TSTP Solution File: SYO544^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO544^1 : TPTP v7.5.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:52:04 EDT 2022
% Result : Timeout 300.06s 300.58s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SYO544^1 : TPTP v7.5.0. Released v5.2.0.
% 0.08/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Mar 13 19:17:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.38/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x160cb00>, <kernel.DependentProduct object at 0x160cb48>) of role type named eps
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring eps:((fofType->Prop)->fofType)
% 0.38/0.61 FOF formula (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P)))) of role axiom named choiceax
% 0.38/0.61 A new axiom: (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P))))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x16323b0>, <kernel.DependentProduct object at 0x160cd40>) of role type named caseoo
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring case:((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.38/0.61 FOF formula (((eq ((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType)))))) case) (fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V))))))) of role definition named caseood
% 0.38/0.61 A new definition: (((eq ((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType)))))) case) (fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V)))))))
% 0.38/0.61 Defined: case:=(fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V))))))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2afde2c3af80>, <kernel.DependentProduct object at 0x160cb48>) of role type named f0
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring f0:(Prop->Prop)
% 0.38/0.61 FOF formula (((eq Prop) (f0 False)) False) of role axiom named f0f
% 0.38/0.61 A new axiom: (((eq Prop) (f0 False)) False)
% 0.38/0.61 FOF formula (((eq Prop) (f0 True)) False) of role axiom named f0t
% 0.38/0.61 A new axiom: (((eq Prop) (f0 True)) False)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2afde2c169e0>, <kernel.DependentProduct object at 0x160ca70>) of role type named f1
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring f1:(Prop->Prop)
% 0.38/0.61 FOF formula (((eq Prop) (f1 False)) True) of role axiom named f1f
% 0.38/0.61 A new axiom: (((eq Prop) (f1 False)) True)
% 0.38/0.61 FOF formula (((eq Prop) (f1 True)) False) of role axiom named f1t
% 0.38/0.61 A new axiom: (((eq Prop) (f1 True)) False)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x160c998>, <kernel.DependentProduct object at 0x160ca70>) of role type named f2
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring f2:(Prop->Prop)
% 0.38/0.61 FOF formula (((eq Prop) (f2 False)) False) of role axiom named f2f
% 0.38/0.61 A new axiom: (((eq Prop) (f2 False)) False)
% 0.38/0.61 FOF formula (((eq Prop) (f2 True)) True) of role axiom named f2t
% 0.38/0.61 A new axiom: (((eq Prop) (f2 True)) True)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x160c9e0>, <kernel.DependentProduct object at 0x160cc20>) of role type named f3
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring f3:(Prop->Prop)
% 0.38/0.61 FOF formula (((eq Prop) (f3 False)) True) of role axiom named f3f
% 0.38/0.61 A new axiom: (((eq Prop) (f3 False)) True)
% 0.38/0.61 FOF formula (((eq Prop) (f3 True)) True) of role axiom named f3t
% 0.38/0.61 A new axiom: (((eq Prop) (f3 True)) True)
% 0.38/0.61 FOF formula (forall (X:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))) of role conjecture named conj
% 0.38/0.61 Conjecture to prove = (forall (X:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))):Prop
% 15.31/15.50 Parameter fofType_DUMMY:fofType.
% 15.31/15.50 We need to prove ['(forall (X:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))']
% 15.31/15.50 Parameter fofType:Type.
% 15.31/15.50 Parameter eps:((fofType->Prop)->fofType).
% 15.31/15.50 Axiom choiceax:(forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P)))).
% 15.31/15.50 Definition case:=(fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V)))))):((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 15.31/15.50 Parameter f0:(Prop->Prop).
% 15.31/15.50 Axiom f0f:(((eq Prop) (f0 False)) False).
% 15.31/15.50 Axiom f0t:(((eq Prop) (f0 True)) False).
% 15.31/15.50 Parameter f1:(Prop->Prop).
% 15.31/15.50 Axiom f1f:(((eq Prop) (f1 False)) True).
% 15.31/15.50 Axiom f1t:(((eq Prop) (f1 True)) False).
% 15.31/15.50 Parameter f2:(Prop->Prop).
% 15.31/15.50 Axiom f2f:(((eq Prop) (f2 False)) False).
% 15.31/15.50 Axiom f2t:(((eq Prop) (f2 True)) True).
% 15.31/15.50 Parameter f3:(Prop->Prop).
% 15.31/15.50 Axiom f3f:(((eq Prop) (f3 False)) True).
% 15.31/15.50 Axiom f3t:(((eq Prop) (f3 True)) True).
% 15.31/15.50 Trying to prove (forall (X:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 15.31/15.50 Found eq_ref00:=(eq_ref0 (((((case f3) X) Y) U) V)):(((eq fofType) (((((case f3) X) Y) U) V)) (((((case f3) X) Y) U) V))
% 15.31/15.50 Found (eq_ref0 (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 15.31/15.50 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 15.31/15.50 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 15.31/15.50 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 15.31/15.50 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 15.31/15.50 Found (eq_ref0 b) as proof of (((eq fofType) b) V)
% 15.31/15.50 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 15.31/15.50 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 15.31/15.50 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 15.31/15.50 Found eq_ref00:=(eq_ref0 (((eq fofType) (((((case f3) X) Y) U) V)) V)):(((eq Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 15.31/15.50 Found (eq_ref0 (((eq fofType) (((((case f3) X) Y) U) V)) V)) as proof of (((eq Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) b)
% 15.31/15.50 Found ((eq_ref Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) as proof of (((eq Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) b)
% 15.31/15.50 Found ((eq_ref Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) as proof of (((eq Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) b)
% 15.31/15.50 Found ((eq_ref Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) as proof of (((eq Prop) (((eq fofType) (((((case f3) X) Y) U) V)) V)) b)
% 15.31/15.50 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) (fun (x:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V)))))
% 16.33/16.49 Found (eta_expansion_dep00 (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) b)
% 16.33/16.49 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) b)
% 16.33/16.49 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) b)
% 16.33/16.49 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) b)
% 16.33/16.49 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))) b)
% 16.33/16.49 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) (fun (x:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 17.46/17.63 Found (eta_expansion_dep00 (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 17.46/17.63 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 17.46/17.63 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 17.46/17.63 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 17.46/17.63 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 17.46/17.63 Found eta_expansion000:=(eta_expansion00 (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) (fun (x:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 18.87/19.03 Found (eta_expansion00 (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 18.87/19.03 Found ((eta_expansion0 Prop) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 18.87/19.03 Found (((eta_expansion fofType) Prop) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 18.87/19.03 Found (((eta_expansion fofType) Prop) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 18.87/19.03 Found (((eta_expansion fofType) Prop) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 18.87/19.04 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) (fun (x:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 20.45/20.63 Found (eta_expansion_dep00 (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 20.45/20.63 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 20.45/20.63 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 20.45/20.63 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 20.45/20.63 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))) b)
% 20.45/20.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 20.45/20.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 20.45/20.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 20.45/20.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 20.45/20.63 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 21.76/21.97 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V)))))
% 21.76/21.97 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 21.76/21.97 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 21.76/21.97 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 21.76/21.97 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 21.76/21.97 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V))))
% 21.76/21.97 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (X0:fofType) (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X0) Y) U) V)) X0)) (((eq fofType) (((((case f1) X0) Y) U) V)) Y))) (((eq fofType) (((((case f2) X0) Y) U) V)) U))) (((eq fofType) (((((case f3) X0) Y) U) V)) V)))))
% 21.76/21.97 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 21.76/21.97 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 21.76/21.97 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 21.76/21.97 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 21.76/21.97 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 21.76/21.97 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 21.76/21.97 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 23.15/23.39 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:fofType) (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 23.15/23.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 23.15/23.39 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 23.15/23.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 23.15/23.39 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 23.15/23.39 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 24.16/24.33 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 24.16/24.33 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (U:fofType) (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 24.16/24.33 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))):(((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) (fun (x:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 24.16/24.33 Found (eta_expansion_dep00 (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) b)
% 24.16/24.33 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) b)
% 24.16/24.33 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) b)
% 24.16/24.33 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) b)
% 24.16/24.33 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))) b)
% 26.55/26.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 26.55/26.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 26.55/26.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 26.55/26.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 26.55/26.73 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (V:fofType), ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))))
% 26.55/26.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 26.55/26.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 26.55/26.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 26.55/26.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 26.55/26.73 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 34.53/34.74 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 34.53/34.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 34.53/34.74 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 34.53/34.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 34.53/34.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 34.53/34.74 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 34.53/34.74 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))) (((eq fofType) (((((case f3) X) Y) U) V)) V))))
% 34.53/34.74 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 34.53/34.74 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 34.53/34.74 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 34.53/34.74 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 34.53/34.74 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 34.53/34.74 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 34.53/34.74 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 34.53/34.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 34.53/34.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 34.53/34.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 34.53/34.74 Found eq_ref00:=(eq_ref0 (((eq fofType) (((((case f2) X) Y) U) V)) U)):(((eq Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) (((eq fofType) (((((case f2) X) Y) U) V)) U))
% 34.53/34.74 Found (eq_ref0 (((eq fofType) (((((case f2) X) Y) U) V)) U)) as proof of (((eq Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) b)
% 34.53/34.74 Found ((eq_ref Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) as proof of (((eq Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) b)
% 34.53/34.74 Found ((eq_ref Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) as proof of (((eq Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) b)
% 34.53/34.74 Found ((eq_ref Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) as proof of (((eq Prop) (((eq fofType) (((((case f2) X) Y) U) V)) U)) b)
% 34.53/34.74 Found x:(P (((((case f3) X) Y) U) V))
% 34.53/34.74 Instantiate: b:=(((((case f3) X) Y) U) V):fofType
% 34.53/34.74 Found x as proof of (P0 b)
% 34.53/34.74 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 34.53/34.74 Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% 34.53/34.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% 34.53/34.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% 34.53/34.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% 34.53/34.74 Found eq_ref00:=(eq_ref0 (((((case f2) X) Y) U) V)):(((eq fofType) (((((case f2) X) Y) U) V)) (((((case f2) X) Y) U) V))
% 34.53/34.74 Found (eq_ref0 (((((case f2) X) Y) U) V)) as proof of (((eq fofType) (((((case f2) X) Y) U) V)) b)
% 34.53/34.74 Found ((eq_ref fofType) (((((case f2) X) Y) U) V)) as proof of (((eq fofType) (((((case f2) X) Y) U) V)) b)
% 34.53/34.74 Found ((eq_ref fofType) (((((case f2) X) Y) U) V)) as proof of (((eq fofType) (((((case f2) X) Y) U) V)) b)
% 42.37/42.55 Found ((eq_ref fofType) (((((case f2) X) Y) U) V)) as proof of (((eq fofType) (((((case f2) X) Y) U) V)) b)
% 42.37/42.55 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 42.37/42.55 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 42.37/42.55 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 42.37/42.55 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 42.37/42.55 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 42.37/42.55 Found eq_ref00:=(eq_ref0 (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 42.37/42.55 Found (eq_ref0 (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) b)
% 42.37/42.55 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) b)
% 42.37/42.55 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) b)
% 42.37/42.55 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f3) X) Y) U) V)) V))) b)
% 42.37/42.55 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 42.37/42.55 Found (eq_ref0 b) as proof of (((eq fofType) b) V)
% 42.37/42.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 42.37/42.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 42.37/42.55 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 42.37/42.55 Found eq_ref00:=(eq_ref0 (((((case f3) X) Y) U) V)):(((eq fofType) (((((case f3) X) Y) U) V)) (((((case f3) X) Y) U) V))
% 42.37/42.55 Found (eq_ref0 (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 42.37/42.55 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 42.37/42.55 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 42.37/42.55 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 42.37/42.55 Found eq_ref00:=(eq_ref0 (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))):(((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))))
% 42.37/42.55 Found (eq_ref0 (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) b)
% 42.37/42.55 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) b)
% 42.37/42.55 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) b)
% 62.88/63.10 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))) b)
% 62.88/63.10 Found eq_ref00:=(eq_ref0 (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))):(((eq (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V))))
% 62.88/63.10 Found (eq_ref0 (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) b)
% 62.88/63.10 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) b)
% 62.88/63.10 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) b)
% 62.88/63.10 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> ((P (((((case f3) X) Y) U) V))->(P V)))) b)
% 62.88/63.10 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 62.88/63.10 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 62.88/63.10 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 62.88/63.10 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 62.88/63.10 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 62.88/63.10 Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> (P V))):(((eq (fofType->Prop)) (fun (X:fofType)=> (P V))) (fun (x:fofType)=> (P V)))
% 62.88/63.10 Found (eta_expansion00 (fun (X:fofType)=> (P V))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (P V))) b)
% 62.88/63.10 Found ((eta_expansion0 Prop) (fun (X:fofType)=> (P V))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (P V))) b)
% 62.88/63.10 Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (P V))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (P V))) b)
% 62.88/63.10 Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (P V))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (P V))) b)
% 62.88/63.10 Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (P V))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (P V))) b)
% 62.88/63.10 Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% 62.88/63.10 Found (eq_ref0 x) as proof of (((eq fofType) x) V)
% 62.88/63.10 Found ((eq_ref fofType) x) as proof of (((eq fofType) x) V)
% 62.88/63.10 Found ((eq_ref fofType) x) as proof of (((eq fofType) x) V)
% 62.88/63.10 Found ((eq_ref fofType) x) as proof of (((eq fofType) x) V)
% 62.88/63.10 Found (ex_intro000 ((eq_ref fofType) x)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) V)))
% 62.88/63.10 Found ((ex_intro00 V) ((eq_ref fofType) V)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) V)))
% 62.88/63.10 Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) X) V))) V) ((eq_ref fofType) V)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) V)))
% 62.88/63.10 Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) X) V))) V) ((eq_ref fofType) V)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) V)))
% 62.88/63.10 Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) X) V))) V) ((eq_ref fofType) V)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) V)))
% 62.88/63.10 Found eq_ref00:=(eq_ref0 (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))):(((eq fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V)))))
% 62.88/63.10 Found (eq_ref0 (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) as proof of (((eq fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) b)
% 62.88/63.10 Found ((eq_ref fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) as proof of (((eq fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) b)
% 66.39/66.64 Found ((eq_ref fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) as proof of (((eq fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) b)
% 66.39/66.64 Found ((eq_ref fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) as proof of (((eq fofType) (((((case f3) X) Y) U) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))) b)
% 66.39/66.64 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 66.39/66.64 Found (eq_ref0 b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))
% 66.39/66.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))
% 66.39/66.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))
% 66.39/66.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) V))))
% 66.39/66.64 Found x:(P V)
% 66.39/66.64 Instantiate: b:=V:fofType
% 66.39/66.64 Found x as proof of (P0 b)
% 66.39/66.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 66.39/66.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 66.39/66.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 66.39/66.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V))
% 66.39/66.64 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq fofType) (((((case f3) X) Y) U) V)) V)))
% 66.39/66.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 66.39/66.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 66.39/66.64 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 66.39/66.64 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))))
% 66.39/66.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 66.39/66.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 66.39/66.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 131.40/131.69 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U)))
% 131.40/131.69 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((and (((eq fofType) (((((case f0) X) Y) U) V)) X)) (((eq fofType) (((((case f1) X) Y) U) V)) Y))) (((eq fofType) (((((case f2) X) Y) U) V)) U))))
% 131.40/131.69 Found eq_ref00:=(eq_ref0 (((((case f3) X) Y) U) V)):(((eq fofType) (((((case f3) X) Y) U) V)) (((((case f3) X) Y) U) V))
% 131.40/131.69 Found (eq_ref0 (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 131.40/131.69 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 131.40/131.69 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 131.40/131.69 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 131.40/131.69 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 131.40/131.69 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 131.40/131.69 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V))))
% 131.40/131.69 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 131.40/131.69 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V)))
% 131.40/131.69 Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((P (((((case f3) X) Y) U) V))->(P V))))
% 131.40/131.69 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 131.40/131.69 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 131.40/131.69 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 131.40/131.69 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (P V)))
% 131.40/131.69 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 131.40/131.69 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (P V))
% 131.40/131.69 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (P V)))
% 131.40/131.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 131.40/131.69 Found (eq_ref0 b) as proof of (((eq fofType) b) V)
% 131.40/131.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 131.40/131.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 131.40/131.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) V)
% 131.40/131.69 Found eq_ref00:=(eq_ref0 (((((case f3) X) Y) U) V)):(((eq fofType) (((((case f3) X) Y) U) V)) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found (eq_ref0 (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 203.70/203.99 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 203.70/203.99 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 203.70/203.99 Found ((eq_ref fofType) (((((case f3) X) Y) U) V)) as proof of (((eq fofType) (((((case f3) X) Y) U) V)) b)
% 203.70/203.99 Found f3t__eq_sym0:=(f3t__eq_sym (fun (x:Prop)=> (P b))):((P b)->(P b))
% 203.70/203.99 Found (f3t__eq_sym (fun (x:Prop)=> (P b))) as proof of (P0 b)
% 203.70/203.99 Found (f3t__eq_sym (fun (x:Prop)=> (P b))) as proof of (P0 b)
% 203.70/203.99 Found eq_ref00:=(eq_ref0 (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V))))
% 203.70/203.99 Found (eq_ref0 (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) b)
% 203.70/203.99 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) b)
% 203.70/203.99 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) b)
% 203.70/203.99 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) V) (((((case f3) X) Y) U) V)))) b)
% 203.70/203.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 203.70/203.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f2) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f2) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f2) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f2) X) Y) U) V))
% 203.70/203.99 Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% 203.70/203.99 Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% 203.70/203.99 Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% 203.70/203.99 Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% 203.70/203.99 Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% 203.70/203.99 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 203.70/203.99 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 203.70/203.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 203.70/203.99 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 203.70/203.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f3) X) Y) U) V))
% 203.70/203.99 Found f2f__eq_sym0:=(f2f__eq_sym (fun (x:Prop)=> (P V))):((P V)->(P V))
% 203.70/203.99 Found (f2f__eq_sym (fun (x:Prop)=> (P V))) as proof of (P0 V)
% 203.70/203.99 Found (f2f__eq_sym (fun (x:Prop)=> (P V))) as proof of (P0 V)
% 203.70/203.99 Found eq_ref00:=(eq_ref0 V):(((eq fofType) V) V)
% 203.70/203.99 Found (eq_ref0 V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fofType) V) b)
% 203.70/203.99 Found ((eq_ref fofType) V) as proof of (((eq fof
%------------------------------------------------------------------------------