TSTP Solution File: ITP001^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP001^5 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.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 13:23:28 EDT 2021
% Result : Theorem 0.58s
% Output : Proof 0.58s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP001^5 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Thu Mar 18 19:11:30 EDT 2021
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.34 Python 2.7.5
% 0.39/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.39/0.62 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/ITP001/ITP001^2.ax, trying next directory
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcac68>, <kernel.Type object at 0xbcabd8>) of role type named del_tp
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring del:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbca200>, <kernel.Constant object at 0xbcafc8>) of role type named bool
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring bool:del
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2af8cb63d1b8>, <kernel.Constant object at 0xbcafc8>) of role type named ind
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring ind:del
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2af8cb63d1b8>, <kernel.DependentProduct object at 0xbca200>) of role type named arr
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring arr:(del->(del->del))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcafc8>, <kernel.DependentProduct object at 0xbad908>) of role type named mem
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring mem:(fofType->(del->Prop))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcabd8>, <kernel.DependentProduct object at 0xbad5f0>) of role type named ap
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring ap:(fofType->(fofType->fofType))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcaef0>, <kernel.DependentProduct object at 0xbade18>) of role type named lam
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring lam:(del->((fofType->fofType)->fofType))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcafc8>, <kernel.DependentProduct object at 0xbad908>) of role type named p
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring p:(fofType->Prop)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcaef0>, <kernel.DependentProduct object at 0xbad950>) of role type named stp_inj_o
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring inj__o:(Prop->fofType)
% 0.39/0.62 FOF formula (forall (X:Prop), (((eq Prop) (p (inj__o X))) X)) of role axiom named stp_inj_surj_o
% 0.39/0.62 A new axiom: (forall (X:Prop), (((eq Prop) (p (inj__o X))) X))
% 0.39/0.62 FOF formula (forall (X:Prop), ((mem (inj__o X)) bool)) of role axiom named stp_inj_mem_o
% 0.39/0.62 A new axiom: (forall (X:Prop), ((mem (inj__o X)) bool))
% 0.39/0.62 FOF formula (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))) of role axiom named stp_iso_mem_o
% 0.39/0.62 A new axiom: (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X)))))
% 0.39/0.62 FOF formula (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (X:fofType), (((mem X) A)->((mem ((ap F) X)) B))))) of role axiom named ap_tp
% 0.39/0.62 A new axiom: (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (X:fofType), (((mem X) A)->((mem ((ap F) X)) B)))))
% 0.39/0.62 FOF formula (forall (A:del) (B:del) (F:(fofType->fofType)), ((forall (X:fofType), (((mem X) A)->((mem (F X)) B)))->((mem ((lam A) F)) ((arr A) B)))) of role axiom named lam_tp
% 0.39/0.62 A new axiom: (forall (A:del) (B:del) (F:(fofType->fofType)), ((forall (X:fofType), (((mem X) A)->((mem (F X)) B)))->((mem ((lam A) F)) ((arr A) B))))
% 0.39/0.62 FOF formula (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (G:fofType), (((mem G) ((arr A) B))->((forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap G) X))))->(((eq fofType) F) G)))))) of role axiom named funcext
% 0.39/0.62 A new axiom: (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (G:fofType), (((mem G) ((arr A) B))->((forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap G) X))))->(((eq fofType) F) G))))))
% 0.39/0.62 FOF formula (forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X)))) of role axiom named beta
% 0.39/0.62 A new axiom: (forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X))))
% 0.39/0.62 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/ITP001/ITP002^5.ax, trying next directory
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcaf38>, <kernel.DependentProduct object at 0xbad950>) of role type named tp_c_2Emin_2E_3D
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring c_2Emin_2E_3D:(del->fofType)
% 0.39/0.62 FOF formula (forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool)))) of role axiom named mem_c_2Emin_2E_3D
% 0.39/0.62 A new axiom: (forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool))))
% 0.47/0.63 FOF formula (forall (A:del) (X:fofType), (((mem X) A)->(forall (Y:fofType), (((mem Y) A)->((iff (p ((ap ((ap (c_2Emin_2E_3D A)) X)) Y))) (((eq fofType) X) Y)))))) of role axiom named ax_eq_p
% 0.47/0.63 A new axiom: (forall (A:del) (X:fofType), (((mem X) A)->(forall (Y:fofType), (((mem Y) A)->((iff (p ((ap ((ap (c_2Emin_2E_3D A)) X)) Y))) (((eq fofType) X) Y))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0xbcae18>, <kernel.Single object at 0xbcaf38>) of role type named tp_c_2Emin_2E_3D_3D_3E
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Emin_2E_3D_3D_3E:fofType
% 0.47/0.63 FOF formula ((mem c_2Emin_2E_3D_3D_3E) ((arr bool) ((arr bool) bool))) of role axiom named mem_c_2Emin_2E_3D_3D_3E
% 0.47/0.63 A new axiom: ((mem c_2Emin_2E_3D_3D_3E) ((arr bool) ((arr bool) bool)))
% 0.47/0.63 FOF formula (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Emin_2E_3D_3D_3E) Q)) R))) ((p Q)->(p R))))))) of role axiom named ax_imp_p
% 0.47/0.63 A new axiom: (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Emin_2E_3D_3D_3E) Q)) R))) ((p Q)->(p R)))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0xbcabd8>, <kernel.DependentProduct object at 0xbadc68>) of role type named tp_c_2Emin_2E_40
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Emin_2E_40:(del->fofType)
% 0.47/0.63 FOF formula (forall (A_27a:del), ((mem (c_2Emin_2E_40 A_27a)) ((arr ((arr A_27a) bool)) A_27a))) of role axiom named mem_c_2Emin_2E_40
% 0.47/0.63 A new axiom: (forall (A_27a:del), ((mem (c_2Emin_2E_40 A_27a)) ((arr ((arr A_27a) bool)) A_27a)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0xe72a70>, <kernel.DependentProduct object at 0x2af8cb63a0e0>) of role type named tp_ty_2Ebool_2Eitself
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ty_2Ebool_2Eitself:(del->del)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0xe72a70>, <kernel.DependentProduct object at 0x2af8cb63a560>) of role type named tp_c_2Ebool_2E_21
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Ebool_2E_21:(del->fofType)
% 0.47/0.63 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool))) of role axiom named mem_c_2Ebool_2E_21
% 0.47/0.63 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool)))
% 0.47/0.63 FOF formula (forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_21 A)) Q))) (forall (X:fofType), (((mem X) A)->(p ((ap Q) X))))))) of role axiom named ax_all_p
% 0.47/0.63 A new axiom: (forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_21 A)) Q))) (forall (X:fofType), (((mem X) A)->(p ((ap Q) X)))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0xbd4ea8>, <kernel.Single object at 0x2af8cb63a878>) of role type named tp_c_2Ebool_2E_2F_5C
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Ebool_2E_2F_5C:fofType
% 0.47/0.63 FOF formula ((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool))) of role axiom named mem_c_2Ebool_2E_2F_5C
% 0.47/0.63 A new axiom: ((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool)))
% 0.47/0.63 FOF formula (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_2F_5C) Q)) R))) ((and (p Q)) (p R))))))) of role axiom named ax_and_p
% 0.47/0.63 A new axiom: (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_2F_5C) Q)) R))) ((and (p Q)) (p R)))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2af8cb63a488>, <kernel.DependentProduct object at 0x2af8cb63a560>) of role type named tp_c_2Ebool_2E_3F
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Ebool_2E_3F:(del->fofType)
% 0.47/0.63 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2E_3F A_27a)) ((arr ((arr A_27a) bool)) bool))) of role axiom named mem_c_2Ebool_2E_3F
% 0.47/0.63 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2E_3F A_27a)) ((arr ((arr A_27a) bool)) bool)))
% 0.47/0.63 FOF formula (forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_3F A)) Q))) ((ex fofType) (fun (X:fofType)=> ((and ((mem X) A)) (p ((ap Q) X)))))))) of role axiom named ax_ex_p
% 0.47/0.63 A new axiom: (forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_3F A)) Q))) ((ex fofType) (fun (X:fofType)=> ((and ((mem X) A)) (p ((ap Q) X))))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2af8cb63a560>, <kernel.DependentProduct object at 0x2af8cb63a290>) of role type named tp_c_2Ebool_2E_3F_21
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2E_3F_21:(del->fofType)
% 0.47/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2E_3F_21 A_27a)) ((arr ((arr A_27a) bool)) bool))) of role axiom named mem_c_2Ebool_2E_3F_21
% 0.47/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2E_3F_21 A_27a)) ((arr ((arr A_27a) bool)) bool)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63a560>, <kernel.DependentProduct object at 0x2af8cb63fef0>) of role type named tp_c_2Ebool_2EARB
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EARB:(del->fofType)
% 0.47/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2EARB A_27a)) A_27a)) of role axiom named mem_c_2Ebool_2EARB
% 0.47/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2EARB A_27a)) A_27a))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63a560>, <kernel.Single object at 0x2af8cb63a998>) of role type named tp_c_2Ebool_2EBOUNDED
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EBOUNDED:fofType
% 0.47/0.64 FOF formula ((mem c_2Ebool_2EBOUNDED) ((arr bool) bool)) of role axiom named mem_c_2Ebool_2EBOUNDED
% 0.47/0.64 A new axiom: ((mem c_2Ebool_2EBOUNDED) ((arr bool) bool))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63a560>, <kernel.DependentProduct object at 0x2af8cb63fb00>) of role type named tp_c_2Ebool_2ECOND
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2ECOND:(del->fofType)
% 0.47/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2ECOND A_27a)) ((arr bool) ((arr A_27a) ((arr A_27a) A_27a))))) of role axiom named mem_c_2Ebool_2ECOND
% 0.47/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2ECOND A_27a)) ((arr bool) ((arr A_27a) ((arr A_27a) A_27a)))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63a560>, <kernel.DependentProduct object at 0xbca200>) of role type named tp_c_2Ebool_2EDATATYPE
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EDATATYPE:(del->fofType)
% 0.47/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2EDATATYPE A_27a)) ((arr A_27a) bool))) of role axiom named mem_c_2Ebool_2EDATATYPE
% 0.47/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2EDATATYPE A_27a)) ((arr A_27a) bool)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63aea8>, <kernel.Single object at 0x2af8cb63fef0>) of role type named tp_c_2Ebool_2EF
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EF:fofType
% 0.47/0.64 FOF formula ((mem c_2Ebool_2EF) bool) of role axiom named mem_c_2Ebool_2EF
% 0.47/0.64 A new axiom: ((mem c_2Ebool_2EF) bool)
% 0.47/0.64 FOF formula ((p c_2Ebool_2EF)->False) of role axiom named ax_false_p
% 0.47/0.64 A new axiom: ((p c_2Ebool_2EF)->False)
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63fdd0>, <kernel.DependentProduct object at 0xbca200>) of role type named tp_c_2Ebool_2EIN
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EIN:(del->fofType)
% 0.47/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2EIN A_27a)) ((arr A_27a) ((arr ((arr A_27a) bool)) bool)))) of role axiom named mem_c_2Ebool_2EIN
% 0.47/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2EIN A_27a)) ((arr A_27a) ((arr ((arr A_27a) bool)) bool))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63fdd0>, <kernel.DependentProduct object at 0xbcabd8>) of role type named tp_c_2Ebool_2ELET
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2ELET:(del->(del->fofType))
% 0.47/0.64 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ELET A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b)))) of role axiom named mem_c_2Ebool_2ELET
% 0.47/0.64 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ELET A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2af8cb63fd88>, <kernel.DependentProduct object at 0xbcac20>) of role type named tp_c_2Ebool_2EONE__ONE
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EONE__ONE:(del->(del->fofType))
% 0.47/0.64 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2EONE__ONE A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) bool))) of role axiom named mem_c_2Ebool_2EONE__ONE
% 0.47/0.64 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2EONE__ONE A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) bool)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0xbcac20>, <kernel.DependentProduct object at 0xbcaf38>) of role type named tp_c_2Ebool_2EONTO
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring c_2Ebool_2EONTO:(del->(del->fofType))
% 0.47/0.64 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2EONTO A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) bool))) of role axiom named mem_c_2Ebool_2EONTO
% 0.47/0.65 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2EONTO A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) bool)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbcaf38>, <kernel.DependentProduct object at 0xbcaf80>) of role type named tp_c_2Ebool_2ERES__ABSTRACT
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ERES__ABSTRACT:(del->(del->fofType))
% 0.47/0.65 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b))))) of role axiom named mem_c_2Ebool_2ERES__ABSTRACT
% 0.47/0.65 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b)))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbcaf80>, <kernel.DependentProduct object at 0xbadab8>) of role type named tp_c_2Ebool_2ERES__EXISTS
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ERES__EXISTS:(del->fofType)
% 0.47/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2ERES__EXISTS A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool)))) of role axiom named mem_c_2Ebool_2ERES__EXISTS
% 0.47/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2ERES__EXISTS A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbad5a8>, <kernel.DependentProduct object at 0xbad638>) of role type named tp_c_2Ebool_2ERES__EXISTS__UNIQUE
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ERES__EXISTS__UNIQUE:(del->fofType)
% 0.47/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool)))) of role axiom named mem_c_2Ebool_2ERES__EXISTS__UNIQUE
% 0.47/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbcacf8>, <kernel.DependentProduct object at 0xbadb48>) of role type named tp_c_2Ebool_2ERES__FORALL
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ERES__FORALL:(del->fofType)
% 0.47/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2ERES__FORALL A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool)))) of role axiom named mem_c_2Ebool_2ERES__FORALL
% 0.47/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2ERES__FORALL A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbadab8>, <kernel.DependentProduct object at 0xbade18>) of role type named tp_c_2Ebool_2ERES__SELECT
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ERES__SELECT:(del->fofType)
% 0.47/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2ERES__SELECT A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) A_27a)))) of role axiom named mem_c_2Ebool_2ERES__SELECT
% 0.47/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2ERES__SELECT A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) A_27a))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbada28>, <kernel.Single object at 0xbad950>) of role type named tp_c_2Ebool_2ET
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ET:fofType
% 0.47/0.65 FOF formula ((mem c_2Ebool_2ET) bool) of role axiom named mem_c_2Ebool_2ET
% 0.47/0.65 A new axiom: ((mem c_2Ebool_2ET) bool)
% 0.47/0.65 FOF formula (p c_2Ebool_2ET) of role axiom named ax_true_p
% 0.47/0.65 A new axiom: (p c_2Ebool_2ET)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbad5a8>, <kernel.DependentProduct object at 0xbadcb0>) of role type named tp_c_2Ebool_2ETYPE__DEFINITION
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring c_2Ebool_2ETYPE__DEFINITION:(del->(del->fofType))
% 0.47/0.65 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27b) A_27a)) bool)))) of role axiom named mem_c_2Ebool_2ETYPE__DEFINITION
% 0.47/0.65 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27b) A_27a)) bool))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xbadcb0>, <kernel.Single object at 0xbada28>) of role type named tp_c_2Ebool_2E_5C_2F
% 0.47/0.65 Using role type
% 0.47/0.66 Declaring c_2Ebool_2E_5C_2F:fofType
% 0.47/0.66 FOF formula ((mem c_2Ebool_2E_5C_2F) ((arr bool) ((arr bool) bool))) of role axiom named mem_c_2Ebool_2E_5C_2F
% 0.47/0.66 A new axiom: ((mem c_2Ebool_2E_5C_2F) ((arr bool) ((arr bool) bool)))
% 0.47/0.66 FOF formula (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_5C_2F) Q)) R))) ((or (p Q)) (p R))))))) of role axiom named ax_or_p
% 0.47/0.66 A new axiom: (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_5C_2F) Q)) R))) ((or (p Q)) (p R)))))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xbadd88>, <kernel.DependentProduct object at 0xbadcf8>) of role type named tp_c_2Ebool_2Eitself__case
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring c_2Ebool_2Eitself__case:(del->(del->fofType))
% 0.47/0.66 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2Eitself__case A_27a) A_27b)) ((arr (ty_2Ebool_2Eitself A_27a)) ((arr A_27b) A_27b)))) of role axiom named mem_c_2Ebool_2Eitself__case
% 0.47/0.66 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2Eitself__case A_27a) A_27b)) ((arr (ty_2Ebool_2Eitself A_27a)) ((arr A_27b) A_27b))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xbadd88>, <kernel.DependentProduct object at 0xbcfd40>) of role type named tp_c_2Ebool_2Eliteral__case
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring c_2Ebool_2Eliteral__case:(del->(del->fofType))
% 0.47/0.66 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2Eliteral__case A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b)))) of role axiom named mem_c_2Ebool_2Eliteral__case
% 0.47/0.66 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2Eliteral__case A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xbadcf8>, <kernel.DependentProduct object at 0xbcfa70>) of role type named tp_c_2Ebool_2Ethe__value
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring c_2Ebool_2Ethe__value:(del->fofType)
% 0.47/0.66 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2Ethe__value A_27a)) (ty_2Ebool_2Eitself A_27a))) of role axiom named mem_c_2Ebool_2Ethe__value
% 0.47/0.66 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2Ethe__value A_27a)) (ty_2Ebool_2Eitself A_27a)))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xbadcf8>, <kernel.Single object at 0xbcf128>) of role type named tp_c_2Ebool_2E_7E
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring c_2Ebool_2E_7E:fofType
% 0.47/0.66 FOF formula ((mem c_2Ebool_2E_7E) ((arr bool) bool)) of role axiom named mem_c_2Ebool_2E_7E
% 0.47/0.66 A new axiom: ((mem c_2Ebool_2E_7E) ((arr bool) bool))
% 0.47/0.66 FOF formula (forall (Q:fofType), (((mem Q) bool)->((iff (p ((ap c_2Ebool_2E_7E) Q))) ((p Q)->False)))) of role axiom named ax_neg_p
% 0.47/0.66 A new axiom: (forall (Q:fofType), (((mem Q) bool)->((iff (p ((ap c_2Ebool_2E_7E) Q))) ((p Q)->False))))
% 0.47/0.66 FOF formula ((iff True) (((eq fofType) ((lam bool) (fun (V0x:fofType)=> V0x))) ((lam bool) (fun (V1x:fofType)=> V1x)))) of role axiom named ax_thm_2Ebool_2ET__DEF
% 0.47/0.66 A new axiom: ((iff True) (((eq fofType) ((lam bool) (fun (V0x:fofType)=> V0x))) ((lam bool) (fun (V1x:fofType)=> V1x))))
% 0.47/0.66 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_21 A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap ((ap (c_2Emin_2E_3D ((arr A_27a) bool))) V0P)) ((lam A_27a) (fun (V1x:fofType)=> c_2Ebool_2ET))))))) of role axiom named ax_thm_2Ebool_2EFORALL__DEF
% 0.47/0.66 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_21 A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap ((ap (c_2Emin_2E_3D ((arr A_27a) bool))) V0P)) ((lam A_27a) (fun (V1x:fofType)=> c_2Ebool_2ET)))))))
% 0.47/0.66 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_3F A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap V0P) ((ap (c_2Emin_2E_40 A_27a)) V0P)))))) of role axiom named ax_thm_2Ebool_2EEXISTS__DEF
% 0.47/0.66 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_3F A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap V0P) ((ap (c_2Emin_2E_40 A_27a)) V0P))))))
% 0.47/0.66 FOF formula (((eq fofType) c_2Ebool_2E_2F_5C) ((lam bool) (fun (V0t1:fofType)=> ((lam bool) (fun (V1t2:fofType)=> ((ap (c_2Ebool_2E_21 bool)) ((lam bool) (fun (V2t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t1)) ((ap ((ap c_2Emin_2E_3D_3D_3E) V1t2)) V2t)))) V2t))))))))) of role axiom named ax_thm_2Ebool_2EAND__DEF
% 0.51/0.68 A new axiom: (((eq fofType) c_2Ebool_2E_2F_5C) ((lam bool) (fun (V0t1:fofType)=> ((lam bool) (fun (V1t2:fofType)=> ((ap (c_2Ebool_2E_21 bool)) ((lam bool) (fun (V2t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t1)) ((ap ((ap c_2Emin_2E_3D_3D_3E) V1t2)) V2t)))) V2t)))))))))
% 0.51/0.68 FOF formula (((eq fofType) c_2Ebool_2E_5C_2F) ((lam bool) (fun (V0t1:fofType)=> ((lam bool) (fun (V1t2:fofType)=> ((ap (c_2Ebool_2E_21 bool)) ((lam bool) (fun (V2t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t1)) V2t))) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V1t2)) V2t))) V2t)))))))))) of role axiom named ax_thm_2Ebool_2EOR__DEF
% 0.51/0.68 A new axiom: (((eq fofType) c_2Ebool_2E_5C_2F) ((lam bool) (fun (V0t1:fofType)=> ((lam bool) (fun (V1t2:fofType)=> ((ap (c_2Ebool_2E_21 bool)) ((lam bool) (fun (V2t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t1)) V2t))) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V1t2)) V2t))) V2t))))))))))
% 0.51/0.68 FOF formula ((iff False) (forall (V0t:fofType), (((mem V0t) bool)->(p V0t)))) of role axiom named ax_thm_2Ebool_2EF__DEF
% 0.51/0.68 A new axiom: ((iff False) (forall (V0t:fofType), (((mem V0t) bool)->(p V0t))))
% 0.51/0.68 FOF formula (((eq fofType) c_2Ebool_2E_7E) ((lam bool) (fun (V0t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t)) c_2Ebool_2EF)))) of role axiom named ax_thm_2Ebool_2ENOT__DEF
% 0.51/0.68 A new axiom: (((eq fofType) c_2Ebool_2E_7E) ((lam bool) (fun (V0t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t)) c_2Ebool_2EF))))
% 0.51/0.68 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_3F_21 A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Ebool_2E_3F A_27a)) V0P))) ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap V0P) V1x))) ((ap V0P) V2y)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V1x)) V2y))))))))))))) of role axiom named ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF
% 0.51/0.68 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_3F_21 A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Ebool_2E_3F A_27a)) V0P))) ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap V0P) V1x))) ((ap V0P) V2y)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V1x)) V2y)))))))))))))
% 0.51/0.68 FOF formula (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2ELET A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((lam A_27a) (fun (V1x:fofType)=> ((ap V0f) V1x))))))) of role axiom named ax_thm_2Ebool_2ELET__DEF
% 0.51/0.68 A new axiom: (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2ELET A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((lam A_27a) (fun (V1x:fofType)=> ((ap V0f) V1x)))))))
% 0.51/0.68 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ECOND A_27a)) ((lam bool) (fun (V0t:fofType)=> ((lam A_27a) (fun (V1t1:fofType)=> ((lam A_27a) (fun (V2t2:fofType)=> ((ap (c_2Emin_2E_40 A_27a)) ((lam A_27a) (fun (V3x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D bool)) V0t)) c_2Ebool_2ET))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V1t1)))) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D bool)) V0t)) c_2Ebool_2EF))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V2t2)))))))))))))) of role axiom named ax_thm_2Ebool_2ECOND__DEF
% 0.51/0.68 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ECOND A_27a)) ((lam bool) (fun (V0t:fofType)=> ((lam A_27a) (fun (V1t1:fofType)=> ((lam A_27a) (fun (V2t2:fofType)=> ((ap (c_2Emin_2E_40 A_27a)) ((lam A_27a) (fun (V3x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D bool)) V0t)) c_2Ebool_2ET))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V1t1)))) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D bool)) V0t)) c_2Ebool_2EF))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V2t2))))))))))))))
% 0.51/0.69 FOF formula (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2EONE__ONE A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V1x1:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2x2:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D A_27b)) ((ap V0f) V1x1))) ((ap V0f) V2x2)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V1x1)) V2x2)))))))))))) of role axiom named ax_thm_2Ebool_2EONE__ONE__DEF
% 0.51/0.69 A new axiom: (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2EONE__ONE A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V1x1:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2x2:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D A_27b)) ((ap V0f) V1x1))) ((ap V0f) V2x2)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V1x1)) V2x2))))))))))))
% 0.51/0.69 FOF formula (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2EONTO A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V1y:fofType)=> ((ap (c_2Ebool_2E_3F A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap (c_2Emin_2E_3D A_27b)) V1y)) ((ap V0f) V2x)))))))))))) of role axiom named ax_thm_2Ebool_2EONTO__DEF
% 0.51/0.69 A new axiom: (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2EONTO A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V1y:fofType)=> ((ap (c_2Ebool_2E_3F A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap (c_2Emin_2E_3D A_27b)) V1y)) ((ap V0f) V2x))))))))))))
% 0.51/0.69 FOF formula (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((lam ((arr A_27b) A_27a)) (fun (V1rep:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V2x_27:fofType)=> ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V3x_27_27:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D A_27a)) ((ap V1rep) V2x_27))) ((ap V1rep) V3x_27_27)))) ((ap ((ap (c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27)))))))))) ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V4x:fofType)=> ((ap ((ap (c_2Emin_2E_3D bool)) ((ap V0P) V4x))) ((ap (c_2Ebool_2E_3F A_27b)) ((lam A_27b) (fun (V5x_27:fofType)=> ((ap ((ap (c_2Emin_2E_3D A_27a)) V4x)) ((ap V1rep) V5x_27)))))))))))))))) of role axiom named ax_thm_2Ebool_2ETYPE__DEFINITION
% 0.51/0.69 A new axiom: (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((lam ((arr A_27b) A_27a)) (fun (V1rep:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V2x_27:fofType)=> ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V3x_27_27:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D A_27a)) ((ap V1rep) V2x_27))) ((ap V1rep) V3x_27_27)))) ((ap ((ap (c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27)))))))))) ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V4x:fofType)=> ((ap ((ap (c_2Emin_2E_3D bool)) ((ap V0P) V4x))) ((ap (c_2Ebool_2E_3F A_27b)) ((lam A_27b) (fun (V5x_27:fofType)=> ((ap ((ap (c_2Emin_2E_3D A_27a)) V4x)) ((ap V1rep) V5x_27))))))))))))))))
% 0.51/0.69 FOF formula (forall (V0t:fofType), (((mem V0t) bool)->((or ((iff (p V0t)) True)) ((iff (p V0t)) False)))) of role axiom named ax_thm_2Ebool_2EBOOL__CASES__AX
% 0.51/0.69 A new axiom: (forall (V0t:fofType), (((mem V0t) bool)->((or ((iff (p V0t)) True)) ((iff (p V0t)) False))))
% 0.51/0.69 FOF formula (forall (A_27a:del) (A_27b:del) (V0t:fofType), (((mem V0t) ((arr A_27a) A_27b))->(((eq fofType) ((lam A_27a) (fun (V1x:fofType)=> ((ap V0t) V1x)))) V0t))) of role axiom named ax_thm_2Ebool_2EETA__AX
% 0.51/0.69 A new axiom: (forall (A_27a:del) (A_27b:del) (V0t:fofType), (((mem V0t) ((arr A_27a) A_27b))->(((eq fofType) ((lam A_27a) (fun (V1x:fofType)=> ((ap V0t) V1x)))) V0t)))
% 0.51/0.69 FOF formula (forall (A_27a:del) (V0P:fofType), (((mem V0P) ((arr A_27a) bool))->(forall (V1x:fofType), (((mem V1x) A_27a)->((p ((ap V0P) V1x))->(p ((ap V0P) ((ap (c_2Emin_2E_40 A_27a)) V0P)))))))) of role axiom named ax_thm_2Ebool_2ESELECT__AX
% 0.51/0.71 A new axiom: (forall (A_27a:del) (V0P:fofType), (((mem V0P) ((arr A_27a) bool))->(forall (V1x:fofType), (((mem V1x) A_27a)->((p ((ap V0P) V1x))->(p ((ap V0P) ((ap (c_2Emin_2E_40 A_27a)) V0P))))))))
% 0.51/0.71 FOF formula (<kernel.Constant object at 0xbd03b0>, <kernel.Type object at 0xbd08c0>) of role type named stp_i
% 0.51/0.71 Using role type
% 0.51/0.71 Declaring tp__i:Type
% 0.51/0.71 FOF formula (<kernel.Constant object at 0xbd0e60>, <kernel.DependentProduct object at 0x2af8c3b6a3b0>) of role type named stp_inj_i
% 0.51/0.71 Using role type
% 0.51/0.71 Declaring inj__i:(tp__i->fofType)
% 0.51/0.71 FOF formula (<kernel.Constant object at 0xbd0b00>, <kernel.DependentProduct object at 0x2af8c3b6a710>) of role type named stp_surj_i
% 0.51/0.71 Using role type
% 0.51/0.71 Declaring surj__i:(fofType->tp__i)
% 0.51/0.71 FOF formula (forall (X:tp__i), (((eq tp__i) (surj__i (inj__i X))) X)) of role axiom named stp_inj_surj_i
% 0.51/0.71 A new axiom: (forall (X:tp__i), (((eq tp__i) (surj__i (inj__i X))) X))
% 0.51/0.71 FOF formula (forall (X:tp__i), ((mem (inj__i X)) ind)) of role axiom named stp_inj_mem_i
% 0.51/0.71 A new axiom: (forall (X:tp__i), ((mem (inj__i X)) ind))
% 0.51/0.71 FOF formula (forall (X:fofType), (((mem X) ind)->(((eq fofType) X) (inj__i (surj__i X))))) of role axiom named stp_iso_mem_i
% 0.51/0.71 A new axiom: (forall (X:fofType), (((mem X) ind)->(((eq fofType) X) (inj__i (surj__i X)))))
% 0.51/0.71 FOF formula ((ex fofType) (fun (V0f:fofType)=> ((and ((and ((mem V0f) ((arr ind) ind))) (p ((ap ((c_2Ebool_2EONE__ONE ind) ind)) V0f)))) ((p ((ap ((c_2Ebool_2EONTO ind) ind)) V0f))->False)))) of role axiom named ax_thm_2Ebool_2EINFINITY__AX
% 0.51/0.71 A new axiom: ((ex fofType) (fun (V0f:fofType)=> ((and ((and ((mem V0f) ((arr ind) ind))) (p ((ap ((c_2Ebool_2EONE__ONE ind) ind)) V0f)))) ((p ((ap ((c_2Ebool_2EONTO ind) ind)) V0f))->False))))
% 0.51/0.71 FOF formula (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2Eliteral__case A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((lam A_27a) (fun (V1x:fofType)=> ((ap V0f) V1x))))))) of role axiom named ax_thm_2Ebool_2Eliteral__case__DEF
% 0.51/0.71 A new axiom: (forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2Eliteral__case A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((lam A_27a) (fun (V1x:fofType)=> ((ap V0f) V1x)))))))
% 0.51/0.71 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2EIN A_27a)) ((lam A_27a) (fun (V0x:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1f:fofType)=> ((ap V1f) V0x))))))) of role axiom named ax_thm_2Ebool_2EIN__DEF
% 0.51/0.71 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2EIN A_27a)) ((lam A_27a) (fun (V0x:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1f:fofType)=> ((ap V1f) V0x)))))))
% 0.51/0.71 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__FORALL A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x))))))))))) of role axiom named ax_thm_2Ebool_2ERES__FORALL__DEF
% 0.51/0.71 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__FORALL A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x)))))))))))
% 0.51/0.71 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__EXISTS A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Ebool_2E_3F A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x))))))))))) of role axiom named ax_thm_2Ebool_2ERES__EXISTS__DEF
% 0.51/0.71 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__EXISTS A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Ebool_2E_3F A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x)))))))))))
% 0.51/0.72 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2ERES__EXISTS A_27a)) V0p)) ((lam A_27a) (fun (V2x:fofType)=> ((ap V1m) V2x)))))) ((ap ((ap (c_2Ebool_2ERES__FORALL A_27a)) V0p)) ((lam A_27a) (fun (V3x:fofType)=> ((ap ((ap (c_2Ebool_2ERES__FORALL A_27a)) V0p)) ((lam A_27a) (fun (V4y:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap V1m) V3x))) ((ap V1m) V4y)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))) of role axiom named ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF
% 0.51/0.72 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2ERES__EXISTS A_27a)) V0p)) ((lam A_27a) (fun (V2x:fofType)=> ((ap V1m) V2x)))))) ((ap ((ap (c_2Ebool_2ERES__FORALL A_27a)) V0p)) ((lam A_27a) (fun (V3x:fofType)=> ((ap ((ap (c_2Ebool_2ERES__FORALL A_27a)) V0p)) ((lam A_27a) (fun (V4y:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap V1m) V3x))) ((ap V1m) V4y)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V4y)))))))))))))))
% 0.51/0.72 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__SELECT A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Emin_2E_40 A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x))))))))))) of role axiom named ax_thm_2Ebool_2ERES__SELECT__DEF
% 0.51/0.72 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__SELECT A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Emin_2E_40 A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x)))))))))))
% 0.51/0.72 FOF formula (((eq fofType) c_2Ebool_2EBOUNDED) ((lam bool) (fun (V0v:fofType)=> c_2Ebool_2ET))) of role axiom named ax_thm_2Ebool_2EBOUNDED__DEF
% 0.51/0.72 A new axiom: (((eq fofType) c_2Ebool_2EBOUNDED) ((lam bool) (fun (V0v:fofType)=> c_2Ebool_2ET)))
% 0.51/0.72 FOF formula (forall (A_27a:del), (((eq fofType) (c_2Ebool_2EDATATYPE A_27a)) ((lam A_27a) (fun (V0x:fofType)=> c_2Ebool_2ET)))) of role axiom named ax_thm_2Ebool_2EDATATYPE__TAG__DEF
% 0.51/0.72 A new axiom: (forall (A_27a:del), (((eq fofType) (c_2Ebool_2EDATATYPE A_27a)) ((lam A_27a) (fun (V0x:fofType)=> c_2Ebool_2ET))))
% 0.51/0.72 FOF formula True of role conjecture named conj_thm_2Ebool_2ETRUTH
% 0.51/0.72 Conjecture to prove = True:Prop
% 0.51/0.72 Parameter tp__i_DUMMY:tp__i.
% 0.51/0.72 We need to prove ['True']
% 0.51/0.72 Parameter del:Type.
% 0.51/0.72 Parameter bool:del.
% 0.51/0.72 Parameter ind:del.
% 0.51/0.72 Parameter arr:(del->(del->del)).
% 0.51/0.72 Parameter fofType:Type.
% 0.51/0.72 Parameter mem:(fofType->(del->Prop)).
% 0.51/0.72 Parameter ap:(fofType->(fofType->fofType)).
% 0.51/0.72 Parameter lam:(del->((fofType->fofType)->fofType)).
% 0.51/0.72 Parameter p:(fofType->Prop).
% 0.51/0.72 Parameter inj__o:(Prop->fofType).
% 0.51/0.72 Axiom stp_inj_surj_o:(forall (X:Prop), (((eq Prop) (p (inj__o X))) X)).
% 0.51/0.72 Axiom stp_inj_mem_o:(forall (X:Prop), ((mem (inj__o X)) bool)).
% 0.51/0.72 Axiom stp_iso_mem_o:(forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))).
% 0.51/0.72 Axiom ap_tp:(forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (X:fofType), (((mem X) A)->((mem ((ap F) X)) B))))).
% 0.51/0.72 Axiom lam_tp:(forall (A:del) (B:del) (F:(fofType->fofType)), ((forall (X:fofType), (((mem X) A)->((mem (F X)) B)))->((mem ((lam A) F)) ((arr A) B)))).
% 0.51/0.72 Axiom funcext:(forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (G:fofType), (((mem G) ((arr A) B))->((forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap G) X))))->(((eq fofType) F) G)))))).
% 0.51/0.72 Axiom beta:(forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X)))).
% 0.51/0.72 Parameter c_2Emin_2E_3D:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Emin_2E_3D:(forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool)))).
% 0.51/0.72 Axiom ax_eq_p:(forall (A:del) (X:fofType), (((mem X) A)->(forall (Y:fofType), (((mem Y) A)->((iff (p ((ap ((ap (c_2Emin_2E_3D A)) X)) Y))) (((eq fofType) X) Y)))))).
% 0.51/0.72 Parameter c_2Emin_2E_3D_3D_3E:fofType.
% 0.51/0.72 Axiom mem_c_2Emin_2E_3D_3D_3E:((mem c_2Emin_2E_3D_3D_3E) ((arr bool) ((arr bool) bool))).
% 0.51/0.72 Axiom ax_imp_p:(forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Emin_2E_3D_3D_3E) Q)) R))) ((p Q)->(p R))))))).
% 0.51/0.72 Parameter c_2Emin_2E_40:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Emin_2E_40:(forall (A_27a:del), ((mem (c_2Emin_2E_40 A_27a)) ((arr ((arr A_27a) bool)) A_27a))).
% 0.51/0.72 Parameter ty_2Ebool_2Eitself:(del->del).
% 0.51/0.72 Parameter c_2Ebool_2E_21:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2E_21:(forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool))).
% 0.51/0.72 Axiom ax_all_p:(forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_21 A)) Q))) (forall (X:fofType), (((mem X) A)->(p ((ap Q) X))))))).
% 0.51/0.72 Parameter c_2Ebool_2E_2F_5C:fofType.
% 0.51/0.72 Axiom mem_c_2Ebool_2E_2F_5C:((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool))).
% 0.51/0.72 Axiom ax_and_p:(forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_2F_5C) Q)) R))) ((and (p Q)) (p R))))))).
% 0.51/0.72 Parameter c_2Ebool_2E_3F:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2E_3F:(forall (A_27a:del), ((mem (c_2Ebool_2E_3F A_27a)) ((arr ((arr A_27a) bool)) bool))).
% 0.51/0.72 Axiom ax_ex_p:(forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_3F A)) Q))) ((ex fofType) (fun (X:fofType)=> ((and ((mem X) A)) (p ((ap Q) X)))))))).
% 0.51/0.72 Parameter c_2Ebool_2E_3F_21:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2E_3F_21:(forall (A_27a:del), ((mem (c_2Ebool_2E_3F_21 A_27a)) ((arr ((arr A_27a) bool)) bool))).
% 0.51/0.72 Parameter c_2Ebool_2EARB:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2EARB:(forall (A_27a:del), ((mem (c_2Ebool_2EARB A_27a)) A_27a)).
% 0.51/0.72 Parameter c_2Ebool_2EBOUNDED:fofType.
% 0.51/0.72 Axiom mem_c_2Ebool_2EBOUNDED:((mem c_2Ebool_2EBOUNDED) ((arr bool) bool)).
% 0.51/0.72 Parameter c_2Ebool_2ECOND:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2ECOND:(forall (A_27a:del), ((mem (c_2Ebool_2ECOND A_27a)) ((arr bool) ((arr A_27a) ((arr A_27a) A_27a))))).
% 0.51/0.72 Parameter c_2Ebool_2EDATATYPE:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2EDATATYPE:(forall (A_27a:del), ((mem (c_2Ebool_2EDATATYPE A_27a)) ((arr A_27a) bool))).
% 0.51/0.72 Parameter c_2Ebool_2EF:fofType.
% 0.51/0.72 Axiom mem_c_2Ebool_2EF:((mem c_2Ebool_2EF) bool).
% 0.51/0.72 Axiom ax_false_p:((p c_2Ebool_2EF)->False).
% 0.51/0.72 Parameter c_2Ebool_2EIN:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2EIN:(forall (A_27a:del), ((mem (c_2Ebool_2EIN A_27a)) ((arr A_27a) ((arr ((arr A_27a) bool)) bool)))).
% 0.51/0.72 Parameter c_2Ebool_2ELET:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2ELET:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ELET A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b)))).
% 0.51/0.72 Parameter c_2Ebool_2EONE__ONE:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2EONE__ONE:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2EONE__ONE A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) bool))).
% 0.51/0.72 Parameter c_2Ebool_2EONTO:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2EONTO:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2EONTO A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) bool))).
% 0.51/0.72 Parameter c_2Ebool_2ERES__ABSTRACT:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2ERES__ABSTRACT:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b))))).
% 0.51/0.72 Parameter c_2Ebool_2ERES__EXISTS:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2ERES__EXISTS:(forall (A_27a:del), ((mem (c_2Ebool_2ERES__EXISTS A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool)))).
% 0.51/0.72 Parameter c_2Ebool_2ERES__EXISTS__UNIQUE:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2ERES__EXISTS__UNIQUE:(forall (A_27a:del), ((mem (c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool)))).
% 0.51/0.72 Parameter c_2Ebool_2ERES__FORALL:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2ERES__FORALL:(forall (A_27a:del), ((mem (c_2Ebool_2ERES__FORALL A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) bool)))).
% 0.51/0.72 Parameter c_2Ebool_2ERES__SELECT:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2ERES__SELECT:(forall (A_27a:del), ((mem (c_2Ebool_2ERES__SELECT A_27a)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27a) bool)) A_27a)))).
% 0.51/0.72 Parameter c_2Ebool_2ET:fofType.
% 0.51/0.72 Axiom mem_c_2Ebool_2ET:((mem c_2Ebool_2ET) bool).
% 0.51/0.72 Axiom ax_true_p:(p c_2Ebool_2ET).
% 0.51/0.72 Parameter c_2Ebool_2ETYPE__DEFINITION:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2ETYPE__DEFINITION:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) ((arr ((arr A_27a) bool)) ((arr ((arr A_27b) A_27a)) bool)))).
% 0.51/0.72 Parameter c_2Ebool_2E_5C_2F:fofType.
% 0.51/0.72 Axiom mem_c_2Ebool_2E_5C_2F:((mem c_2Ebool_2E_5C_2F) ((arr bool) ((arr bool) bool))).
% 0.51/0.72 Axiom ax_or_p:(forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_5C_2F) Q)) R))) ((or (p Q)) (p R))))))).
% 0.51/0.72 Parameter c_2Ebool_2Eitself__case:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2Eitself__case:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2Eitself__case A_27a) A_27b)) ((arr (ty_2Ebool_2Eitself A_27a)) ((arr A_27b) A_27b)))).
% 0.51/0.72 Parameter c_2Ebool_2Eliteral__case:(del->(del->fofType)).
% 0.51/0.72 Axiom mem_c_2Ebool_2Eliteral__case:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Ebool_2Eliteral__case A_27a) A_27b)) ((arr ((arr A_27a) A_27b)) ((arr A_27a) A_27b)))).
% 0.51/0.72 Parameter c_2Ebool_2Ethe__value:(del->fofType).
% 0.51/0.72 Axiom mem_c_2Ebool_2Ethe__value:(forall (A_27a:del), ((mem (c_2Ebool_2Ethe__value A_27a)) (ty_2Ebool_2Eitself A_27a))).
% 0.51/0.72 Parameter c_2Ebool_2E_7E:fofType.
% 0.51/0.72 Axiom mem_c_2Ebool_2E_7E:((mem c_2Ebool_2E_7E) ((arr bool) bool)).
% 0.51/0.72 Axiom ax_neg_p:(forall (Q:fofType), (((mem Q) bool)->((iff (p ((ap c_2Ebool_2E_7E) Q))) ((p Q)->False)))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ET__DEF:((iff True) (((eq fofType) ((lam bool) (fun (V0x:fofType)=> V0x))) ((lam bool) (fun (V1x:fofType)=> V1x)))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EFORALL__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_21 A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap ((ap (c_2Emin_2E_3D ((arr A_27a) bool))) V0P)) ((lam A_27a) (fun (V1x:fofType)=> c_2Ebool_2ET))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EEXISTS__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_3F A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap V0P) ((ap (c_2Emin_2E_40 A_27a)) V0P)))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EAND__DEF:(((eq fofType) c_2Ebool_2E_2F_5C) ((lam bool) (fun (V0t1:fofType)=> ((lam bool) (fun (V1t2:fofType)=> ((ap (c_2Ebool_2E_21 bool)) ((lam bool) (fun (V2t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t1)) ((ap ((ap c_2Emin_2E_3D_3D_3E) V1t2)) V2t)))) V2t))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EOR__DEF:(((eq fofType) c_2Ebool_2E_5C_2F) ((lam bool) (fun (V0t1:fofType)=> ((lam bool) (fun (V1t2:fofType)=> ((ap (c_2Ebool_2E_21 bool)) ((lam bool) (fun (V2t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t1)) V2t))) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Emin_2E_3D_3D_3E) V1t2)) V2t))) V2t)))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EF__DEF:((iff False) (forall (V0t:fofType), (((mem V0t) bool)->(p V0t)))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ENOT__DEF:(((eq fofType) c_2Ebool_2E_7E) ((lam bool) (fun (V0t:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) V0t)) c_2Ebool_2EF)))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2E_3F_21 A_27a)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Ebool_2E_3F A_27a)) V0P))) ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap V0P) V1x))) ((ap V0P) V2y)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V1x)) V2y))))))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ELET__DEF:(forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2ELET A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((lam A_27a) (fun (V1x:fofType)=> ((ap V0f) V1x))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ECOND__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2ECOND A_27a)) ((lam bool) (fun (V0t:fofType)=> ((lam A_27a) (fun (V1t1:fofType)=> ((lam A_27a) (fun (V2t2:fofType)=> ((ap (c_2Emin_2E_40 A_27a)) ((lam A_27a) (fun (V3x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D bool)) V0t)) c_2Ebool_2ET))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V1t1)))) ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D bool)) V0t)) c_2Ebool_2EF))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V2t2)))))))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EONE__ONE__DEF:(forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2EONE__ONE A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V1x1:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2x2:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D A_27b)) ((ap V0f) V1x1))) ((ap V0f) V2x2)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V1x1)) V2x2)))))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EONTO__DEF:(forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2EONTO A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V1y:fofType)=> ((ap (c_2Ebool_2E_3F A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap (c_2Emin_2E_3D A_27b)) V1y)) ((ap V0f) V2x)))))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ETYPE__DEFINITION:(forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) ((lam ((arr A_27a) bool)) (fun (V0P:fofType)=> ((lam ((arr A_27b) A_27a)) (fun (V1rep:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V2x_27:fofType)=> ((ap (c_2Ebool_2E_21 A_27b)) ((lam A_27b) (fun (V3x_27_27:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Emin_2E_3D A_27a)) ((ap V1rep) V2x_27))) ((ap V1rep) V3x_27_27)))) ((ap ((ap (c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27)))))))))) ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V4x:fofType)=> ((ap ((ap (c_2Emin_2E_3D bool)) ((ap V0P) V4x))) ((ap (c_2Ebool_2E_3F A_27b)) ((lam A_27b) (fun (V5x_27:fofType)=> ((ap ((ap (c_2Emin_2E_3D A_27a)) V4x)) ((ap V1rep) V5x_27)))))))))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EBOOL__CASES__AX:(forall (V0t:fofType), (((mem V0t) bool)->((or ((iff (p V0t)) True)) ((iff (p V0t)) False)))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EETA__AX:(forall (A_27a:del) (A_27b:del) (V0t:fofType), (((mem V0t) ((arr A_27a) A_27b))->(((eq fofType) ((lam A_27a) (fun (V1x:fofType)=> ((ap V0t) V1x)))) V0t))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ESELECT__AX:(forall (A_27a:del) (V0P:fofType), (((mem V0P) ((arr A_27a) bool))->(forall (V1x:fofType), (((mem V1x) A_27a)->((p ((ap V0P) V1x))->(p ((ap V0P) ((ap (c_2Emin_2E_40 A_27a)) V0P)))))))).
% 0.51/0.72 Parameter tp__i:Type.
% 0.51/0.72 Parameter inj__i:(tp__i->fofType).
% 0.51/0.72 Parameter surj__i:(fofType->tp__i).
% 0.51/0.72 Axiom stp_inj_surj_i:(forall (X:tp__i), (((eq tp__i) (surj__i (inj__i X))) X)).
% 0.51/0.72 Axiom stp_inj_mem_i:(forall (X:tp__i), ((mem (inj__i X)) ind)).
% 0.51/0.72 Axiom stp_iso_mem_i:(forall (X:fofType), (((mem X) ind)->(((eq fofType) X) (inj__i (surj__i X))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EINFINITY__AX:((ex fofType) (fun (V0f:fofType)=> ((and ((and ((mem V0f) ((arr ind) ind))) (p ((ap ((c_2Ebool_2EONE__ONE ind) ind)) V0f)))) ((p ((ap ((c_2Ebool_2EONTO ind) ind)) V0f))->False)))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2Eliteral__case__DEF:(forall (A_27a:del) (A_27b:del), (((eq fofType) ((c_2Ebool_2Eliteral__case A_27a) A_27b)) ((lam ((arr A_27a) A_27b)) (fun (V0f:fofType)=> ((lam A_27a) (fun (V1x:fofType)=> ((ap V0f) V1x))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2EIN__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2EIN A_27a)) ((lam A_27a) (fun (V0x:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1f:fofType)=> ((ap V1f) V0x))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ERES__FORALL__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__FORALL A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Ebool_2E_21 A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x))))))))))).
% 0.51/0.72 Axiom ax_thm_2Ebool_2ERES__EXISTS__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__EXISTS A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Ebool_2E_3F A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x))))))))))).
% 0.58/0.74 Axiom ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2ERES__EXISTS A_27a)) V0p)) ((lam A_27a) (fun (V2x:fofType)=> ((ap V1m) V2x)))))) ((ap ((ap (c_2Ebool_2ERES__FORALL A_27a)) V0p)) ((lam A_27a) (fun (V3x:fofType)=> ((ap ((ap (c_2Ebool_2ERES__FORALL A_27a)) V0p)) ((lam A_27a) (fun (V4y:fofType)=> ((ap ((ap c_2Emin_2E_3D_3D_3E) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap V1m) V3x))) ((ap V1m) V4y)))) ((ap ((ap (c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))).
% 0.58/0.74 Axiom ax_thm_2Ebool_2ERES__SELECT__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2ERES__SELECT A_27a)) ((lam ((arr A_27a) bool)) (fun (V0p:fofType)=> ((lam ((arr A_27a) bool)) (fun (V1m:fofType)=> ((ap (c_2Emin_2E_40 A_27a)) ((lam A_27a) (fun (V2x:fofType)=> ((ap ((ap c_2Ebool_2E_2F_5C) ((ap ((ap (c_2Ebool_2EIN A_27a)) V2x)) V0p))) ((ap V1m) V2x))))))))))).
% 0.58/0.74 Axiom ax_thm_2Ebool_2EBOUNDED__DEF:(((eq fofType) c_2Ebool_2EBOUNDED) ((lam bool) (fun (V0v:fofType)=> c_2Ebool_2ET))).
% 0.58/0.74 Axiom ax_thm_2Ebool_2EDATATYPE__TAG__DEF:(forall (A_27a:del), (((eq fofType) (c_2Ebool_2EDATATYPE A_27a)) ((lam A_27a) (fun (V0x:fofType)=> c_2Ebool_2ET)))).
% 0.58/0.74 Trying to prove True
% 0.58/0.74 Found I:True
% 0.58/0.74 Found I as proof of True
% 0.58/0.74 Got proof I
% 0.58/0.74 Time elapsed = 0.000764s
% 0.58/0.74 node=0 cost=0.000000 depth=0
% 0.58/0.74::::::::::::::::::::::
% 0.58/0.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.74 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.74 I
% 0.58/0.74 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------