TSTP Solution File: ITP008^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP008^2 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 13:23:35 EDT 2021
% Result : Timeout 292.57s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP008^2 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Mar 18 21:48:48 EDT 2021
% 0.13/0.35 % CPUTime :
% 0.13/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.36 Python 2.7.5
% 0.50/0.64 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.50/0.64 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/ITP001/ITP001^2.ax, trying next directory
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x151f710>, <kernel.Type object at 0x1521050>) of role type named del_tp
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring del:Type
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x151ff38>, <kernel.Constant object at 0x1521368>) of role type named bool
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring bool:del
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x151f710>, <kernel.Constant object at 0x1521878>) of role type named ind
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring ind:del
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x151f710>, <kernel.DependentProduct object at 0x1521098>) of role type named arr
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring arr:(del->(del->del))
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x1525128>, <kernel.DependentProduct object at 0x1521098>) of role type named mem
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring mem:(fofType->(del->Prop))
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x1525128>, <kernel.DependentProduct object at 0x15213f8>) of role type named ap
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring ap:(fofType->(fofType->fofType))
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x15217a0>, <kernel.DependentProduct object at 0x1521dd0>) of role type named lam
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring lam:(del->((fofType->fofType)->fofType))
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x1521b00>, <kernel.DependentProduct object at 0x1521098>) of role type named p
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring p:(fofType->Prop)
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x15213f8>, <kernel.DependentProduct object at 0x1521b48>) of role type named stp_inj_o
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring inj__o:(Prop->fofType)
% 0.50/0.64 FOF formula (forall (X:Prop), (((eq Prop) (p (inj__o X))) X)) of role axiom named stp_inj_surj_o
% 0.50/0.64 A new axiom: (forall (X:Prop), (((eq Prop) (p (inj__o X))) X))
% 0.50/0.64 FOF formula (forall (X:Prop), ((mem (inj__o X)) bool)) of role axiom named stp_inj_mem_o
% 0.50/0.64 A new axiom: (forall (X:Prop), ((mem (inj__o X)) bool))
% 0.50/0.64 FOF formula (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))) of role axiom named stp_iso_mem_o
% 0.50/0.64 A new axiom: (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X)))))
% 0.50/0.64 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
% 0.50/0.64 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)))))
% 0.50/0.64 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
% 0.50/0.64 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))))
% 0.50/0.64 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
% 0.50/0.64 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))))))
% 0.50/0.64 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
% 0.50/0.64 A new axiom: (forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X))))
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x1524830>, <kernel.DependentProduct object at 0x1524e60>) of role type named tp_ty_2Epair_2Eprod
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring ty_2Epair_2Eprod:(del->(del->del))
% 0.50/0.64 FOF formula (<kernel.Constant object at 0x15245f0>, <kernel.DependentProduct object at 0x1524f80>) of role type named tp_c_2Epair_2E_2C
% 0.50/0.64 Using role type
% 0.50/0.64 Declaring c_2Epair_2E_2C:(del->(del->fofType))
% 0.50/0.64 FOF formula (forall (A_27a:del) (A_27b:del), ((mem ((c_2Epair_2E_2C A_27a) A_27b)) ((arr A_27a) ((arr A_27b) ((ty_2Epair_2Eprod A_27a) A_27b))))) of role axiom named mem_c_2Epair_2E_2C
% 0.50/0.65 A new axiom: (forall (A_27a:del) (A_27b:del), ((mem ((c_2Epair_2E_2C A_27a) A_27b)) ((arr A_27a) ((arr A_27b) ((ty_2Epair_2Eprod A_27a) A_27b)))))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x15245f0>, <kernel.DependentProduct object at 0x2b7c61ba8680>) of role type named tp_c_2Epair_2ECURRY
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring c_2Epair_2ECURRY:(del->(del->(del->fofType)))
% 0.50/0.65 FOF formula (forall (A_27a:del) (A_27b:del) (A_27c:del), ((mem (((c_2Epair_2ECURRY A_27a) A_27b) A_27c)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) ((arr A_27a) ((arr A_27b) A_27c))))) of role axiom named mem_c_2Epair_2ECURRY
% 0.50/0.65 A new axiom: (forall (A_27a:del) (A_27b:del) (A_27c:del), ((mem (((c_2Epair_2ECURRY A_27a) A_27b) A_27c)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) ((arr A_27a) ((arr A_27b) A_27c)))))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x2b7c61ba8680>, <kernel.DependentProduct object at 0x2b7c61bc5128>) of role type named tp_c_2Erelation_2EWF
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring c_2Erelation_2EWF:(del->fofType)
% 0.50/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Erelation_2EWF A_27a)) ((arr ((arr A_27a) ((arr A_27a) bool))) bool))) of role axiom named mem_c_2Erelation_2EWF
% 0.50/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Erelation_2EWF A_27a)) ((arr ((arr A_27a) ((arr A_27a) bool))) bool)))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x1524200>, <kernel.DependentProduct object at 0x2b7c61bc5440>) of role type named tp_c_2Emin_2E_3D
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring c_2Emin_2E_3D:(del->fofType)
% 0.50/0.65 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
% 0.50/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool))))
% 0.50/0.65 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
% 0.50/0.65 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))))))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x1524200>, <kernel.DependentProduct object at 0x2b7c61bc61b8>) of role type named tp_ty_2Ewellorder_2Ewellorder
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring ty_2Ewellorder_2Ewellorder:(del->del)
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x2b7c61bc5290>, <kernel.DependentProduct object at 0x2b7c61bc6cf8>) of role type named tp_c_2Ewellorder_2Ewellorder__REP
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring c_2Ewellorder_2Ewellorder__REP:(del->fofType)
% 0.50/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Ewellorder_2Ewellorder__REP A_27a)) ((arr (ty_2Ewellorder_2Ewellorder A_27a)) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)))) of role axiom named mem_c_2Ewellorder_2Ewellorder__REP
% 0.50/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Ewellorder_2Ewellorder__REP A_27a)) ((arr (ty_2Ewellorder_2Ewellorder A_27a)) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool))))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x2b7c61bc5440>, <kernel.DependentProduct object at 0x2b7c61bc6cf8>) of role type named tp_c_2Eset__relation_2Estrict
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring c_2Eset__relation_2Estrict:(del->fofType)
% 0.50/0.65 FOF formula (forall (A_27a:del), ((mem (c_2Eset__relation_2Estrict A_27a)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)))) of role axiom named mem_c_2Eset__relation_2Estrict
% 0.50/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Eset__relation_2Estrict A_27a)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool))))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x2b7c61bc5128>, <kernel.DependentProduct object at 0x151fc20>) of role type named tp_c_2Ebool_2EIN
% 0.50/0.65 Using role type
% 0.50/0.65 Declaring c_2Ebool_2EIN:(del->fofType)
% 0.50/0.65 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
% 0.50/0.65 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2EIN A_27a)) ((arr A_27a) ((arr ((arr A_27a) bool)) bool))))
% 0.50/0.65 FOF formula (<kernel.Constant object at 0x2b7c61bc64d0>, <kernel.DependentProduct object at 0x151fef0>) of role type named tp_c_2Ewellorder_2Ewellfounded
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_2Ewellorder_2Ewellfounded:(del->fofType)
% 0.50/0.67 FOF formula (forall (A_27a:del), ((mem (c_2Ewellorder_2Ewellfounded A_27a)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)) bool))) of role axiom named mem_c_2Ewellorder_2Ewellfounded
% 0.50/0.67 A new axiom: (forall (A_27a:del), ((mem (c_2Ewellorder_2Ewellfounded A_27a)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)) bool)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2b7c61bc6cb0>, <kernel.DependentProduct object at 0x151f5a8>) of role type named tp_c_2Ebool_2E_21
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_2Ebool_2E_21:(del->fofType)
% 0.50/0.67 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
% 0.50/0.67 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool)))
% 0.50/0.67 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
% 0.50/0.67 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)))))))
% 0.50/0.67 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
% 0.50/0.67 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)))
% 0.50/0.67 FOF formula (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr ((ty_2Epair_2Eprod A_27a) A_27b)) A_27c))->(forall (V1x:fofType), (((mem V1x) A_27a)->(forall (V2y:fofType), (((mem V2y) A_27b)->(((eq fofType) ((ap ((ap ((ap (((c_2Epair_2ECURRY A_27a) A_27b) A_27c)) V0f)) V1x)) V2y)) ((ap V0f) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))))))))) of role axiom named ax_thm_2Epair_2ECURRY__DEF
% 0.50/0.67 A new axiom: (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr ((ty_2Epair_2Eprod A_27a) A_27b)) A_27c))->(forall (V1x:fofType), (((mem V1x) A_27a)->(forall (V2y:fofType), (((mem V2y) A_27b)->(((eq fofType) ((ap ((ap ((ap (((c_2Epair_2ECURRY A_27a) A_27b) A_27c)) V0f)) V1x)) V2y)) ((ap V0f) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y)))))))))
% 0.50/0.67 FOF formula (forall (A_27a:del) (V0R:fofType), (((mem V0R) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool))->((iff (p ((ap (c_2Ewellorder_2Ewellfounded A_27a)) V0R))) (p ((ap (c_2Erelation_2EWF A_27a)) ((ap (((c_2Epair_2ECURRY A_27a) A_27a) bool)) V0R)))))) of role axiom named conj_thm_2Ewellorder_2Ewellfounded__WF
% 0.50/0.67 A new axiom: (forall (A_27a:del) (V0R:fofType), (((mem V0R) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool))->((iff (p ((ap (c_2Ewellorder_2Ewellfounded A_27a)) V0R))) (p ((ap (c_2Erelation_2EWF A_27a)) ((ap (((c_2Epair_2ECURRY A_27a) A_27a) bool)) V0R))))))
% 0.50/0.67 FOF formula (forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Ewellorder_2Ewellfounded A_27a)) ((lam ((ty_2Epair_2Eprod A_27a) A_27a)) (fun (V1p:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) V1p)) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) of role axiom named conj_thm_2Ewellorder_2EWIN__WF
% 0.50/0.67 A new axiom: (forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Ewellorder_2Ewellfounded A_27a)) ((lam ((ty_2Epair_2Eprod A_27a) A_27a)) (fun (V1p:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) V1p)) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w)))))))))
% 0.50/0.67 FOF formula (forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))))) of role conjecture named conj_thm_2Ewellorder_2EWIN__WF2
% 0.53/0.67 Conjecture to prove = (forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))))):Prop
% 0.53/0.67 Parameter fofType_DUMMY:fofType.
% 0.53/0.67 We need to prove ['(forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w)))))))))))']
% 0.53/0.67 Parameter del:Type.
% 0.53/0.67 Parameter bool:del.
% 0.53/0.67 Parameter ind:del.
% 0.53/0.67 Parameter arr:(del->(del->del)).
% 0.53/0.67 Parameter fofType:Type.
% 0.53/0.67 Parameter mem:(fofType->(del->Prop)).
% 0.53/0.67 Parameter ap:(fofType->(fofType->fofType)).
% 0.53/0.67 Parameter lam:(del->((fofType->fofType)->fofType)).
% 0.53/0.67 Parameter p:(fofType->Prop).
% 0.53/0.67 Parameter inj__o:(Prop->fofType).
% 0.53/0.67 Axiom stp_inj_surj_o:(forall (X:Prop), (((eq Prop) (p (inj__o X))) X)).
% 0.53/0.67 Axiom stp_inj_mem_o:(forall (X:Prop), ((mem (inj__o X)) bool)).
% 0.53/0.67 Axiom stp_iso_mem_o:(forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))).
% 0.53/0.67 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))))).
% 0.53/0.67 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)))).
% 0.53/0.67 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)))))).
% 0.53/0.67 Axiom beta:(forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X)))).
% 0.53/0.67 Parameter ty_2Epair_2Eprod:(del->(del->del)).
% 0.53/0.67 Parameter c_2Epair_2E_2C:(del->(del->fofType)).
% 0.53/0.67 Axiom mem_c_2Epair_2E_2C:(forall (A_27a:del) (A_27b:del), ((mem ((c_2Epair_2E_2C A_27a) A_27b)) ((arr A_27a) ((arr A_27b) ((ty_2Epair_2Eprod A_27a) A_27b))))).
% 0.53/0.67 Parameter c_2Epair_2ECURRY:(del->(del->(del->fofType))).
% 0.53/0.67 Axiom mem_c_2Epair_2ECURRY:(forall (A_27a:del) (A_27b:del) (A_27c:del), ((mem (((c_2Epair_2ECURRY A_27a) A_27b) A_27c)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) ((arr A_27a) ((arr A_27b) A_27c))))).
% 0.53/0.67 Parameter c_2Erelation_2EWF:(del->fofType).
% 0.53/0.67 Axiom mem_c_2Erelation_2EWF:(forall (A_27a:del), ((mem (c_2Erelation_2EWF A_27a)) ((arr ((arr A_27a) ((arr A_27a) bool))) bool))).
% 0.53/0.67 Parameter c_2Emin_2E_3D:(del->fofType).
% 0.53/0.67 Axiom mem_c_2Emin_2E_3D:(forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool)))).
% 0.53/0.67 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)))))).
% 0.53/0.67 Parameter ty_2Ewellorder_2Ewellorder:(del->del).
% 0.53/0.67 Parameter c_2Ewellorder_2Ewellorder__REP:(del->fofType).
% 0.53/0.67 Axiom mem_c_2Ewellorder_2Ewellorder__REP:(forall (A_27a:del), ((mem (c_2Ewellorder_2Ewellorder__REP A_27a)) ((arr (ty_2Ewellorder_2Ewellorder A_27a)) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)))).
% 0.53/0.67 Parameter c_2Eset__relation_2Estrict:(del->fofType).
% 0.53/0.67 Axiom mem_c_2Eset__relation_2Estrict:(forall (A_27a:del), ((mem (c_2Eset__relation_2Estrict A_27a)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)))).
% 0.53/0.67 Parameter c_2Ebool_2EIN:(del->fofType).
% 0.53/0.67 Axiom mem_c_2Ebool_2EIN:(forall (A_27a:del), ((mem (c_2Ebool_2EIN A_27a)) ((arr A_27a) ((arr ((arr A_27a) bool)) bool)))).
% 0.53/0.67 Parameter c_2Ewellorder_2Ewellfounded:(del->fofType).
% 1.77/1.92 Axiom mem_c_2Ewellorder_2Ewellfounded:(forall (A_27a:del), ((mem (c_2Ewellorder_2Ewellfounded A_27a)) ((arr ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool)) bool))).
% 1.77/1.92 Parameter c_2Ebool_2E_21:(del->fofType).
% 1.77/1.92 Axiom mem_c_2Ebool_2E_21:(forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool))).
% 1.77/1.92 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))))))).
% 1.77/1.92 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))).
% 1.77/1.92 Axiom ax_thm_2Epair_2ECURRY__DEF:(forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr ((ty_2Epair_2Eprod A_27a) A_27b)) A_27c))->(forall (V1x:fofType), (((mem V1x) A_27a)->(forall (V2y:fofType), (((mem V2y) A_27b)->(((eq fofType) ((ap ((ap ((ap (((c_2Epair_2ECURRY A_27a) A_27b) A_27c)) V0f)) V1x)) V2y)) ((ap V0f) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))))))))).
% 1.77/1.92 Axiom conj_thm_2Ewellorder_2Ewellfounded__WF:(forall (A_27a:del) (V0R:fofType), (((mem V0R) ((arr ((ty_2Epair_2Eprod A_27a) A_27a)) bool))->((iff (p ((ap (c_2Ewellorder_2Ewellfounded A_27a)) V0R))) (p ((ap (c_2Erelation_2EWF A_27a)) ((ap (((c_2Epair_2ECURRY A_27a) A_27a) bool)) V0R)))))).
% 1.77/1.92 Axiom conj_thm_2Ewellorder_2EWIN__WF:(forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Ewellorder_2Ewellfounded A_27a)) ((lam ((ty_2Epair_2Eprod A_27a) A_27a)) (fun (V1p:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) V1p)) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))).
% 1.77/1.92 Trying to prove (forall (A_27a:del) (V0w:fofType), (((mem V0w) (ty_2Ewellorder_2Ewellorder A_27a))->(p ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w)))))))))))
% 1.77/1.92 Found eq_ref00:=(eq_ref0 ((ap F) X)):(((eq fofType) ((ap F) X)) ((ap F) X))
% 1.77/1.92 Found (eq_ref0 ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 1.77/1.92 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 1.77/1.92 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 1.77/1.92 Found (fun (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 1.77/1.92 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 17.85/18.02 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 17.85/18.02 Found x0:((mem X) A_27a0)
% 17.85/18.02 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 17.85/18.02 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 17.85/18.02 Found x0:((mem X) A_27a0)
% 17.85/18.02 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 17.85/18.02 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 17.85/18.02 Found eq_ref00:=(eq_ref0 ((ap F) X)):(((eq fofType) ((ap F) X)) ((ap F) X))
% 17.85/18.02 Found (eq_ref0 ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 17.85/18.02 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 17.85/18.02 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 17.85/18.02 Found (fun (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F) X))) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 17.85/18.02 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F) X))) as proof of (((mem X) A0)->(((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 17.85/18.02 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F) X))) as proof of (forall (X:fofType), (((mem X) A0)->(((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 17.85/18.02 Found x0:((mem X) A_27a00)
% 17.85/18.02 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 17.85/18.02 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 17.85/18.02 Found x0:((mem X) A_27a00)
% 17.85/18.02 Found x0 as proof of ((mem X) A_27a00)
% 17.85/18.02 Found eq_ref00:=(eq_ref0 ((ap F) X)):(((eq fofType) ((ap F) X)) ((ap F) X))
% 17.85/18.02 Found (eq_ref0 ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.01/34.18 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.01/34.18 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.01/34.18 Found (fun (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F) X))) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.01/34.18 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F) X))) as proof of (((mem X) A0)->(((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 34.01/34.18 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F) X))) as proof of (forall (X:fofType), (((mem X) A0)->(((eq fofType) ((ap F) X)) ((ap ((ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Found x0 as proof of ((mem X) A_27a0)
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A_27a00)
% 34.01/34.18 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A_27a00)
% 34.01/34.18 Found x0 as proof of ((mem X) A_27a00)
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A_27a0)
% 34.01/34.18 Found x0 as proof of ((mem X) A_27a0)
% 34.01/34.18 Found x0:((mem X) A)
% 34.01/34.18 Instantiate: A0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 34.01/34.18 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 34.01/34.18 Found x0:((mem X) A)
% 34.01/34.18 Found x0 as proof of ((mem X) A)
% 34.01/34.18 Found eq_ref00:=(eq_ref0 ((ap F0) X)):(((eq fofType) ((ap F0) X)) ((ap F0) X))
% 34.01/34.18 Found (eq_ref0 ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found (fun (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((mem X) A)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 34.41/34.55 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 34.41/34.55 Found eq_ref00:=(eq_ref0 ((ap F0) X)):(((eq fofType) ((ap F0) X)) ((ap F0) X))
% 34.41/34.55 Found (eq_ref0 ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found (fun (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 34.41/34.55 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((mem X) A)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 39.63/39.82 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 39.63/39.82 Found x0:((mem X) A_27a0)
% 39.63/39.82 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 39.63/39.82 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 39.63/39.82 Found x0:((mem X) A_27a0)
% 39.63/39.82 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 39.63/39.82 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 39.63/39.82 Found x0:((mem X) A_27a0)
% 39.63/39.82 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 39.63/39.82 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 39.63/39.82 Found x0:((mem X) A_27a0)
% 39.63/39.82 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 39.63/39.82 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 39.63/39.82 Found eq_ref00:=(eq_ref0 ((ap F) X)):(((eq fofType) ((ap F) X)) ((ap F) X))
% 39.63/39.82 Found (eq_ref0 ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 39.63/39.82 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 39.63/39.82 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 39.63/39.82 Found (fun (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 39.63/39.82 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X)))
% 39.63/39.82 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))))
% 59.51/59.70 Found x0:((mem X) A_27a0)
% 59.51/59.70 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 59.51/59.70 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found x0:((mem X) A)
% 59.51/59.70 Instantiate: A0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 59.51/59.70 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found x0:((mem X) A)
% 59.51/59.70 Found x0 as proof of ((mem X) A)
% 59.51/59.70 Found x0:((mem X) A_27a0)
% 59.51/59.70 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 59.51/59.70 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found x1:((mem X0) A_27a0)
% 59.51/59.70 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found x1:((mem X0) A_27a0)
% 59.51/59.70 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found x0:((mem X) A_27a0)
% 59.51/59.70 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 59.51/59.70 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found x0:((mem X) A_27a0)
% 59.51/59.70 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 59.51/59.70 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 59.51/59.70 Found eq_ref00:=(eq_ref0 ((ap F) X)):(((eq fofType) ((ap F) X)) ((ap F) X))
% 59.51/59.70 Found (eq_ref0 ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 59.51/59.70 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 59.51/59.70 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 59.51/59.70 Found (fun (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))
% 59.51/59.70 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X)))
% 59.51/59.70 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F) X))) as proof of (forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap ((lam A_27a0) (fun (V1x:fofType)=> ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) V1x)))) X))))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found eq_ref00:=(eq_ref0 ((ap F0) X)):(((eq fofType) ((ap F0) X)) ((ap F0) X))
% 87.07/87.31 Found (eq_ref0 ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 87.07/87.31 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 87.07/87.31 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 87.07/87.31 Found (fun (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 87.07/87.31 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((mem X) A)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 87.07/87.31 Found (fun (X:fofType) (x0:((mem X) A))=> ((eq_ref fofType) ((ap F0) X))) as proof of (forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Found x0 as proof of ((mem X) A_27a0)
% 87.07/87.31 Found x1:((mem X0) A_27a0)
% 87.07/87.31 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Found x0 as proof of ((mem X) A_27a0)
% 87.07/87.31 Found x0:((mem X) A_27a00)
% 87.07/87.31 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 87.07/87.31 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 87.07/87.31 Found x0:((mem X) A_27a00)
% 87.07/87.31 Found x0 as proof of ((mem X) A_27a00)
% 87.07/87.31 Found x0:((mem X) A_27a0)
% 87.07/87.31 Instantiate: A_27a00:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a00)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a00)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a00)
% 135.36/135.62 Found x1:((mem X0) A_27a0)
% 135.36/135.62 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x1:((mem X0) A_27a0)
% 135.36/135.62 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x1:((mem X0) A_27a0)
% 135.36/135.62 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a00)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a00)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X0) A_27a00)
% 135.36/135.62 Found x0 as proof of ((mem X0) A_27a00)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A_27a00:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Instantiate: A:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a00)
% 135.36/135.62 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 135.36/135.62 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 135.36/135.62 Found x0:((mem X) A_27a00)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a00)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 135.36/135.62 Found x0 as proof of ((mem X) A_27a0)
% 135.36/135.62 Found x0:((mem X) A_27a0)
% 149.20/149.47 Instantiate: A_27a00:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 149.20/149.47 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 149.20/149.47 Found x0:((mem X) A_27a0)
% 149.20/149.47 Found x0 as proof of ((mem X) A_27a0)
% 149.20/149.47 Found x0:((mem X) A_27a00)
% 149.20/149.47 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 149.20/149.47 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 149.20/149.47 Found x0:((mem X) A_27a00)
% 149.20/149.47 Found x0 as proof of ((mem X) A_27a00)
% 149.20/149.47 Found x0:((mem X) A_27a0)
% 149.20/149.47 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 149.20/149.47 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 149.20/149.47 Found x0:((mem X) A_27a0)
% 149.20/149.47 Found x0 as proof of ((mem X) A_27a0)
% 149.20/149.47 Found x0:((mem X) A_27a0)
% 149.20/149.47 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 149.20/149.47 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 149.20/149.47 Found x0:((mem X) A_27a0)
% 149.20/149.47 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 149.20/149.47 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 149.20/149.47 Found x0:((mem X) A_27a0)
% 149.20/149.47 Found x0 as proof of ((mem X) A_27a0)
% 149.20/149.47 Found x0:((mem X) A_27a00)
% 149.20/149.47 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 149.20/149.47 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 149.20/149.47 Found x0:((mem X) A_27a00)
% 149.20/149.47 Found x0 as proof of ((mem X) A_27a00)
% 149.20/149.47 Found eq_ref00:=(eq_ref0 ((ap F0) X)):(((eq fofType) ((ap F0) X)) ((ap F0) X))
% 149.20/149.47 Found (eq_ref0 ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 149.20/149.47 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 149.20/149.47 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 149.20/149.47 Found (fun (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 149.20/149.47 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((mem X) A0)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 149.20/149.47 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F0) X))) as proof of (forall (X:fofType), (((mem X) A0)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 149.20/149.47 Found eq_ref00:=(eq_ref0 ((ap F0) X)):(((eq fofType) ((ap F0) X)) ((ap F0) X))
% 149.20/149.47 Found (eq_ref0 ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 165.49/165.77 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 165.49/165.77 Found ((eq_ref fofType) ((ap F0) X)) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 165.49/165.77 Found (fun (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 165.49/165.77 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F0) X))) as proof of (((mem X) A0)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)))
% 165.49/165.77 Found (fun (X:fofType) (x0:((mem X) A0))=> ((eq_ref fofType) ((ap F0) X))) as proof of (forall (X:fofType), (((mem X) A0)->(((eq fofType) ((ap F0) X)) ((ap ((ap (c_2Erelation_2EWF A_27a)) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))))
% 165.49/165.77 Found x0:((mem X) A_27a00)
% 165.49/165.77 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A_27a00)
% 165.49/165.77 Found x0 as proof of ((mem X) A_27a00)
% 165.49/165.77 Found x0:((mem X) A)
% 165.49/165.77 Instantiate: A1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A)
% 165.49/165.77 Found x0 as proof of ((mem X) A)
% 165.49/165.77 Found x0:((mem X) A)
% 165.49/165.77 Instantiate: A1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A)
% 165.49/165.77 Found x0 as proof of ((mem X) A)
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Instantiate: A:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Found x0 as proof of ((mem X) A_27a0)
% 165.49/165.77 Found x0:((mem X0) A_27a0)
% 165.49/165.77 Found x0 as proof of ((mem X0) A_27a0)
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Found x0 as proof of ((mem X) A_27a0)
% 165.49/165.77 Found x0:((mem X) A)
% 165.49/165.77 Instantiate: A0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A)
% 165.49/165.77 Found x0 as proof of ((mem X) A)
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 165.49/165.77 Found x0:((mem X) A_27a0)
% 165.49/165.77 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 165.49/165.77 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a0)
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a00)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a00)
% 202.88/203.24 Found x0 as proof of ((mem X) A_27a00)
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Found x0 as proof of ((mem X) A_27a0)
% 202.88/203.24 Found x0:((mem X0) A_27a00)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X0) A_27a00)
% 202.88/203.24 Found x0 as proof of ((mem X0) A_27a00)
% 202.88/203.24 Found x0:((mem X) A)
% 202.88/203.24 Instantiate: A1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A)
% 202.88/203.24 Found x0 as proof of ((mem X) A)
% 202.88/203.24 Found x1:((mem X0) A_27a0)
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Found x0 as proof of ((mem X) A_27a0)
% 202.88/203.24 Found x1:((mem X0) A_27a0)
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Found x0 as proof of ((mem X) A_27a0)
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Found x1 as proof of ((mem X0) A_27a00)
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Found x1 as proof of ((mem X0) A_27a00)
% 202.88/203.24 Found x0:((mem X) A_27a00)
% 202.88/203.24 Found x0 as proof of ((mem X) A_27a00)
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Found x1 as proof of ((mem X0) A_27a00)
% 202.88/203.24 Found x1:((mem X0) A_27a0)
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Found x1 as proof of ((mem X0) A_27a00)
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x0:((mem X) A_27a0)
% 202.88/203.24 Found x0 as proof of ((mem X) A_27a0)
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 202.88/203.24 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 202.88/203.24 Found x1:((mem X0) A_27a00)
% 202.88/203.24 Found x1 as proof of ((mem X0) A_27a00)
% 249.10/249.49 Found x1:((mem X0) A_27a00)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a00)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a00:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a0)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a0)
% 249.10/249.49 Found x0:((mem X) A_27a00)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a00)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a00)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a0)
% 249.10/249.49 Found x0:((mem X0) A_27a0)
% 249.10/249.49 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X0) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a0)
% 249.10/249.49 Found x0:((mem X0) A_27a00)
% 249.10/249.49 Found x0 as proof of ((mem X0) A_27a00)
% 249.10/249.49 Found x0:((mem X) A_27a00)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a00)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A)
% 249.10/249.49 Instantiate: A1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A)
% 249.10/249.49 Found x0 as proof of ((mem X) A)
% 249.10/249.49 Found x0:((mem X) A)
% 249.10/249.49 Instantiate: A1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A)
% 249.10/249.49 Found x0 as proof of ((mem X) A)
% 249.10/249.49 Found x0:((mem X0) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a0)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x1:((mem X0) A_27a0)
% 249.10/249.49 Found x1 as proof of ((mem X0) A_27a0)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Found x0 as proof of ((mem X) A_27a0)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A)
% 249.10/249.49 Instantiate: A0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A)
% 249.10/249.49 Found x0 as proof of ((mem X) A)
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 249.10/249.49 Found x0:((mem X) A_27a0)
% 249.10/249.49 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 249.10/249.49 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A)
% 292.57/292.91 Instantiate: A0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A)
% 292.57/292.91 Found x0 as proof of ((mem X) A)
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X0) A_27a00)
% 292.57/292.91 Found x0 as proof of ((mem X0) A_27a00)
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a00)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a00)
% 292.57/292.91 Found x0 as proof of ((mem X) A_27a00)
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Found x0 as proof of ((mem X) A_27a0)
% 292.57/292.91 Found x0:((mem X) A)
% 292.57/292.91 Instantiate: A1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A)
% 292.57/292.91 Found x0 as proof of ((mem X) A)
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Found x0 as proof of ((mem X) A_27a0)
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X0) A_27a0)
% 292.57/292.91 Found x0 as proof of ((mem X0) A_27a0)
% 292.57/292.91 Found x1:((mem X0) A_27a0)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x1 as proof of ((mem X0) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a00)
% 292.57/292.91 Instantiate: A_27a0:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a00)
% 292.57/292.91 Found x0 as proof of ((mem X) A_27a00)
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Instantiate: A_27a1:=(ty_2Ewellorder_2Ewellorder A_27a):del
% 292.57/292.91 Found x0 as proof of ((mem X) (ty_2Ewellorder_2Ewellorder A_27a))
% 292.57/292.91 Found x0:((mem X) A_27a0)
% 292.57/292.91 Found x0 as proof of ((mem X) A_27a0)
% 292.57/292.91 Found eq_ref00:=(eq_ref0 ((ap F) X)):(((eq fofType) ((ap F) X)) ((ap F) X))
% 292.57/292.91 Found (eq_ref0 ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A0) (ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 292.57/292.91 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A0) (ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 292.57/292.91 Found ((eq_ref fofType) ((ap F) X)) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A0) (ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X))
% 292.57/292.91 Found (fun (x0:((mem X) A1))=> ((eq_ref fofType) ((ap F) X))) as proof of (((eq fofType) ((ap F) X)) ((ap ((ap ((lam A0) (ap ((lam A) (ap (c_2Erelation_2EWF A_27a)))))) ((lam A_27a) (fun (V1x:fofType)=> ((lam A_27a) (fun (V2y:fofType)=> ((ap ((ap (c_2Ebool_2EIN ((ty_2Epair_2Eprod A_27a) A_27a))) ((ap ((ap ((c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) ((ap (c_2Eset__relation_2Estrict A_27a)) ((ap (c_2Ewellorder_2Ewellorder__REP A_27a)) V0w))))))))) X)
%------------------------------------------------------------------------------