TSTP Solution File: SYO224^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO224^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 00:50:57 EDT 2022
% Result : Timeout 288.22s 288.59s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO224^5 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n020.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 : Fri Mar 11 19:53:11 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 1.29/1.46 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb2170>, <kernel.Constant object at 0xbb20e0>) of role type named cJ
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cJ:fofType
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb3368>, <kernel.DependentProduct object at 0xbb20e0>) of role type named cLIKE
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cLIKE:(fofType->(fofType->Prop))
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb23b0>, <kernel.DependentProduct object at 0xbb2dd0>) of role type named cWRH
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cWRH:(fofType->Prop)
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb20e0>, <kernel.DependentProduct object at 0xbb2e60>) of role type named cW
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cW:(fofType->Prop)
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb2dd0>, <kernel.DependentProduct object at 0xbb2290>) of role type named cUNIQUE
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cUNIQUE:(fofType->Prop)
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb2e60>, <kernel.Single object at 0xbb20e0>) of role type named cS
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cS:fofType
% 1.29/1.46 FOF formula (<kernel.Constant object at 0xbb23b0>, <kernel.Single object at 0xbb2dd0>) of role type named cP
% 1.29/1.46 Using role type
% 1.29/1.46 Declaring cP:fofType
% 1.29/1.46 FOF formula (((and ((and ((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS))) (cW cS))) (cWRH cS))->((ex (fofType->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))) of role conjecture named cLING1
% 1.29/1.46 Conjecture to prove = (((and ((and ((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS))) (cW cS))) (cWRH cS))->((ex (fofType->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))):Prop
% 1.29/1.46 We need to prove ['(((and ((and ((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS))) (cW cS))) (cWRH cS))->((ex (fofType->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))))']
% 1.29/1.46 Parameter fofType:Type.
% 1.29/1.46 Parameter cJ:fofType.
% 1.29/1.46 Parameter cLIKE:(fofType->(fofType->Prop)).
% 1.29/1.46 Parameter cWRH:(fofType->Prop).
% 1.29/1.46 Parameter cW:(fofType->Prop).
% 1.29/1.46 Parameter cUNIQUE:(fofType->Prop).
% 1.29/1.46 Parameter cS:fofType.
% 1.29/1.46 Parameter cP:fofType.
% 1.29/1.46 Trying to prove (((and ((and ((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS))) (cW cS))) (cWRH cS))->((ex (fofType->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))))
% 1.29/1.46 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 1.29/1.46 Found (eq_ref0 (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 1.29/1.46 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 1.29/1.46 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 1.29/1.46 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 1.29/1.46 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 1.29/1.46 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 1.29/1.46 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 3.91/4.08 Found (eq_ref0 (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 3.91/4.08 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 3.91/4.08 Found (eq_ref0 (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 3.91/4.08 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x4 cJ)):(((eq Prop) (x4 cJ)) (x4 cJ))
% 3.91/4.08 Found (eq_ref0 (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 3.91/4.08 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 3.91/4.08 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 3.91/4.08 Found (eq_ref0 (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 3.91/4.08 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 6.52/6.70 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 6.52/6.70 Found (eq_ref0 (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 6.52/6.70 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found eq_ref00:=(eq_ref0 (x6 cJ)):(((eq Prop) (x6 cJ)) (x6 cJ))
% 6.52/6.70 Found (eq_ref0 (x6 cJ)) as proof of (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found ((eq_ref Prop) (x6 cJ)) as proof of (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found ((eq_ref Prop) (x6 cJ)) as proof of (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found ((eq_ref Prop) (x6 cJ)) as proof of (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 6.52/6.70 Found eq_ref00:=(eq_ref0 (x6 cP)):(((eq Prop) (x6 cP)) (x6 cP))
% 6.52/6.70 Found (eq_ref0 (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 6.52/6.70 Found eta_expansion000:=(eta_expansion00 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))):(((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) (fun (x:(fofType->Prop))=> ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 6.52/6.70 Found (eta_expansion00 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 6.52/6.70 Found ((eta_expansion0 Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 7.99/8.14 Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 7.99/8.14 Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 7.99/8.14 Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 7.99/8.14 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 7.99/8.14 Found (eq_ref0 (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found ((eq_ref Prop) (x0 cJ)) as proof of (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 7.99/8.14 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 7.99/8.14 Found (eq_ref0 (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found ((eq_ref Prop) (x2 cJ)) as proof of (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 7.99/8.14 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 7.99/8.14 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 7.99/8.14 Found eq_ref00:=(eq_ref0 (x4 cJ)):(((eq Prop) (x4 cJ)) (x4 cJ))
% 7.99/8.14 Found (eq_ref0 (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 9.95/10.14 Found ((eq_ref Prop) (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 9.95/10.14 Found ((eq_ref Prop) (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 9.95/10.14 Found ((eq_ref Prop) (x4 cJ)) as proof of (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))
% 9.95/10.14 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 9.95/10.14 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 9.95/10.14 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 9.95/10.14 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 9.95/10.14 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 9.95/10.14 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 9.95/10.14 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 9.95/10.14 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 9.95/10.14 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 9.95/10.14 Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 9.95/10.14 Found eta_expansion000:=(eta_expansion00 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))):(((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) (fun (x:(fofType->Prop))=> ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 11.58/11.74 Found (eta_expansion00 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 11.58/11.74 Found ((eta_expansion0 Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 11.58/11.74 Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 11.58/11.74 Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 11.58/11.74 Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 11.58/11.74 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 11.58/11.74 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 11.58/11.74 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 11.58/11.74 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 11.58/11.74 Found (fun (x2:(fofType->Prop))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 11.58/11.74 Found (fun (x2:(fofType->Prop))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 11.58/11.74 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 11.58/11.74 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 16.25/16.42 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 16.25/16.42 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 16.25/16.42 Found (fun (x2:(fofType->Prop))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 16.25/16.42 Found (fun (x2:(fofType->Prop))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 16.25/16.42 Found eq_ref00:=(eq_ref0 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))):(((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 16.25/16.42 Found (eq_ref0 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 16.25/16.42 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 16.25/16.42 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 16.25/16.42 Found ((eq_ref ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 16.25/16.42 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 16.25/16.42 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 16.25/16.42 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 16.25/16.42 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 16.25/16.42 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 16.25/16.42 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 16.25/16.42 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 16.25/16.42 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 21.22/21.39 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 21.22/21.39 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 21.22/21.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 21.22/21.39 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 21.22/21.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 21.22/21.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 21.22/21.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 21.22/21.39 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 21.22/21.39 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found (fun (x4:(fofType->Prop))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found (fun (x4:(fofType->Prop))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 21.22/21.39 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 21.22/21.39 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found (fun (x4:(fofType->Prop))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 21.22/21.39 Found (fun (x4:(fofType->Prop))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 21.22/21.39 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))):(((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) (fun (x:(fofType->Prop))=> ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 21.22/21.39 Found (eta_expansion_dep00 (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 23.62/23.78 Found ((eta_expansion_dep0 (fun (x7:(fofType->Prop))=> Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 23.62/23.78 Found (((eta_expansion_dep (fofType->Prop)) (fun (x7:(fofType->Prop))=> Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 23.62/23.78 Found (((eta_expansion_dep (fofType->Prop)) (fun (x7:(fofType->Prop))=> Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 23.62/23.78 Found (((eta_expansion_dep (fofType->Prop)) (fun (x7:(fofType->Prop))=> Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))) b)
% 23.62/23.78 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 23.62/23.78 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 23.62/23.78 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 23.62/23.78 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 23.62/23.78 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 23.62/23.78 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 23.62/23.78 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 23.62/23.78 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 23.62/23.78 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 23.62/23.78 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 23.62/23.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.62/23.78 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 23.62/23.78 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 23.62/23.78 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 23.62/23.78 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 23.62/23.78 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 23.62/23.78 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 23.62/23.78 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 23.62/23.78 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 23.62/23.78 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 23.62/23.78 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 23.62/23.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.62/23.78 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 23.62/23.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.62/23.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 24.82/25.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 24.82/25.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 24.82/25.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 24.82/25.01 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 24.82/25.01 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 24.82/25.01 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 24.82/25.01 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 24.82/25.01 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 24.82/25.01 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 24.82/25.01 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found (fun (x6:(fofType->Prop))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found (fun (x6:(fofType->Prop))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 24.82/25.01 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 24.82/25.01 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found (fun (x6:(fofType->Prop))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) ((and (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))))
% 24.82/25.01 Found (fun (x6:(fofType->Prop))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((and (((eq Prop) (x cP)) ((cLIKE cP) cS))) (((eq Prop) (x cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 24.82/25.01 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 24.82/25.01 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 24.82/25.01 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 24.82/25.01 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 24.82/25.01 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 24.82/25.01 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 24.82/25.01 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 24.82/25.01 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 24.82/25.01 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 24.82/25.01 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 24.82/25.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.82/25.01 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 24.82/25.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 24.82/25.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 24.82/25.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 32.29/32.46 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 32.29/32.46 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 32.29/32.46 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 32.29/32.46 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 32.29/32.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.29/32.46 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.29/32.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 32.29/32.46 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 32.29/32.46 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 32.29/32.46 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 32.29/32.46 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 32.29/32.46 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 32.29/32.46 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 32.29/32.46 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 32.29/32.46 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 32.29/32.46 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 32.29/32.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.29/32.46 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 32.29/32.46 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 32.29/32.46 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 32.29/32.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.29/32.46 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 32.29/32.46 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 32.29/32.46 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 32.29/32.46 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 32.29/32.46 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 32.29/32.46 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 32.29/32.46 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.97/39.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 38.97/39.14 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 38.97/39.14 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 38.97/39.14 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 38.97/39.14 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 38.97/39.14 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 38.97/39.14 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.97/39.14 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 38.97/39.14 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 38.97/39.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.97/39.14 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 38.97/39.14 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 38.97/39.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.97/39.14 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 38.97/39.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.97/39.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 38.97/39.14 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.97/39.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 38.97/39.14 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 38.97/39.14 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 38.97/39.14 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 49.29/49.48 Found eq_ref00:=(eq_ref0 (x6 cP)):(((eq Prop) (x6 cP)) (x6 cP))
% 49.29/49.48 Found (eq_ref0 (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 49.29/49.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.29/49.48 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found eq_ref000:=(eq_ref00 P):((P (x6 cP))->(P (x6 cP)))
% 49.29/49.48 Found (eq_ref00 P) as proof of (P0 (x6 cP))
% 49.29/49.48 Found ((eq_ref0 (x6 cP)) P) as proof of (P0 (x6 cP))
% 49.29/49.48 Found (((eq_ref Prop) (x6 cP)) P) as proof of (P0 (x6 cP))
% 49.29/49.48 Found (((eq_ref Prop) (x6 cP)) P) as proof of (P0 (x6 cP))
% 49.29/49.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.29/49.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (x4 cP))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 49.29/49.48 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 49.29/49.48 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 49.29/49.48 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 49.29/49.48 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 49.29/49.48 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 49.29/49.48 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 49.29/49.48 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 49.29/49.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.29/49.48 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 49.29/49.48 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 49.29/49.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.29/49.48 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 49.29/49.48 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 49.29/49.48 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 49.29/49.48 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 49.29/49.48 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 49.29/49.48 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 49.29/49.48 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 49.29/49.48 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 49.29/49.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 49.29/49.48 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 49.29/49.48 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 49.29/49.48 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 49.29/49.48 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 49.29/49.48 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 49.29/49.48 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 49.29/49.48 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 55.34/55.55 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 55.34/55.55 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 55.34/55.55 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 55.34/55.55 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 55.34/55.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 55.34/55.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 55.34/55.55 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 55.34/55.55 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 55.34/55.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 55.34/55.55 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 55.34/55.55 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 55.34/55.55 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 55.34/55.55 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 55.34/55.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 55.34/55.55 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 55.34/55.55 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 55.34/55.55 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 55.34/55.55 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 55.34/55.55 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 55.34/55.55 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 55.34/55.55 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 55.34/55.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 55.34/55.55 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 55.34/55.55 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 55.34/55.55 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 55.34/55.55 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 55.34/55.55 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 55.34/55.55 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 55.34/55.55 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 55.34/55.55 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 55.34/55.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 55.34/55.55 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 55.34/55.55 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 61.68/61.88 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 61.68/61.88 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.68/61.88 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 61.68/61.88 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 61.68/61.88 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 61.68/61.88 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 61.68/61.88 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 61.68/61.88 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 61.68/61.88 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 61.68/61.88 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 61.68/61.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.68/61.88 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 61.68/61.88 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 61.68/61.88 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 61.68/61.88 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 61.68/61.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.68/61.88 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 61.68/61.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.68/61.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 61.68/61.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 61.68/61.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 61.68/61.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 61.68/61.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 61.68/61.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 61.68/61.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.68/61.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 61.68/61.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 61.68/61.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 61.68/61.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 82.87/83.12 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 82.87/83.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 82.87/83.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 82.87/83.12 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 82.87/83.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 82.87/83.12 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 82.87/83.12 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 82.87/83.12 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 82.87/83.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 82.87/83.12 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 82.87/83.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 82.87/83.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 82.87/83.12 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% 82.87/83.12 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 82.87/83.12 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 82.87/83.12 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 82.87/83.12 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 90.30/90.51 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 90.30/90.51 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 90.30/90.51 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 90.30/90.51 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 90.30/90.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 90.30/90.51 Found (eq_ref0 b) as proof of (((eq Prop) b) (x6 cP))
% 90.30/90.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x6 cP))
% 90.30/90.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x6 cP))
% 90.30/90.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x6 cP))
% 90.30/90.51 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 90.30/90.51 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 90.30/90.51 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 90.30/90.51 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 90.30/90.51 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 90.30/90.51 Found eq_ref00:=(eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 103.09/103.32 Found (eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 103.09/103.32 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 103.09/103.32 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 103.09/103.32 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 103.09/103.32 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 103.09/103.32 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.09/103.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.09/103.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 103.09/103.32 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 103.09/103.32 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 103.09/103.32 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.09/103.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (x4 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 103.09/103.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 103.09/103.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 103.09/103.32 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 103.09/103.32 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 103.09/103.32 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 104.15/104.45 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 104.15/104.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 104.15/104.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 104.15/104.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (x4 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 104.15/104.45 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 104.15/104.45 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 104.15/104.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 104.15/104.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 104.15/104.45 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 104.15/104.45 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 104.15/104.45 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% 104.15/104.45 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 104.15/104.45 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 104.15/104.45 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 104.15/104.45 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 104.15/104.45 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 104.15/104.45 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 104.15/104.45 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 104.15/104.45 Found ((eta_expansion_dep0 (fun (x3:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 104.15/104.45 Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 104.15/104.45 Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 104.15/104.45 Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 112.86/113.08 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 112.86/113.08 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 112.86/113.08 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 112.86/113.08 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 112.86/113.08 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 112.86/113.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.86/113.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 112.86/113.08 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 112.86/113.08 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 112.86/113.08 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 112.86/113.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.86/113.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 112.86/113.08 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 112.86/113.08 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 112.86/113.08 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 112.86/113.08 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 112.86/113.08 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 112.86/113.08 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 112.86/113.08 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 112.86/113.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 112.86/113.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 112.86/113.08 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 112.86/113.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 112.86/113.08 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 112.86/113.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 112.86/113.08 Found ex_intro0:=(ex_intro (fofType->Prop)):(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P)))
% 112.86/113.08 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)) (x:(fofType->Prop)), ((P x)->((ex (fofType->Prop)) P))):Prop
% 112.86/113.08 Found ex_intro0 as proof of b
% 112.86/113.08 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 112.86/113.08 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 117.00/117.23 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 117.00/117.23 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 117.00/117.23 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 117.00/117.23 Found ((conj00 ((eq_ref Prop) (x0 cP))) ex_intro0) as proof of (P b)
% 117.00/117.23 Found (((conj0 b) ((eq_ref Prop) (x0 cP))) ex_intro0) as proof of (P b)
% 117.00/117.23 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) ex_intro0) as proof of (P b)
% 117.00/117.23 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) ex_intro0) as proof of (P b)
% 117.00/117.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.00/117.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 117.00/117.23 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.00/117.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 117.00/117.23 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 117.00/117.23 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.00/117.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (x4 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 117.00/117.23 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 117.00/117.23 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.00/117.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 117.00/117.23 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 117.00/117.23 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 117.00/117.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.00/117.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 117.00/117.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.62/121.85 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 121.62/121.85 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 121.62/121.85 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.62/121.85 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 121.62/121.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.62/121.85 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 121.62/121.85 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.62/121.85 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 121.62/121.85 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.62/121.85 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 121.62/121.85 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 121.62/121.85 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 121.62/121.85 Found eq_ref00:=(eq_ref0 (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 121.62/121.85 Found (eq_ref0 (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found x1:(P (x0 cP))
% 134.11/134.36 Instantiate: b:=(x0 cP):Prop
% 134.11/134.36 Found x1 as proof of (P0 b)
% 134.11/134.36 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 134.11/134.36 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 134.11/134.36 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 134.11/134.36 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 134.11/134.36 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 134.11/134.36 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 134.11/134.36 Found (eq_ref0 (x0 cJ)) as proof of b
% 134.11/134.36 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 134.11/134.36 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 134.11/134.36 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 134.11/134.36 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 134.11/134.36 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 134.11/134.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 134.11/134.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 134.11/134.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 134.11/134.36 Found eq_ref00:=(eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 134.11/134.36 Found (eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 134.11/134.36 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% 134.11/134.36 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 134.11/134.36 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 134.11/134.36 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 134.11/134.36 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 134.11/134.36 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% 134.11/134.36 Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 140.11/140.36 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 140.11/140.36 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 140.11/140.36 Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 140.11/140.36 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 140.11/140.36 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.11/140.36 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 140.11/140.36 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 140.11/140.36 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 140.11/140.36 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 140.11/140.36 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 140.11/140.36 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 140.11/140.36 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 140.11/140.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.11/140.36 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 140.11/140.36 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 140.11/140.36 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 140.11/140.36 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 140.11/140.36 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 140.11/140.36 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 140.11/140.36 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 140.11/140.36 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 140.11/140.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.11/140.36 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 140.11/140.36 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))))
% 140.11/140.36 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
% 140.11/140.36 Found eq_substitution as proof of b
% 140.11/140.36 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 140.11/140.36 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((conj00 ((eq_ref Prop) (x2 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found (((conj0 b) ((eq_ref Prop) (x2 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found ((((conj (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x2 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found ((((conj (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x2 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 150.40/150.66 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 150.40/150.66 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 150.40/150.66 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 150.40/150.66 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 150.40/150.66 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 150.40/150.66 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 150.40/150.66 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 150.40/150.66 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 150.40/150.66 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 150.40/150.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 150.40/150.66 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 150.40/150.66 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 150.40/150.66 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 150.40/150.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 150.40/150.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 150.40/150.66 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 150.40/150.66 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 150.40/150.66 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))))
% 150.40/150.66 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
% 150.40/150.66 Found eq_substitution as proof of b
% 150.40/150.66 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 150.40/150.66 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 150.40/150.66 Found ((conj00 ((eq_ref Prop) (x0 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found (((conj0 b) ((eq_ref Prop) (x0 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) eq_substitution) as proof of (P b)
% 150.40/150.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 153.39/153.68 Found (eq_ref0 b) as proof of (P b)
% 153.39/153.68 Found ((eq_ref Prop) b) as proof of (P b)
% 153.39/153.68 Found ((eq_ref Prop) b) as proof of (P b)
% 153.39/153.68 Found ((eq_ref Prop) b) as proof of (P b)
% 153.39/153.68 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 153.39/153.68 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found eq_ref00:=(eq_ref0 (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 153.39/153.68 Found (eq_ref0 (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 153.39/153.68 Found ((eq_ref Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 153.39/153.68 Found ((eq_ref Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 153.39/153.68 Found ((eq_ref Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 153.39/153.68 Found x3:(P (x2 cP))
% 153.39/153.68 Instantiate: b:=(x2 cP):Prop
% 153.39/153.68 Found x3 as proof of (P0 b)
% 153.39/153.68 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 153.39/153.68 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 153.39/153.68 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 153.39/153.68 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 153.39/153.68 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 153.39/153.68 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 153.39/153.68 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 153.39/153.68 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 153.39/153.68 Found (eq_ref0 (x2 cJ)) as proof of b
% 153.39/153.68 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 153.39/153.68 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 153.39/153.68 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 153.39/153.68 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 153.39/153.68 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 153.39/153.68 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 153.39/153.68 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 153.39/153.68 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 153.39/153.68 Found x1:(P ((cLIKE cP) cS))
% 153.39/153.68 Instantiate: b:=((cLIKE cP) cS):Prop
% 153.39/153.68 Found x1 as proof of (P0 b)
% 153.39/153.68 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 153.39/153.68 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 153.39/153.68 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 153.39/153.68 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 153.39/153.68 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 153.39/153.68 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 153.39/153.68 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 158.02/158.29 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 158.02/158.29 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 158.02/158.29 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 158.02/158.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 158.02/158.29 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 158.02/158.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 158.02/158.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 158.02/158.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 158.02/158.29 Found eq_ref00:=(eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 158.02/158.29 Found (eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found eq_ref00:=(eq_ref0 (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 158.02/158.29 Found (eq_ref0 (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 158.02/158.29 Found x3:(P (x0 cP))
% 158.02/158.29 Instantiate: b:=(x0 cP):Prop
% 158.02/158.29 Found x3 as proof of (P0 b)
% 158.02/158.29 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 158.02/158.29 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 158.02/158.29 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 158.02/158.29 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 165.23/165.49 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 165.23/165.49 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 165.23/165.49 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 165.23/165.49 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 165.23/165.49 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 165.23/165.49 Found (eq_ref0 (x0 cJ)) as proof of b
% 165.23/165.49 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 165.23/165.49 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 165.23/165.49 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 165.23/165.49 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 165.23/165.49 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 165.23/165.49 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 165.23/165.49 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 165.23/165.49 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 165.23/165.49 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 165.23/165.49 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 165.23/165.49 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 165.23/165.49 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.23/165.49 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 165.23/165.49 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 165.23/165.49 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.23/165.49 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 165.23/165.49 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 165.23/165.49 Found (eq_ref00 P) as proof of (P0 b)
% 165.23/165.49 Found ((eq_ref0 b) P) as proof of (P0 b)
% 165.23/165.49 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 165.23/165.49 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 165.23/165.49 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% 165.23/165.49 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 165.23/165.49 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 165.23/165.49 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 165.23/165.49 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% 165.23/165.49 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% 165.23/165.49 Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 165.23/165.49 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 171.52/171.81 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 171.52/171.81 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 171.52/171.81 Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xan:(fofType->Prop))=> ((and (((eq Prop) (Xan cP)) ((cLIKE cP) cS))) (((eq Prop) (Xan cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))))
% 171.52/171.81 Found x3:(P (x0 cP))
% 171.52/171.81 Instantiate: b:=(x0 cP):Prop
% 171.52/171.81 Found x3 as proof of (P0 b)
% 171.52/171.81 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 171.52/171.81 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found x1:(P (x0 cP))
% 171.52/171.81 Instantiate: b:=(x0 cP):Prop
% 171.52/171.81 Found x1 as proof of (P0 b)
% 171.52/171.81 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 171.52/171.81 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 171.52/171.81 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 171.52/171.81 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 171.52/171.81 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 171.52/171.81 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 171.52/171.81 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 171.52/171.81 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 171.52/171.81 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 171.52/171.81 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 171.52/171.81 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 171.52/171.81 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 171.52/171.81 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 171.52/171.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 171.52/171.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 171.52/171.81 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 171.52/171.81 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.52/171.81 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 171.52/171.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 171.52/171.81 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 171.52/171.81 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 171.52/171.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 173.50/173.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.50/173.76 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 173.50/173.76 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 173.50/173.76 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.50/173.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 173.50/173.76 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.50/173.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.50/173.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 173.50/173.76 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 173.50/173.76 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 173.50/173.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.50/173.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 173.50/173.76 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 173.50/173.76 Found (eq_ref0 (x0 cJ)) as proof of b
% 173.50/173.76 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 173.50/173.76 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 173.50/173.76 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 173.50/173.76 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 173.50/173.76 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 173.50/173.76 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 173.50/173.76 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 173.50/173.76 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 173.50/173.76 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 173.50/173.76 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 173.50/173.76 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 173.50/173.76 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 173.50/173.76 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 173.50/173.76 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 173.50/173.76 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 179.83/180.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.83/180.10 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found x3:(cW cS)
% 179.83/180.10 Instantiate: b:=(cW cS):Prop
% 179.83/180.10 Found x3 as proof of b
% 179.83/180.10 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 179.83/180.10 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 179.83/180.10 Found ((conj00 ((eq_ref Prop) (x4 cP))) x3) as proof of (P b)
% 179.83/180.10 Found (((conj0 b) ((eq_ref Prop) (x4 cP))) x3) as proof of (P b)
% 179.83/180.10 Found ((((conj (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x4 cP))) x3) as proof of (P b)
% 179.83/180.10 Found ((((conj (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x4 cP))) x3) as proof of (P b)
% 179.83/180.10 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 179.83/180.10 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 179.83/180.10 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 179.83/180.10 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 179.83/180.10 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 179.83/180.10 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 179.83/180.10 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.83/180.10 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 179.83/180.10 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 179.83/180.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.83/180.10 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 179.83/180.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.83/180.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 179.83/180.10 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 179.83/180.10 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 179.83/180.10 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 179.83/180.10 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 179.83/180.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.83/180.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 179.83/180.10 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 179.83/180.10 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 179.83/180.10 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 179.83/180.10 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 181.63/181.93 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 181.63/181.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.63/181.93 Found (eq_ref0 b) as proof of (P b)
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (P b)
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (P b)
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (P b)
% 181.63/181.93 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 181.63/181.93 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 181.63/181.93 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 181.63/181.93 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 181.63/181.93 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 181.63/181.93 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 181.63/181.93 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 181.63/181.93 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 181.63/181.93 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 181.63/181.93 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 181.63/181.93 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 181.63/181.93 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 181.63/181.93 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 181.63/181.93 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 181.63/181.93 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 181.63/181.93 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 181.63/181.93 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 181.63/181.93 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 181.63/181.93 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 181.63/181.93 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 181.63/181.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.63/181.93 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found x3:((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS))
% 181.63/181.93 Instantiate: b:=((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS)):Prop
% 181.63/181.93 Found x3 as proof of b
% 181.63/181.93 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 181.63/181.93 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 181.63/181.93 Found ((conj00 ((eq_ref Prop) (x0 cP))) x3) as proof of (P b)
% 181.63/181.93 Found (((conj0 b) ((eq_ref Prop) (x0 cP))) x3) as proof of (P b)
% 181.63/181.93 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) x3) as proof of (P b)
% 181.63/181.93 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) x3) as proof of (P b)
% 181.63/181.93 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 181.63/181.93 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 181.63/181.93 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 181.63/181.93 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 181.63/181.93 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 181.63/181.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.63/181.93 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 181.63/181.93 Found x3:((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS))
% 181.63/181.93 Instantiate: b:=((and (forall (X:fofType), ((cUNIQUE X)->(forall (Z:fofType), (((and (cWRH Z)) (cW Z))->(((eq fofType) X) Z)))))) (cUNIQUE cS)):Prop
% 181.63/181.93 Found x3 as proof of b
% 181.63/181.93 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 181.63/181.93 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 181.63/181.93 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 187.38/187.62 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 187.38/187.62 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 187.38/187.62 Found ((conj00 ((eq_ref Prop) (x2 cP))) x3) as proof of (P b)
% 187.38/187.62 Found (((conj0 b) ((eq_ref Prop) (x2 cP))) x3) as proof of (P b)
% 187.38/187.62 Found ((((conj (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x2 cP))) x3) as proof of (P b)
% 187.38/187.62 Found ((((conj (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x2 cP))) x3) as proof of (P b)
% 187.38/187.62 Found x3:(P ((cLIKE cP) cS))
% 187.38/187.62 Instantiate: b:=((cLIKE cP) cS):Prop
% 187.38/187.62 Found x3 as proof of (P0 b)
% 187.38/187.62 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 187.38/187.62 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 187.38/187.62 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 187.38/187.62 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 187.38/187.62 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 187.38/187.62 Found eq_ref00:=(eq_ref0 (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 187.38/187.62 Found (eq_ref0 (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 187.38/187.62 Found ((eq_ref Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 187.38/187.62 Found ((eq_ref Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 187.38/187.62 Found ((eq_ref Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x6 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 187.38/187.62 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 187.38/187.62 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 187.38/187.62 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 187.38/187.62 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 187.38/187.62 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 187.38/187.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 187.38/187.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 187.38/187.62 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 187.38/187.62 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 187.38/187.62 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 187.38/187.62 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 187.38/187.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 187.38/187.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 187.38/187.62 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 187.38/187.62 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 187.38/187.62 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 187.38/187.62 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found x5:(P (x4 cP))
% 190.06/190.31 Instantiate: b:=(x4 cP):Prop
% 190.06/190.31 Found x5 as proof of (P0 b)
% 190.06/190.31 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 190.06/190.31 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found eq_ref00:=(eq_ref0 (x4 cJ)):(((eq Prop) (x4 cJ)) (x4 cJ))
% 190.06/190.31 Found (eq_ref0 (x4 cJ)) as proof of b
% 190.06/190.31 Found ((eq_ref Prop) (x4 cJ)) as proof of b
% 190.06/190.31 Found ((eq_ref Prop) (x4 cJ)) as proof of b
% 190.06/190.31 Found ((eq_ref Prop) (x4 cJ)) as proof of b
% 190.06/190.31 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 190.06/190.31 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 190.06/190.31 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 190.06/190.31 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 190.06/190.31 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 190.06/190.31 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 190.06/190.31 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 190.06/190.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.06/190.31 Found (eq_ref0 b) as proof of (P b)
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (P b)
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (P b)
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (P b)
% 190.06/190.31 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 190.06/190.31 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 190.06/190.31 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 190.06/190.31 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 190.06/190.31 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 190.06/190.31 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 190.06/190.31 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 190.06/190.31 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 190.06/190.31 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.06/190.31 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 190.06/190.31 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 190.06/190.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.06/190.31 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 190.06/190.31 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 190.06/190.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.06/190.31 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 190.06/190.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 194.80/195.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 194.80/195.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 194.80/195.07 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 194.80/195.07 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 194.80/195.07 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 194.80/195.07 Found x3:(P ((cLIKE cP) cS))
% 194.80/195.07 Instantiate: b:=((cLIKE cP) cS):Prop
% 194.80/195.07 Found x3 as proof of (P0 b)
% 194.80/195.07 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 194.80/195.07 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 194.80/195.07 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 194.80/195.07 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 194.80/195.07 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 194.80/195.07 Found eq_ref00:=(eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 194.80/195.07 Found (eq_ref0 (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 194.80/195.07 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 194.80/195.07 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 194.80/195.07 Found ((eq_ref Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x0 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 194.80/195.07 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 194.80/195.07 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 194.80/195.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 194.80/195.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 194.80/195.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 194.80/195.07 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 194.80/195.07 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 194.80/195.07 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 194.80/195.07 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 194.80/195.07 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 194.80/195.07 Found eq_ref00:=(eq_ref0 (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 194.80/195.07 Found (eq_ref0 (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found ((eq_ref Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x2 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found eq_ref00:=(eq_ref0 (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))):(((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X))))))
% 196.42/196.68 Found (eq_ref0 (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found ((eq_ref Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found ((eq_ref Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found ((eq_ref Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) as proof of (((eq Prop) (((eq Prop) (x4 cJ)) ((ex fofType) (fun (X:fofType)=> ((and ((and ((and (cUNIQUE X)) (cW X))) (cWRH X))) ((cLIKE cJ) X)))))) b)
% 196.42/196.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 196.42/196.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 196.42/196.68 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 196.42/196.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 196.42/196.68 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 196.42/196.68 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 196.42/196.68 Found x5:(P (x0 cP))
% 196.42/196.68 Instantiate: b:=(x0 cP):Prop
% 196.42/196.68 Found x5 as proof of (P0 b)
% 196.42/196.68 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 196.42/196.68 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.94/204.26 Found (eq_ref0 b) as proof of (P b)
% 203.94/204.26 Found ((eq_ref Prop) b) as proof of (P b)
% 203.94/204.26 Found ((eq_ref Prop) b) as proof of (P b)
% 203.94/204.26 Found ((eq_ref Prop) b) as proof of (P b)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 203.94/204.26 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 203.94/204.26 Found (eq_ref0 (x0 cJ)) as proof of b
% 203.94/204.26 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 203.94/204.26 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 203.94/204.26 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 203.94/204.26 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 203.94/204.26 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found x5:(P (x2 cP))
% 203.94/204.26 Instantiate: b:=(x2 cP):Prop
% 203.94/204.26 Found x5 as proof of (P0 b)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 203.94/204.26 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 203.94/204.26 Found (eq_ref0 (x2 cJ)) as proof of b
% 203.94/204.26 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 203.94/204.26 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 203.94/204.26 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 203.94/204.26 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 203.94/204.26 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 203.94/204.26 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 203.94/204.26 Found (eq_ref00 P) as proof of (P0 b)
% 203.94/204.26 Found ((eq_ref0 b) P) as proof of (P0 b)
% 203.94/204.26 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 203.94/204.26 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 203.94/204.26 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 203.94/204.26 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 203.94/204.26 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 203.94/204.26 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 203.94/204.26 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 203.94/204.26 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 203.94/204.26 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 203.94/204.26 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 203.94/204.26 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 203.94/204.26 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 203.94/204.26 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 203.94/204.26 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 203.94/204.26 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 203.94/204.26 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 208.96/209.25 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.96/209.25 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 208.96/209.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 208.96/209.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 208.96/209.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 208.96/209.25 Found x3:(P ((cLIKE cP) cS))
% 208.96/209.25 Instantiate: b:=((cLIKE cP) cS):Prop
% 208.96/209.25 Found x3 as proof of (P0 b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 208.96/209.25 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 208.96/209.25 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 208.96/209.25 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 208.96/209.25 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 208.96/209.25 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 208.96/209.25 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 208.96/209.25 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b0)
% 208.96/209.25 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b0)
% 208.96/209.25 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b0)
% 208.96/209.25 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b0)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.96/209.25 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 208.96/209.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 208.96/209.25 Found x5:(P (x0 cP))
% 208.96/209.25 Instantiate: b:=(x0 cP):Prop
% 208.96/209.25 Found x5 as proof of (P0 b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 208.96/209.25 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found x5:(P (x2 cP))
% 208.96/209.25 Instantiate: b:=(x2 cP):Prop
% 208.96/209.25 Found x5 as proof of (P0 b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 208.96/209.25 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 208.96/209.25 Found x5:(P (x0 cP))
% 208.96/209.25 Instantiate: b:=(x0 cP):Prop
% 208.96/209.25 Found x5 as proof of (P0 b)
% 208.96/209.25 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 208.96/209.25 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 213.26/213.54 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 213.26/213.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 213.26/213.54 Found (eq_ref0 b) as proof of (P b)
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (P b)
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (P b)
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (P b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 213.26/213.54 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 213.26/213.54 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 213.26/213.54 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 213.26/213.54 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 213.26/213.54 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 213.26/213.54 Found x1:(P (x0 cP))
% 213.26/213.54 Instantiate: b:=(x0 cP):Prop
% 213.26/213.54 Found x1 as proof of (P0 b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 213.26/213.54 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 213.26/213.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 213.26/213.54 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 213.26/213.54 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found x3:(P (x0 cP))
% 213.26/213.54 Instantiate: b:=(x0 cP):Prop
% 213.26/213.54 Found x3 as proof of (P0 b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 213.26/213.54 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found x3:(P (x2 cP))
% 213.26/213.54 Instantiate: b:=(x2 cP):Prop
% 213.26/213.54 Found x3 as proof of (P0 b)
% 213.26/213.54 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 213.26/213.54 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 213.26/213.54 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found x3:(P (x0 cP))
% 216.57/216.88 Instantiate: b:=(x0 cP):Prop
% 216.57/216.88 Found x3 as proof of (P0 b)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 216.57/216.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 216.57/216.88 Found (eq_ref00 P) as proof of (P0 b)
% 216.57/216.88 Found ((eq_ref0 b) P) as proof of (P0 b)
% 216.57/216.88 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 216.57/216.88 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 216.57/216.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.57/216.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 216.57/216.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.57/216.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 216.57/216.88 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 216.57/216.88 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.57/216.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 216.57/216.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.57/216.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 216.57/216.88 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 216.57/216.88 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 216.57/216.88 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 219.94/220.21 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 219.94/220.21 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 219.94/220.21 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 219.94/220.21 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 219.94/220.21 Found (eq_ref0 (x0 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 219.94/220.21 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 219.94/220.21 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 219.94/220.21 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 219.94/220.21 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 219.94/220.21 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 219.94/220.21 Found (eq_ref0 (x2 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 219.94/220.21 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 219.94/220.21 Found (eq_ref0 (x0 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 219.94/220.21 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 219.94/220.21 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 219.94/220.21 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.94/220.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 219.94/220.21 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 219.94/220.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.94/220.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 219.94/220.21 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 219.94/220.21 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 219.94/220.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 219.94/220.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 219.94/220.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 226.73/227.00 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.73/227.00 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 226.73/227.00 Found x3:(P ((cLIKE cP) cS))
% 226.73/227.00 Instantiate: b:=((cLIKE cP) cS):Prop
% 226.73/227.00 Found x3 as proof of (P0 b)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 226.73/227.00 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 226.73/227.00 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 226.73/227.00 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 226.73/227.00 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 226.73/227.00 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 226.73/227.00 Found x1:(P ((cLIKE cP) cS))
% 226.73/227.00 Instantiate: b:=((cLIKE cP) cS):Prop
% 226.73/227.00 Found x1 as proof of (P0 b)
% 226.73/227.00 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 226.73/227.00 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 226.73/227.00 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 226.73/227.00 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 226.73/227.00 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 226.73/227.00 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 226.73/227.00 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 226.73/227.00 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 226.73/227.00 Found (eq_ref00 P) as proof of (P0 b)
% 226.73/227.00 Found ((eq_ref0 b) P) as proof of (P0 b)
% 226.73/227.00 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 226.73/227.00 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 226.73/227.00 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))))))))))
% 226.73/227.00 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
% 226.73/227.00 Found relational_choice as proof of b
% 226.73/227.00 Found eq_ref00:=(eq_ref0 (x6 cP)):(((eq Prop) (x6 cP)) (x6 cP))
% 226.73/227.00 Found (eq_ref0 (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 230.65/230.97 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 230.65/230.97 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 230.65/230.97 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 230.65/230.97 Found ((conj00 ((eq_ref Prop) (x6 cP))) relational_choice) as proof of (P b)
% 230.65/230.97 Found (((conj0 b) ((eq_ref Prop) (x6 cP))) relational_choice) as proof of (P b)
% 230.65/230.97 Found ((((conj (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x6 cP))) relational_choice) as proof of (P b)
% 230.65/230.97 Found ((((conj (((eq Prop) (x6 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x6 cP))) relational_choice) as proof of (P b)
% 230.65/230.97 Found eq_ref00:=(eq_ref0 (x6 cP)):(((eq Prop) (x6 cP)) (x6 cP))
% 230.65/230.97 Found (eq_ref0 (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 230.65/230.97 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 230.65/230.97 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 230.65/230.97 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) b)
% 230.65/230.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.65/230.97 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 230.65/230.97 Found eq_ref000:=(eq_ref00 P):((P (x6 cP))->(P (x6 cP)))
% 230.65/230.97 Found (eq_ref00 P) as proof of (P0 (x6 cP))
% 230.65/230.97 Found ((eq_ref0 (x6 cP)) P) as proof of (P0 (x6 cP))
% 230.65/230.97 Found (((eq_ref Prop) (x6 cP)) P) as proof of (P0 (x6 cP))
% 230.65/230.97 Found (((eq_ref Prop) (x6 cP)) P) as proof of (P0 (x6 cP))
% 230.65/230.97 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 230.65/230.97 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 230.65/230.97 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 230.65/230.97 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 230.65/230.97 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 230.65/230.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.65/230.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 230.65/230.97 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.65/230.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 230.65/230.97 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 230.65/230.97 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 230.65/230.97 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 230.65/230.97 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 230.65/230.97 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 230.65/230.97 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 230.65/230.97 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 230.65/230.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.65/230.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 230.65/230.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.40/235.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 235.40/235.69 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 235.40/235.69 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 235.40/235.69 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 235.40/235.69 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 235.40/235.69 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 235.40/235.69 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 235.40/235.69 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 235.40/235.69 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 235.40/235.69 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 235.40/235.69 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.40/235.69 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 235.40/235.69 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.40/235.69 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 235.40/235.69 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.40/235.69 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 235.40/235.69 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 235.40/235.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.40/235.69 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 235.40/235.69 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 235.40/235.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 235.40/235.69 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 235.40/235.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 241.49/241.81 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 241.49/241.81 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 241.49/241.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 241.49/241.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 241.49/241.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 241.49/241.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.49/241.81 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 241.49/241.81 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 241.49/241.81 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 241.49/241.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 241.49/241.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 241.49/241.81 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 241.49/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.49/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 241.49/241.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.49/241.81 Found (eq_ref0 b) as proof of (P b)
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (P b)
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (P b)
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (P b)
% 241.49/241.81 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 241.49/241.81 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.49/241.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 241.49/241.81 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 241.49/241.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x4 cP))
% 241.49/241.81 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 241.49/241.81 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 241.49/241.81 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 241.49/241.81 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 241.49/241.81 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 241.49/241.81 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 241.49/241.81 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 241.49/241.81 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))))))))))
% 241.49/241.81 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
% 243.56/243.86 Found relational_choice as proof of b
% 243.56/243.86 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 243.56/243.86 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((conj00 ((eq_ref Prop) (x0 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found (((conj0 b) ((eq_ref Prop) (x0 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found ((((conj (((eq Prop) (x0 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x0 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 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))))))))))
% 243.56/243.86 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
% 243.56/243.86 Found relational_choice as proof of b
% 243.56/243.86 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 243.56/243.86 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((conj00 ((eq_ref Prop) (x2 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found (((conj0 b) ((eq_ref Prop) (x2 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found ((((conj (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x2 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found ((((conj (((eq Prop) (x2 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x2 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 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))))))))))
% 243.56/243.86 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
% 243.56/243.86 Found relational_choice as proof of b
% 243.56/243.86 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 243.56/243.86 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 243.56/243.86 Found ((conj00 ((eq_ref Prop) (x4 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found (((conj0 b) ((eq_ref Prop) (x4 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found ((((conj (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x4 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found ((((conj (((eq Prop) (x4 cP)) ((cLIKE cP) cS))) b) ((eq_ref Prop) (x4 cP))) relational_choice) as proof of (P b)
% 243.56/243.86 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 243.56/243.86 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 243.56/243.86 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 243.56/243.86 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 243.56/243.86 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 243.56/243.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 243.56/243.86 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 246.82/247.13 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 246.82/247.13 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 246.82/247.13 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 246.82/247.13 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 246.82/247.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.82/247.13 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 246.82/247.13 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 246.82/247.13 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 246.82/247.13 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 246.82/247.13 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 246.82/247.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.82/247.13 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 246.82/247.13 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 246.82/247.13 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 246.82/247.13 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 246.82/247.13 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 246.82/247.13 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 246.82/247.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.82/247.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 246.82/247.13 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.82/247.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 246.82/247.13 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 246.82/247.13 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 246.82/247.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.82/247.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.82/247.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 246.82/247.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 260.36/260.65 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 260.36/260.65 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 260.36/260.65 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 260.36/260.65 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 260.36/260.65 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 260.36/260.65 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 260.36/260.65 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 260.36/260.65 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 260.36/260.65 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 260.36/260.65 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 260.36/260.65 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 260.36/260.65 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 260.36/260.65 Found (eq_ref00 P) as proof of (P0 b)
% 260.36/260.65 Found ((eq_ref0 b) P) as proof of (P0 b)
% 260.36/260.65 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 260.36/260.65 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 260.36/260.65 Found (eq_ref0 b) as proof of (P b)
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (P b)
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (P b)
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (P b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 260.36/260.65 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found x5:(P ((cLIKE cP) cS))
% 260.36/260.65 Instantiate: b:=((cLIKE cP) cS):Prop
% 260.36/260.65 Found x5 as proof of (P0 b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 260.36/260.65 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 260.36/260.65 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 260.36/260.65 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 260.36/260.65 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 260.36/260.65 Found (eq_ref0 b) as proof of (P b)
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (P b)
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (P b)
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (P b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 260.36/260.65 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 260.36/260.65 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 260.36/260.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 260.36/260.65 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 260.36/260.65 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 260.36/260.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 260.36/260.65 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 260.36/260.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 265.14/265.45 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 265.14/265.45 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 265.14/265.45 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 265.14/265.45 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 265.14/265.45 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b0)
% 265.14/265.45 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.14/265.45 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 265.14/265.45 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 265.14/265.45 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.14/265.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.14/265.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 265.14/265.45 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 265.14/265.45 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found eq_ref00:=(eq_ref0 (x6 cJ)):(((eq Prop) (x6 cJ)) (x6 cJ))
% 265.14/265.45 Found (eq_ref0 (x6 cJ)) as proof of b
% 265.14/265.45 Found ((eq_ref Prop) (x6 cJ)) as proof of b
% 265.14/265.45 Found ((eq_ref Prop) (x6 cJ)) as proof of b
% 265.14/265.45 Found ((eq_ref Prop) (x6 cJ)) as proof of b
% 265.14/265.45 Found eq_ref00:=(eq_ref0 (x6 cP)):(((eq Prop) (x6 cP)) (x6 cP))
% 265.14/265.45 Found (eq_ref0 (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) (x6 cP)) as proof of (((eq Prop) (x6 cP)) ((cLIKE cP) cS))
% 265.14/265.45 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 265.14/265.45 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 265.14/265.45 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 265.14/265.45 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 265.14/265.45 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 265.14/265.45 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 265.14/265.45 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 265.14/265.45 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 265.14/265.45 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 265.14/265.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.14/265.45 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 265.14/265.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 265.14/265.45 Found x7:(P (x6 cP))
% 265.14/265.45 Instantiate: b:=(x6 cP):Prop
% 265.14/265.45 Found x7 as proof of (P0 b)
% 265.14/265.45 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 265.14/265.45 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 265.14/265.45 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 268.92/269.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 268.92/269.23 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 268.92/269.23 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 268.92/269.23 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 268.92/269.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.92/269.23 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 268.92/269.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 268.92/269.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 268.92/269.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 268.92/269.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 268.92/269.23 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 268.92/269.23 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 268.92/269.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 268.92/269.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 268.92/269.23 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 268.92/269.23 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 268.92/269.23 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 268.92/269.23 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) b)
% 268.92/269.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.92/269.23 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 268.92/269.23 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 268.92/269.23 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 268.92/269.23 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 268.92/269.23 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 268.92/269.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.92/269.23 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 268.92/269.23 Found eq_ref000:=(eq_ref00 P):((P (x4 cP))->(P (x4 cP)))
% 268.92/269.23 Found (eq_ref00 P) as proof of (P0 (x4 cP))
% 268.92/269.23 Found ((eq_ref0 (x4 cP)) P) as proof of (P0 (x4 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x4 cP)) P) as proof of (P0 (x4 cP))
% 268.92/269.23 Found eq_ref000:=(eq_ref00 P):((P (x2 cP))->(P (x2 cP)))
% 268.92/269.23 Found (eq_ref00 P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found ((eq_ref0 (x2 cP)) P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found (((eq_ref Prop) (x2 cP)) P) as proof of (P0 (x2 cP))
% 268.92/269.23 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 276.01/276.34 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 276.01/276.34 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 276.01/276.34 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 276.01/276.34 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.01/276.34 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found eq_ref000:=(eq_ref00 P):((P (x0 cP))->(P (x0 cP)))
% 276.01/276.34 Found (eq_ref00 P) as proof of (P0 (x0 cP))
% 276.01/276.34 Found ((eq_ref0 (x0 cP)) P) as proof of (P0 (x0 cP))
% 276.01/276.34 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 276.01/276.34 Found (((eq_ref Prop) (x0 cP)) P) as proof of (P0 (x0 cP))
% 276.01/276.34 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 276.01/276.34 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 276.01/276.34 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 276.01/276.34 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 276.01/276.34 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.01/276.34 Found (eq_ref0 b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cLIKE cP) cS))
% 276.01/276.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 276.01/276.34 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 276.01/276.34 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.01/276.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.01/276.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 276.01/276.34 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 276.01/276.34 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 276.01/276.34 Found (eq_ref0 a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cS)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.01/276.34 Found (eq_ref0 b) as proof of (P b)
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (P b)
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (P b)
% 276.01/276.34 Found ((eq_ref Prop) b) as proof of (P b)
% 276.01/276.34 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 276.01/276.34 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 276.01/276.34 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.85/284.16 Found (eq_ref0 b) as proof of (P b)
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (P b)
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (P b)
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (P b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 283.85/284.16 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found x5:(P ((cLIKE cP) cS))
% 283.85/284.16 Instantiate: b:=((cLIKE cP) cS):Prop
% 283.85/284.16 Found x5 as proof of (P0 b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 283.85/284.16 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 283.85/284.16 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 283.85/284.16 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 283.85/284.16 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) b)
% 283.85/284.16 Found x5:(P ((cLIKE cP) cS))
% 283.85/284.16 Instantiate: b:=((cLIKE cP) cS):Prop
% 283.85/284.16 Found x5 as proof of (P0 b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 283.85/284.16 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 283.85/284.16 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 283.85/284.16 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 283.85/284.16 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.85/284.16 Found (eq_ref0 b) as proof of (P b)
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (P b)
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (P b)
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (P b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 283.85/284.16 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 283.85/284.16 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.85/284.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 283.85/284.16 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.85/284.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 283.85/284.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.85/284.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 283.85/284.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 283.85/284.16 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 283.85/284.16 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 283.85/284.16 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.22/288.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (x2 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x2 cP))
% 288.22/288.59 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 288.22/288.59 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 288.22/288.59 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.22/288.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 288.22/288.59 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.22/288.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found eq_ref00:=(eq_ref0 (x0 cJ)):(((eq Prop) (x0 cJ)) (x0 cJ))
% 288.22/288.59 Found (eq_ref0 (x0 cJ)) as proof of b
% 288.22/288.59 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 288.22/288.59 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 288.22/288.59 Found ((eq_ref Prop) (x0 cJ)) as proof of b
% 288.22/288.59 Found eq_ref00:=(eq_ref0 (x0 cP)):(((eq Prop) (x0 cP)) (x0 cP))
% 288.22/288.59 Found (eq_ref0 (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 288.22/288.59 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 288.22/288.59 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 288.22/288.59 Found ((eq_ref Prop) (x0 cP)) as proof of (((eq Prop) (x0 cP)) ((cLIKE cP) cS))
% 288.22/288.59 Found eq_ref000:=(eq_ref00 P):((P ((cLIKE cP) cS))->(P ((cLIKE cP) cS)))
% 288.22/288.59 Found (eq_ref00 P) as proof of (P0 ((cLIKE cP) cS))
% 288.22/288.59 Found ((eq_ref0 ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 288.22/288.59 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 288.22/288.59 Found (((eq_ref Prop) ((cLIKE cP) cS)) P) as proof of (P0 ((cLIKE cP) cS))
% 288.22/288.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.22/288.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 288.22/288.59 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 288.22/288.59 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 288.22/288.59 Found eq_ref00:=(eq_ref0 (x2 cJ)):(((eq Prop) (x2 cJ)) (x2 cJ))
% 288.22/288.59 Found (eq_ref0 (x2 cJ)) as proof of b
% 288.22/288.59 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 288.22/288.59 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 288.22/288.59 Found ((eq_ref Prop) (x2 cJ)) as proof of b
% 288.22/288.59 Found eq_ref00:=(eq_ref0 (x2 cP)):(((eq Prop) (x2 cP)) (x2 cP))
% 288.22/288.59 Found (eq_ref0 (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) (x2 cP)) as proof of (((eq Prop) (x2 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 292.87/293.20 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.87/293.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (x0 cP))
% 292.87/293.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 292.87/293.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 292.87/293.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x0 cP))
% 292.87/293.20 Found eq_ref00:=(eq_ref0 (x4 cJ)):(((eq Prop) (x4 cJ)) (x4 cJ))
% 292.87/293.20 Found (eq_ref0 (x4 cJ)) as proof of b
% 292.87/293.20 Found ((eq_ref Prop) (x4 cJ)) as proof of b
% 292.87/293.20 Found ((eq_ref Prop) (x4 cJ)) as proof of b
% 292.87/293.20 Found ((eq_ref Prop) (x4 cJ)) as proof of b
% 292.87/293.20 Found eq_ref00:=(eq_ref0 (x4 cP)):(((eq Prop) (x4 cP)) (x4 cP))
% 292.87/293.20 Found (eq_ref0 (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) (x4 cP)) as proof of (((eq Prop) (x4 cP)) ((cLIKE cP) cS))
% 292.87/293.20 Found x7:(P (x0 cP))
% 292.87/293.20 Instantiate: b:=(x0 cP):Prop
% 292.87/293.20 Found x7 as proof of (P0 b)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 292.87/293.20 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 292.87/293.20 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b0)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 292.87/293.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 292.87/293.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 292.87/293.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 292.87/293.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 292.87/293.20 Found x7:(P (x2 cP))
% 292.87/293.20 Instantiate: b:=(x2 cP):Prop
% 292.87/293.20 Found x7 as proof of (P0 b)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 292.87/293.20 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.87/293.20 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 292.87/293.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 292.87/293.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 292.87/293.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 292.87/293.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 292.87/293.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cLIKE cP) cS))
% 292.87/293.20 Found x7:(P (x4 cP))
% 292.87/293.20 Instantiate: b:=(x4 cP):Prop
% 292.87/293.20 Found x7 as proof of (P0 b)
% 292.87/293.20 Found eq_ref00:=(eq_ref0 ((cLIKE cP) cS)):(((eq Prop) ((cLIKE cP) cS)) ((cLIKE cP) cS))
% 292.87/293.20 Found (eq_ref0 ((cLIKE cP) cS)) as proof of (((eq Prop) ((cLIKE cP) cS)) b)
% 292.87/293.20 Found ((eq_ref Prop) ((cLIKE cP) c
%------------------------------------------------------------------------------