TSTP Solution File: SEV379^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV379^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n116.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 13:34:07 EDT 2014
% Result : Timeout 300.05s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV379^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.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 09:00:26 CDT 2014
% % CPUTime : 300.05
% 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 0xae3b00>, <kernel.DependentProduct object at 0xae3c68>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xf1e7e8>, <kernel.DependentProduct object at 0xae35f0>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (Xd:fofType), (((and ((and ((and ((and (cGVB_M Xa)) (cGVB_M Xb))) (cGVB_M Xc))) (cGVB_M Xd))) (((eq fofType) ((cGVB_OP Xa) Xb)) ((cGVB_OP Xc) Xd)))->((and (((eq fofType) Xa) Xc)) (((eq fofType) Xb) Xd)))) of role conjecture named cGVB_OP_PROP_1
% Conjecture to prove = (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (Xd:fofType), (((and ((and ((and ((and (cGVB_M Xa)) (cGVB_M Xb))) (cGVB_M Xc))) (cGVB_M Xd))) (((eq fofType) ((cGVB_OP Xa) Xb)) ((cGVB_OP Xc) Xd)))->((and (((eq fofType) Xa) Xc)) (((eq fofType) Xb) Xd)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (Xd:fofType), (((and ((and ((and ((and (cGVB_M Xa)) (cGVB_M Xb))) (cGVB_M Xc))) (cGVB_M Xd))) (((eq fofType) ((cGVB_OP Xa) Xb)) ((cGVB_OP Xc) Xd)))->((and (((eq fofType) Xa) Xc)) (((eq fofType) Xb) Xd))))']
% Parameter fofType:Type.
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Parameter cGVB_M:(fofType->Prop).
% Trying to prove (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (Xd:fofType), (((and ((and ((and ((and (cGVB_M Xa)) (cGVB_M Xb))) (cGVB_M Xc))) (cGVB_M Xd))) (((eq fofType) ((cGVB_OP Xa) Xb)) ((cGVB_OP Xc) Xd)))->((and (((eq fofType) Xa) Xc)) (((eq fofType) Xb) Xd))))
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref fofType) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref fofType) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xb)->(P Xb))
% Found (eq_ref00 P) as proof of (P0 Xb)
% Found ((eq_ref0 Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 (((eq fofType) Xb) Xd)):(((eq Prop) (((eq fofType) Xb) Xd)) (((eq fofType) Xb) Xd))
% Found (eq_ref0 (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found eq_ref00:=(eq_ref0 (((eq fofType) Xb) Xd)):(((eq Prop) (((eq fofType) Xb) Xd)) (((eq fofType) Xb) Xd))
% Found (eq_ref0 (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% Found conj as proof of b
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 (((eq fofType) Xb) Xd)):(((eq Prop) (((eq fofType) Xb) Xd)) (((eq fofType) Xb) Xd))
% Found (eq_ref0 (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% Found conj as proof of b
% Found x10:=(x1 (fun (x4:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x6:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xb)->(P Xb))
% Found (eq_ref00 P) as proof of (P0 Xb)
% Found ((eq_ref0 Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x0:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found x0:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_ref00:=(eq_ref0 (((eq fofType) Xb) Xd)):(((eq Prop) (((eq fofType) Xb) Xd)) (((eq fofType) Xb) Xd))
% Found (eq_ref0 (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x10:=(x1 (fun (x4:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x2:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x2 as proof of (P0 b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found x10:=(x1 (fun (x6:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x6:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x6:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x6:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref fofType) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref fofType) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref000:=(eq_ref00 P):((P Xb)->(P Xb))
% Found (eq_ref00 P) as proof of (P0 Xb)
% Found ((eq_ref0 Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found x3:(cGVB_M Xd)
% Instantiate: b:=(cGVB_M Xd):Prop
% Found x3 as proof of 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 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) 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 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found x10:=(x1 (fun (x8:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x8:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x8:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x8:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x8:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x8:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found x3:(cGVB_M Xd)
% Instantiate: b:=(cGVB_M Xd):Prop
% Found x3 as proof of b
% Found x3:(cGVB_M Xd)
% Instantiate: b:=(cGVB_M Xd):Prop
% Found x3 as proof of b
% Found x3:(cGVB_M Xd)
% Instantiate: b:=(cGVB_M Xd):Prop
% Found x3 as proof of b
% Found x0:(P Xd)
% Instantiate: b:=Xd:fofType
% Found x0 as proof of (P0 b)
% Found x0:(P Xc)
% Instantiate: b:=Xc:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) Xb) Xd)):(((eq Prop) (((eq fofType) Xb) Xd)) (((eq fofType) Xb) Xd))
% Found (eq_ref0 (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found ((eq_ref Prop) (((eq fofType) Xb) Xd)) as proof of (((eq Prop) (((eq fofType) Xb) Xd)) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found x4:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x4 as proof of (P0 b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x4 as proof of (P0 b)
% Found x10:=(x1 (fun (x6:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x6:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x6:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x6:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x2 as proof of (P0 b)
% Found x2:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) 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 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) 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 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found x0:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x0 as proof of (P0 b)
% Found x0:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref fofType) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref fofType) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xb)->(P Xb))
% Found (eq_ref00 P) as proof of (P0 Xb)
% Found ((eq_ref0 Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found (((eq_ref fofType) Xb) P) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found x10:=(x1 (fun (x8:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x8:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x8:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x8:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x8:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x8:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% Found relational_choice as proof of b
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found x2:(P Xc)
% Instantiate: b:=Xc:fofType
% Found x2 as proof of (P0 b)
% Found x2:(P Xd)
% Instantiate: b:=Xd:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% Found relational_choice as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x4:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x4:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% Found relational_choice as proof of b
% Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% Found relational_choice as proof of b
% Found x10:=(x1 (fun (x6:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x6:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x6:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x6:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x6:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y)))))))))):Prop
% Found relational_choice as proof of b
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref000:=(eq_ref00 P):((P Xd)->(P Xd))
% Found (eq_ref00 P) as proof of (P0 Xd)
% Found ((eq_ref0 Xd) P) as proof of (P0 Xd)
% Found (((eq_ref fofType) Xd) P) as proof of (P0 Xd)
% Found (((eq_ref fofType) Xd) P) as proof of (P0 Xd)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref000:=(eq_ref00 P):((P Xc)->(P Xc))
% Found (eq_ref00 P) as proof of (P0 Xc)
% Found ((eq_ref0 Xc) P) as proof of (P0 Xc)
% Found (((eq_ref fofType) Xc) P) as proof of (P0 Xc)
% Found (((eq_ref fofType) Xc) P) as proof of (P0 Xc)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x2:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x2:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found x4:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x4 as proof of (P0 b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x2 as proof of (P0 b)
% Found x2:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x2 as proof of (P0 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 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) 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 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found x6:(P Xb)
% Instantiate: b:=Xb:fofType
% Found x6 as proof of (P0 b)
% Found x6:(P Xa)
% Instantiate: b:=Xa:fofType
% Found x6 as proof of (P0 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 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) 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 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found x10:=(x1 (fun (x8:fofType)=> (P Xa))):((P Xa)->(P Xa))
% Found (x1 (fun (x8:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found (x1 (fun (x8:fofType)=> (P Xa))) as proof of (P0 Xa)
% Found x10:=(x1 (fun (x8:fofType)=> (P Xb))):((P Xb)->(P Xb))
% Found (x1 (fun (x8:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found (x1 (fun (x8:fofType)=> (P Xb))) as proof of (P0 Xb)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found x10:=(x1 (fun (x2:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found x10:=(x1 (fun (x2:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 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 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) 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 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xd)
% Found eq_ref00:=(eq_ref0 Xc):(((eq fofType) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq fofType) Xc) b0)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b0)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b0)
% Found ((eq_ref fofType) Xc) as proof of (((eq fofType) Xc) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xa)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xa)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xa)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xa)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xb)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xb)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xb)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xb)
% Found eq_ref00:=(eq_ref0 Xd):(((eq fofType) Xd) Xd)
% Found (eq_ref0 Xd) as proof of (((eq fofType) Xd) b0)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b0)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b0)
% Found ((eq_ref fofType) Xd) as proof of (((eq fofType) Xd) b0)
% Found x2:(P Xd)
% Instantiate: b:=Xd:fofType
% Found x2 as proof of (P0 b)
% Found x2:(P Xc)
% Instantiate: b:=Xc:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found x4:(P Xd)
% Instantiate: b:=Xd:fofType
% Found x4 as proof of (P0 b)
% Found x4:(P Xc)
% Instantiate: b:=Xc:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found eq_ref00:=(eq_ref0 Xa):(((eq fofType) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found ((eq_ref fofType) Xa) as proof of (((eq fofType) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xc)
% Found eq_ref00:=(eq_ref0 Xb):(((eq fofType) Xb) Xb)
% Found (eq_ref0 Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found ((eq_ref fofType) Xb) as proof of (((eq fofType) Xb) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xd)
% Found eq_ref00
% EOF
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