TSTP Solution File: MSC025^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : MSC025^1 : TPTP v6.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n106.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:26:43 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : MSC025^1 : TPTP v6.1.0. Released v5.5.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:38:51 CDT 2014
% % CPUTime : 300.02
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x888a70>, <kernel.Constant object at 0x8885a8>) of role type named one
% Using role type
% Declaring one:fofType
% FOF formula (<kernel.Constant object at 0xc605f0>, <kernel.Single object at 0x888f80>) of role type named two
% Using role type
% Declaring two:fofType
% FOF formula (forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))) of role axiom named binary_exhaust
% A new axiom: (forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two)))
% FOF formula (not (((eq fofType) one) two)) of role axiom named binary_distinc
% A new axiom: (not (((eq fofType) one) two))
% FOF formula ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) of role conjecture named goal
% Conjecture to prove = ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))):Prop
% We need to prove ['((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))']
% Parameter fofType:Type.
% Parameter one:fofType.
% Parameter two:fofType.
% Axiom binary_exhaust:(forall (X:fofType), ((or (((eq fofType) X) one)) (((eq fofType) X) two))).
% Axiom binary_distinc:(not (((eq fofType) one) two)).
% Trying to prove ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found eta_expansion000:=(eta_expansion00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))):(((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) (fun (x:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found (eta_expansion00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found ((eta_expansion0 Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))):(((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) (fun (x:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found (eta_expansion00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found ((eta_expansion0 Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X0:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X0) two)->False)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X))))))
% Found (fun (x:(Prop->fofType))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X0:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X0) two)->False)
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found (x10 ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of ((((eq fofType) X0) one)->False)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found x1:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of (((eq fofType) one) two)
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x0:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found x0 as proof of (((eq fofType) one) two)
% Found (binary_distinc x0) as proof of False
% Found (fun (x00:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc x0)) as proof of False
% Found (fun (x0:(((eq fofType) X0) two)) (x00:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc x0)) as proof of (not (((eq fofType) (x X)) (x (X->False))))
% Found (fun (x0:(((eq fofType) X0) two)) (x00:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc x0)) as proof of ((((eq fofType) X0) two)->(not (((eq fofType) (x X)) (x (X->False)))))
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found (x01 ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0))) as proof of False
% Found (fun (x00:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)))) as proof of False
% Found (fun (x0:(((eq fofType) X0) one)) (x00:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)))) as proof of (not (((eq fofType) (x X)) (x (X->False))))
% Found (fun (x0:(((eq fofType) X0) one)) (x00:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)))) as proof of ((((eq fofType) X0) one)->(not (((eq fofType) (x X)) (x (X->False)))))
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found (x10 ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of ((((eq fofType) X0) one)->False)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x0:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found x0 as proof of (((eq fofType) one) two)
% Found (binary_distinc x0) as proof of False
% Found (fun (x00:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc x0)) as proof of False
% Found (fun (x0:(((eq fofType) X0) two)) (x00:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc x0)) as proof of (not (((eq fofType) (x X)) (x (not X))))
% Found (fun (x0:(((eq fofType) X0) two)) (x00:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc x0)) as proof of ((((eq fofType) X0) two)->(not (((eq fofType) (x X)) (x (not X)))))
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found (x01 ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0))) as proof of False
% Found (fun (x00:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)))) as proof of False
% Found (fun (x0:(((eq fofType) X0) one)) (x00:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)))) as proof of (not (((eq fofType) (x X)) (x (not X))))
% Found (fun (x0:(((eq fofType) X0) one)) (x00:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc ((x0 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X0)))) as proof of ((((eq fofType) X0) one)->(not (((eq fofType) (x X)) (x (not X)))))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x:(((eq fofType) X) two)
% Instantiate: X:=one:fofType
% Found x as proof of (((eq fofType) one) two)
% Found (binary_distinc x) as proof of False
% Found (fun (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc x)) as proof of False
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc x)) as proof of (not (((eq fofType) (x0 X0)) (x0 (X0->False))))
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc x)) as proof of (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False)))))
% Found (ex_intro000 (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc x))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found x:(((eq fofType) X) two)
% Instantiate: X:=one:fofType
% Found x as proof of (((eq fofType) one) two)
% Found (binary_distinc x) as proof of False
% Found (fun (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc x)) as proof of False
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc x)) as proof of (not (((eq fofType) (x0 X0)) (x0 (not X0))))
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc x)) as proof of (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X)))))
% Found (ex_intro000 (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc x))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found (x2 ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X))) as proof of False
% Found (fun (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)))) as proof of False
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)))) as proof of (not (((eq fofType) (x0 X0)) (x0 (X0->False))))
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)))) as proof of (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False)))))
% Found (ex_intro000 (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (X0->False))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X))))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found (x2 ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X))) as proof of False
% Found (fun (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)))) as proof of False
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)))) as proof of (not (((eq fofType) (x0 X0)) (x0 (not X0))))
% Found (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X)))) as proof of (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X)))))
% Found (ex_intro000 (fun (X0:Prop) (x1:(((eq fofType) (x0 X0)) (x0 (not X0))))=> (binary_distinc ((x (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X))))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X0:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X0) two)->False)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X0:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X0) two)->False)
% Found eq_ref00:=(eq_ref0 a):(((eq ((Prop->fofType)->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found ((eq_ref ((Prop->fofType)->Prop)) a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found ((eq_ref ((Prop->fofType)->Prop)) a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found ((eq_ref ((Prop->fofType)->Prop)) a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((Prop->fofType)->Prop)) b) (fun (x:(Prop->fofType))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found ((eta_expansion_dep0 (fun (x1:(Prop->fofType))=> Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found (x10 ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of ((((eq fofType) X0) one)->False)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found x1:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of (((eq fofType) one) two)
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 a):(((eq ((Prop->fofType)->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found ((eq_ref ((Prop->fofType)->Prop)) a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found ((eq_ref ((Prop->fofType)->Prop)) a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found ((eq_ref ((Prop->fofType)->Prop)) a) as proof of (((eq ((Prop->fofType)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((Prop->fofType)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found ((eq_ref ((Prop->fofType)->Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found ((eq_ref ((Prop->fofType)->Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found ((eq_ref ((Prop->fofType)->Prop)) b) as proof of (((eq ((Prop->fofType)->Prop)) b) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) two)
% Found (x10 ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of False
% Found (fun (x1:(((eq fofType) X0) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X0)))) as proof of ((((eq fofType) X0) one)->False)
% Found x1:(P one)
% Instantiate: b:=one:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x1:(P one)
% Instantiate: b:=one:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x01:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))):(((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) (fun (x:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found (eta_expansion_dep00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found ((eta_expansion_dep0 (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))):(((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) (fun (x:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found (eta_expansion_dep00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found ((eta_expansion_dep0 (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False))))))) b)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x000:=(x00 (fun (x1:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x10 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))):(((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) (fun (x:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found (eta_expansion_dep00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found ((eta_expansion_dep0 (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion_dep (Prop->fofType)) (fun (x1:(Prop->fofType))=> Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))):(((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) (fun (x:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found (eta_expansion00 (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found ((eta_expansion0 Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found (((eta_expansion (Prop->fofType)) Prop) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) as proof of (((eq ((Prop->fofType)->Prop)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X))))))) b)
% Found x01:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x20 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:(((eq fofType) X1) two)
% Instantiate: X1:=one:fofType
% Found x00 as proof of (((eq fofType) one) two)
% Found (binary_distinc x00) as proof of False
% Found (fun (x01:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc x00)) as proof of False
% Found (fun (x00:(((eq fofType) X1) two)) (x01:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc x00)) as proof of (not (((eq fofType) (x X)) (x (X->False))))
% Found (fun (x00:(((eq fofType) X1) two)) (x01:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc x00)) as proof of ((((eq fofType) X1) two)->(not (((eq fofType) (x X)) (x (X->False)))))
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x000 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x01:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x00:(((eq fofType) X1) one)) (x01:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)))) as proof of (not (((eq fofType) (x X)) (x (X->False))))
% Found (fun (x00:(((eq fofType) X1) one)) (x01:(((eq fofType) (x X)) (x (X->False))))=> (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->(not (((eq fofType) (x X)) (x (X->False)))))
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (X->False))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (X->False)))))))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x000:=(x00 (fun (x1:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x10 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x20 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:(((eq fofType) X1) two)
% Instantiate: X1:=one:fofType
% Found x00 as proof of (((eq fofType) one) two)
% Found (binary_distinc x00) as proof of False
% Found (fun (x01:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc x00)) as proof of False
% Found (fun (x00:(((eq fofType) X1) two)) (x01:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc x00)) as proof of (not (((eq fofType) (x X)) (x (not X))))
% Found (fun (x00:(((eq fofType) X1) two)) (x01:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc x00)) as proof of ((((eq fofType) X1) two)->(not (((eq fofType) (x X)) (x (not X)))))
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x000 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x01:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x00:(((eq fofType) X1) one)) (x01:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)))) as proof of (not (((eq fofType) (x X)) (x (not X))))
% Found (fun (x00:(((eq fofType) X1) one)) (x01:(((eq fofType) (x X)) (x (not X))))=> (binary_distinc ((x00 (fun (x2:fofType)=> (((eq fofType) x2) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->(not (((eq fofType) (x X)) (x (not X)))))
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:Prop), (not (((eq fofType) (x0 X)) (x0 (not X))))))
% Found (fun (x0:(Prop->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(Prop->fofType)), (((eq Prop) (f x)) (forall (X:Prop), (not (((eq fofType) (x X)) (x (not X)))))))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) one)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) one)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) one)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) two)->(P two))
% Found x2:(P one)
% Instantiate: X1:=one:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P two)
% Found ((x3 P) x2) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) two)->(P two))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P two)
% Found ((x3 P) x1) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x01:=(x0 (fun (x1:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found x2:(P one)
% Instantiate: X1:=one:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P two)
% Found ((x3 P) x2) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P two)
% Found ((x3 P) x1) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) two)->(P two))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) one)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) one)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) one)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found x1:(((eq fofType) X1) two)
% Instantiate: X1:=one:fofType
% Found (fun (x1:(((eq fofType) X1) two))=> x1) as proof of (((eq fofType) one) X0)
% Found (fun (x1:(((eq fofType) X1) two))=> x1) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) X0))
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1:(P1 two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P1 X0)
% Found (x20 x1) as proof of (P1 one)
% Found ((x2 P1) x1) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of ((((eq fofType) X0) one)->(P1 one))
% Found x1:(P1 two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P1 X0)
% Found (x20 x1) as proof of (P1 one)
% Found ((x2 P1) x1) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of ((((eq fofType) X0) one)->(P1 one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) two)->(P two))
% Found x1:(P b)
% Instantiate: X0:=b:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x2:(P one)
% Instantiate: X1:=one:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P two)
% Found ((x3 P) x2) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P two)
% Found ((x3 P) x1) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x01:=(x0 (fun (x1:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found x2:(P one)
% Instantiate: X1:=one:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P two)
% Found ((x3 P) x2) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P two)
% Found ((x3 P) x1) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of (P two)
% Found (fun (x3:(((eq fofType) X1) two))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) two)->(P two))
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) X0))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) X0))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) X0))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) X0))
% Found x1:(P1 two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P1 X0)
% Found (x20 x1) as proof of (P1 one)
% Found ((x2 P1) x1) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of ((((eq fofType) X0) one)->(P1 one))
% Found x1:(P1 two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P1 X0)
% Found (x20 x1) as proof of (P1 one)
% Found ((x2 P1) x1) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of (P1 one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P1) x1)) as proof of ((((eq fofType) X0) one)->(P1 one))
% Found x1:(P b)
% Instantiate: X0:=b:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) b))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) b))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) one))
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) two) one)->(((eq fofType) one) two))
% Instantiate: X0:=two:fofType
% Found eq_sym000 as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found x2:(P two)
% Instantiate: X1:=two:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P one)
% Found ((x3 P) x2) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x2:(P two)
% Instantiate: X1:=two:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P one)
% Found ((x3 P) x2) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P X0)
% Found ((x2 P) x1) as proof of (P X0)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of (P X0)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) two)->(P X0))
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) one))
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P one)
% Found ((x3 P) x1) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x0:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found x0 as proof of (((eq fofType) one) two)
% Found (binary_distinc x0) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0)) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0)) as proof of (not (((eq fofType) (x1 X1)) (x1 (X1->False))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0)) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (X->False)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found x:(((eq fofType) X) two)
% Instantiate: X:=one:fofType
% Found x as proof of (((eq fofType) one) two)
% Found (binary_distinc x) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x)) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x)) as proof of (not (((eq fofType) (x1 X1)) (x1 (X1->False))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x)) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (X->False)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found x0:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found x0 as proof of (((eq fofType) one) two)
% Found (binary_distinc x0) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0)) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0)) as proof of (not (((eq fofType) (x1 X1)) (x1 (X1->False))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0)) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (X->False)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc x0))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x2:(P two)
% Instantiate: X1:=two:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P one)
% Found ((x3 P) x2) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) one)->(P one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) two) one)->(((eq fofType) one) two))
% Instantiate: X0:=two:fofType
% Found eq_sym000 as proof of ((((eq fofType) X0) one)->(((eq fofType) one) b))
% Found x1:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of (((eq fofType) one) b)
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of ((((eq fofType) X0) two)->(((eq fofType) one) b))
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P one)
% Found ((x3 P) x1) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P b)
% Found ((x2 P) x1) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P b))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P b)
% Found ((x2 P) x1) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P b))
% Found x2:(P two)
% Instantiate: X1:=two:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P one)
% Found ((x3 P) x2) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) one)->(P one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) X0))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) X0))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) X0))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) two) X0))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) X0))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) X0))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) two) X0))
% Found x2:(P two)
% Instantiate: X1:=two:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P one)
% Found ((x3 P) x2) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x1:(P one)
% Instantiate: X1:=one:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P X0)
% Found ((x2 P) x1) as proof of (P X0)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of (P X0)
% Found (fun (x2:(((eq fofType) X1) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) two)->(P X0))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X1) two)->(((eq fofType) two) X1))
% Found (eq_sym01 two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found ((eq_sym0 X1) two) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X1) one))):((((eq fofType) X1) one)->(((eq fofType) X1) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X1) one))) as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) one))
% Found x0:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found x0 as proof of (((eq fofType) one) two)
% Found (binary_distinc x0) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0)) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0)) as proof of (not (((eq fofType) (x1 X1)) (x1 (not X1))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0)) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (not X)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found x0:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found x0 as proof of (((eq fofType) one) two)
% Found (binary_distinc x0) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0)) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0)) as proof of (not (((eq fofType) (x1 X1)) (x1 (not X1))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0)) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (not X)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x0))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found x:(((eq fofType) X) two)
% Instantiate: X:=one:fofType
% Found x as proof of (((eq fofType) one) two)
% Found (binary_distinc x) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x)) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x)) as proof of (not (((eq fofType) (x1 X1)) (x1 (not X1))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x)) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (not X)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc x))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found x1:(P one)
% Instantiate: b:=one:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x1:(P one)
% Instantiate: b:=one:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P one)
% Found ((x3 P) x1) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x2:(P two)
% Instantiate: X1:=two:fofType
% Found x2 as proof of (P X1)
% Found (x30 x2) as proof of (P one)
% Found ((x3 P) x2) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x2)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x1:(P b)
% Instantiate: X0:=b:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P b)
% Found ((x2 P) x1) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P b))
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x30 x1) as proof of (P one)
% Found ((x3 P) x1) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of (P one)
% Found (fun (x3:(((eq fofType) X1) one))=> ((x3 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x1:(P one)
% Instantiate: b:=one:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x1:(P one)
% Instantiate: b:=one:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 X0):(((eq fofType) X0) X0)
% Found (eq_ref0 X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found ((eq_ref fofType) X0) as proof of (((eq fofType) X0) b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) two) one)->(((eq fofType) one) two))
% Instantiate: X1:=two:fofType
% Found eq_sym000 as proof of ((((eq fofType) X1) one)->(((eq fofType) X0) two))
% Found x1:(((eq fofType) X1) two)
% Instantiate: X1:=one:fofType
% Found (fun (x1:(((eq fofType) X1) two))=> x1) as proof of (((eq fofType) X0) two)
% Found (fun (x1:(((eq fofType) X1) two))=> x1) as proof of ((((eq fofType) X1) two)->(((eq fofType) X0) two))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found x1:(P b)
% Instantiate: X0:=b:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x1:(P X0)
% Instantiate: X1:=X0:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) two)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x01:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x01:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P two)
% Found ((x2 P) x1) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P two)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P two))
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found x1:(P two)
% Instantiate: X1:=two:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P X0)
% Found ((x2 P) x1) as proof of (P X0)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of (P X0)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) one)->(P X0))
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found binary_distinc:(not (((eq fofType) one) two))
% Instantiate: X1:=one:fofType
% Found binary_distinc as proof of ((((eq fofType) X1) two)->False)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found (x3 ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X))) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)))) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)))) as proof of (not (((eq fofType) (x1 X1)) (x1 (X1->False))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)))) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (X->False)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (X1->False))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X))))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (X->False)))))))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x000:=(x00 (fun (x1:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found x1:(P one)
% Instantiate: X0:=one:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P b)
% Found ((x2 P) x1) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of (P b)
% Found (fun (x2:(((eq fofType) X0) two))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) two)->(P b))
% Found x1:(P X0)
% Instantiate: X1:=X0:fofType
% Found x1 as proof of (P X1)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X1) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X1) one)->(P one))
% Found x01:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x01:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x10 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x20 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x2:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x2:fofType)=> (P one))) as proof of (P0 one)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) two)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) two)
% Found (x3 ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X))) as proof of False
% Found (fun (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)))) as proof of False
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)))) as proof of (not (((eq fofType) (x1 X1)) (x1 (not X1))))
% Found (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X)))) as proof of (forall (X:Prop), (not (((eq fofType) (x1 X)) (x1 (not X)))))
% Found (ex_intro000 (fun (X1:Prop) (x2:(((eq fofType) (x1 X1)) (x1 (not X1))))=> (binary_distinc ((x (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X))))) as proof of ((ex (Prop->fofType)) (fun (F:(Prop->fofType))=> (forall (X:Prop), (not (((eq fofType) (F X)) (F (not X)))))))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x000:=(x00 (fun (x1:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x00 (fun (x1:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x1:(((eq fofType) X0) two)
% Instantiate: X0:=one:fofType
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of (((eq fofType) b) two)
% Found (fun (x1:(((eq fofType) X0) two))=> x1) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P b))):((P b)->(P b))
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found (x0 (fun (x1:fofType)=> (P b))) as proof of (P0 b)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x0 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x10 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x1:(((eq fofType) X1) one))=> (binary_distinc ((x1 (fun (x3:fofType)=> (((eq fofType) x3) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found eq_ref00:=(eq_ref0 X1):(((eq fofType) X1) X1)
% Found (eq_ref0 X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found ((eq_ref fofType) X1) as proof of (((eq fofType) X1) two)
% Found (x20 ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)) as proof of (((eq fofType) one) two)
% Found (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of False
% Found (fun (x2:(((eq fofType) X1) one))=> (binary_distinc ((x2 (fun (x4:fofType)=> (((eq fofType) x4) two))) ((eq_ref fofType) X1)))) as proof of ((((eq fofType) X1) one)->False)
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X1) one)->(((eq fofType) one) X1))
% Found (eq_sym00 one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found ((eq_sym0 X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found (((eq_sym fofType) X1) one) as proof of ((((eq fofType) X1) one)->(((eq fofType) one) two))
% Found x10:=(x1 (fun (x2:fofType)=> (((eq fofType) X1) two))):((((eq fofType) X1) two)->(((eq fofType) X1) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found (x1 (fun (x2:fofType)=> (((eq fofType) X1) two))) as proof of ((((eq fofType) X1) two)->(((eq fofType) one) two))
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found x00:=(x0 (fun (x1:fofType)=> (P two))):((P two)->(P two))
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found (x0 (fun (x1:fofType)=> (P two))) as proof of (P0 two)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) one))):((((eq fofType) X0) one)->(((eq fofType) X0) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) one))) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_ref00:=(eq_ref0 two):(((eq fofType) two) two)
% Found (eq_ref0 two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found ((eq_ref fofType) two) as proof of (((eq fofType) two) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) one)
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found eq_sym010:=(eq_sym01 two):((((eq fofType) X0) two)->(((eq fofType) two) X0))
% Found (eq_sym01 two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found ((eq_sym0 X0) two) as proof of ((((eq fofType) X0) two)->(((eq fofType) two) one))
% Found x1:(((eq fofType) X0) one)
% Instantiate: X0:=two:fofType
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of (((eq fofType) two) one)
% Found (fun (x1:(((eq fofType) X0) one))=> x1) as proof of ((((eq fofType) X0) one)->(((eq fofType) two) one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found x1:(P two)
% Instantiate: X0:=two:fofType
% Found x1 as proof of (P X0)
% Found (x20 x1) as proof of (P one)
% Found ((x2 P) x1) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of (P one)
% Found (fun (x2:(((eq fofType) X0) one))=> ((x2 P) x1)) as proof of ((((eq fofType) X0) one)->(P one))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found eq_sym000:=(eq_sym00 one):((((eq fofType) X0) one)->(((eq fofType) one) X0))
% Found (eq_sym00 one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found ((eq_sym0 X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found (((eq_sym fofType) X0) one) as proof of ((((eq fofType) X0) one)->(((eq fofType) b) two))
% Found x00:=(x0 (fun (x1:fofType)=> (((eq fofType) X0) two))):((((eq fofType) X0) two)->(((eq fofType) X0) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found (x0 (fun (x1:fofType)=> (((eq fofType) X0) two))) as proof of ((((eq fofType) X0) two)->(((eq fofType) b) two))
% Found x1:(P two)
% Instantiate: b:=two:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 one):(((eq fofType) one) one)
% Found (eq_ref0 one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found ((eq_ref fofType) one) as proof of (((eq fofType) one) b)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found (x0 (fun (x1:fofType)=> (P one))) as proof of (P0 one)
% Found x00:=(x0 (fun (x1:fofType)=> (P one))):((P one)->(P one))
% Found (x0 (fun (
% EOF
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