5C_2F_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_5C_2F_2E2:(du->(du->u)).
% 0.55/0.70 Parameter c_2Ecardinal_2Ecardleq_2E0:u.
% 0.55/0.70 Parameter c_2Ecardinal_2Ecardleq_2E2:(du->(du->u)).
% 0.55/0.70 Parameter c_2Ebool_2E_7E_2E0:u.
% 0.55/0.70 Parameter c_2Ebool_2E_7E_2E1:(du->u).
% 0.55/0.70 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:((Prop->Prop)->(Prop->Prop)).
% 0.55/0.70 Parameter mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))).
% 0.55/0.70 Parameter mono_2Ec_2Ebool_2E_2F_5C:(Prop->(Prop->Prop)).
% 0.55/0.70 Parameter mono_2Ec_2Emin_2E_3D_3D_3E:(Prop->(Prop->Prop)).
% 0.55/0.70 Parameter mono_2Ec_2Ebool_2EF:Prop.
% 0.55/0.70 Parameter mono_2Ec_2Ebool_2ET:Prop.
% 0.55/0.70 Parameter mono_2Ec_2Ebool_2E_5C_2F:(Prop->(Prop->Prop)).
% 0.55/0.70 Parameter mono_2Ec_2Ebool_2E_7E:(Prop->Prop).
% 0.55/0.70 Parameter i_mono_2Etyop_2Emin_2Ebool:(Prop->u).
% 0.55/0.70 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:((Prop->Prop)->u).
% 0.55/0.70 Parameter i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:((Prop->(Prop->Prop))->u).
% 0.55/0.70 Parameter j_mono_2Etyop_2Emin_2Ebool:(du->Prop).
% 0.55/0.70 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29:(du->(Prop->Prop)).
% 0.55/0.70 Parameter j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29:(du->(Prop->(Prop->Prop))).
% 0.55/0.70 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)))).
% 0.55/0.70 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))).
% 0.55/0.70 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))).
% 0.55/0.70 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))))))).
% 0.55/0.71 Axiom reserved_2Elogic_2E_2F_5C:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_2F_5C V0) V1)) ((and V0) V1))).
% 0.55/0.71 Axiom reserved_2Elogic_2E_5C_2F:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Ebool_2E_5C_2F V0) V1)) ((or V0) V1))).
% 0.55/0.71 Axiom reserved_2Elogic_2E_7E:(forall (V0:Prop), ((iff (mono_2Ec_2Ebool_2E_7E V0)) (not V0))).
% 0.55/0.71 Axiom reserved_2Elogic_2E_3D_3D_3E:(forall (V0:Prop) (V1:Prop), ((iff ((mono_2Ec_2Emin_2E_3D_3D_3E V0) V1)) (V0->V1))).
% 0.55/0.71 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)))).
% 0.55/0.71 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))))))).
% 0.55/0.71 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)))))))).
% 0.55/0.71 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))).
% 0.55/0.71 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))).
% 0.55/0.71 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))).
% 0.55/0.71 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)).
% 0.55/0.71 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)).
% 0.55/0.71 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)).
% 0.55/0.71 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)))))).
% 0.55/0.71 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)))))).
% 0.55/0.71 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)))))).
% 0.55/0.71 Axiom arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27b:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ecardinal_2Ecardleq_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X1_2E0)))))).
% 0.55/0.71 Axiom arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27a:(forall (A_27a:d) (A_27b:d) (X0_2E0:u) (X1_2E0:u), (((eq Prop) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool)) ((app_2E2 ((s ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) ((tyop_2Emin_2Efun ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) tyop_2Emin_2Ebool))) c_2Ecardinal_2Ecardleq_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) X0_2E0)))) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) X1_2E0)))))).
% 0.55/0.71 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)))))).
% 0.55/0.71 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)))))).
% 0.55/0.71 Axiom monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool:(forall (V0:(Prop->Prop)) (V1:Prop), (((eq Prop) (V0 V1)) (V0 V1))).
% 0.55/0.71 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))).
% 0.55/0.71 Axiom thm_2Ebool_2ETRUTH:mono_2Ec_2Ebool_2ET.
% 0.55/0.71 Axiom thm_2Ebool_2EFALSITY:(forall (V0t:Prop), (mono_2Ec_2Ebool_2EF->V0t)).
% 0.55/0.71 Axiom thm_2Ebool_2EFORALL__SIMP:(d->(forall (V0t:Prop), ((iff (u->V0t)) V0t))).
% 0.55/0.71 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)))).
% 0.55/0.71 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)).
% 0.55/0.71 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)).
% 0.55/0.71 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)))).
% 0.55/0.71 Axiom thm_2Ecardinal_2ECARD__LE__TOTAL:(forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((or (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))) (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)) ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)))))).
% 0.92/1.17 Axiom thm_2Esat_2ENOT__NOT:(forall (V0t:Prop), ((iff (not (not V0t))) V0t)).
% 0.92/1.17 Axiom thm_2Esat_2EAND__INV__IMP:(forall (V0A:Prop), (V0A->((not V0A)->mono_2Ec_2Ebool_2EF))).
% 0.92/1.17 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)))).
% 0.92/1.17 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)))).
% 0.92/1.17 Axiom thm_2Esat_2EAND__INV2:(forall (V0A:Prop), (((not V0A)->mono_2Ec_2Ebool_2EF)->((V0A->mono_2Ec_2Ebool_2EF)->mono_2Ec_2Ebool_2EF))).
% 0.92/1.17 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))))).
% 0.92/1.17 Axiom thm_2Esat_2Edc__neg:(forall (V0q:Prop) (V1p:Prop), ((iff ((iff V1p) (not V0q))) ((and ((or V1p) V0q)) ((or (not V0q)) (not V1p))))).
% 0.92/1.17 Trying to prove (forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 0.92/1.17 Found iff_refl0:=(iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))):((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))
% 0.92/1.17 Found (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) as proof of ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))
% 0.92/1.17 Found (fun (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))) as proof of ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))
% 0.92/1.17 Found (fun (V0s_2E0:u) (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))) as proof of (forall (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 1.02/1.18 Found (fun (A_27b:d) (V0s_2E0:u) (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))) as proof of (forall (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 1.02/1.18 Found (fun (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))) as proof of (forall (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 1.02/1.18 Found (fun (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0))))))) as proof of (forall (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u), ((iff (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))) (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 1.02/1.18 Got proof (fun (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 1.02/1.18 Time elapsed = 0.456603s
% 1.02/1.18 node=9 cost=-55.000000 depth=5
% 1.02/1.18::::::::::::::::::::::
% 1.02/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.02/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.02/1.18 (fun (A_27a:d) (A_27b:d) (V0s_2E0:u) (V1t_2E0:u)=> (iff_refl (not (j_mono_2Etyop_2Emin_2Ebool ((s tyop_2Emin_2Ebool) ((c_2Ecardinal_2Ecardleq_2E2 ((s ((tyop_2Emin_2Efun A_27a) tyop_2Emin_2Ebool)) V0s_2E0)) ((s ((tyop_2Emin_2Efun A_27b) tyop_2Emin_2Ebool)) V1t_2E0)))))))
% 1.02/1.18 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------