TSTP Solution File: SYO317^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO317^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 00:51:09 EDT 2022
% Result : Unknown 20.82s 21.04s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO317^5 : 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 : n013.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 : Sat Mar 12 03:20:37 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 1.67/1.91 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.67/1.91 FOF formula (<kernel.Constant object at 0x1482c20>, <kernel.DependentProduct object at 0x1486ef0>) of role type named cP
% 1.67/1.91 Using role type
% 1.67/1.91 Declaring cP:(fofType->Prop)
% 1.67/1.91 FOF formula (<kernel.Constant object at 0x14826c8>, <kernel.DependentProduct object at 0x2af2b07cc290>) of role type named f
% 1.67/1.91 Using role type
% 1.67/1.91 Declaring f:(fofType->fofType)
% 1.67/1.91 FOF formula (<kernel.Constant object at 0x1486ef0>, <kernel.DependentProduct object at 0x2af2b07cc5a8>) of role type named cEQ
% 1.67/1.91 Using role type
% 1.67/1.91 Declaring cEQ:(fofType->(fofType->Prop))
% 1.67/1.91 FOF formula (<kernel.Constant object at 0x1482950>, <kernel.Single object at 0x1482128>) of role type named a
% 1.67/1.91 Using role type
% 1.67/1.91 Declaring a:fofType
% 1.67/1.91 FOF formula (((and ((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xx:fofType), ((A (f Xx))->(cP Xx)))) ((ex fofType) (fun (Xz:fofType)=> (A Xz))))))) of role conjecture named cTHM304
% 1.67/1.91 Conjecture to prove = (((and ((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xx:fofType), ((A (f Xx))->(cP Xx)))) ((ex fofType) (fun (Xz:fofType)=> (A Xz))))))):Prop
% 1.67/1.91 We need to prove ['(((and ((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xx:fofType), ((A (f Xx))->(cP Xx)))) ((ex fofType) (fun (Xz:fofType)=> (A Xz)))))))']
% 1.67/1.91 Parameter fofType:Type.
% 1.67/1.91 Parameter cP:(fofType->Prop).
% 1.67/1.91 Parameter f:(fofType->fofType).
% 1.67/1.91 Parameter cEQ:(fofType->(fofType->Prop)).
% 1.67/1.91 Parameter a:fofType.
% 1.67/1.91 Trying to prove (((and ((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))->((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> ((and (forall (Xx:fofType), ((A (f Xx))->(cP Xx)))) ((ex fofType) (fun (Xz:fofType)=> (A Xz)))))))
% 1.67/1.91 Found x000:=(x00 Xx):(cP Xx)
% 1.67/1.91 Found (x00 Xx) as proof of (cP Xx)
% 1.67/1.91 Found (x00 Xx) as proof of (cP Xx)
% 1.67/1.91 Found (fun (x00:(x0 (f Xx)))=> (x00 Xx)) as proof of (cP Xx)
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> (x00 Xx)) as proof of ((x0 (f Xx))->(cP Xx))
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> (x00 Xx)) as proof of (forall (Xx:fofType), ((x0 (f Xx))->(cP Xx)))
% 1.67/1.91 Found x000:=(x00 Xx):(cP Xx)
% 1.67/1.91 Found (x00 Xx) as proof of (cP Xx)
% 1.67/1.91 Found (x00 Xx) as proof of (cP Xx)
% 1.67/1.91 Found (fun (x00:(x2 (f Xx)))=> (x00 Xx)) as proof of (cP Xx)
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x2 (f Xx)))=> (x00 Xx)) as proof of ((x2 (f Xx))->(cP Xx))
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x2 (f Xx)))=> (x00 Xx)) as proof of (forall (Xx:fofType), ((x2 (f Xx))->(cP Xx)))
% 1.67/1.91 Found x000:=(x00 Xx):(cP Xx)
% 1.67/1.91 Found (x00 Xx) as proof of (cP Xx)
% 1.67/1.91 Found (x00 Xx) as proof of (cP Xx)
% 1.67/1.91 Found (fun (x00:(x4 (f Xx)))=> (x00 Xx)) as proof of (cP Xx)
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x4 (f Xx)))=> (x00 Xx)) as proof of ((x4 (f Xx))->(cP Xx))
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x4 (f Xx)))=> (x00 Xx)) as proof of (forall (Xx:fofType), ((x4 (f Xx))->(cP Xx)))
% 1.67/1.91 Found x00000:=(x0000 Xx):(cP Xx)
% 1.67/1.91 Found (x0000 Xx) as proof of (cP Xx)
% 1.67/1.91 Found ((fun (Xx0:fofType)=> ((x000 Xx0) x1)) Xx) as proof of (cP Xx)
% 1.67/1.91 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x1)) Xx) as proof of (cP Xx)
% 1.67/1.91 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x1)) Xx) as proof of (cP Xx)
% 1.67/1.91 Found (fun (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x1)) Xx)) as proof of (cP Xx)
% 1.67/1.91 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x1)) Xx)) as proof of ((x0 (f Xx))->(cP Xx))
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x1)) Xx)) as proof of (forall (Xx:fofType), ((x0 (f Xx))->(cP Xx)))
% 3.13/3.32 Found x00000:=(x0000 Xx):(cP Xx)
% 3.13/3.32 Found (x0000 Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> ((x000 Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x3)) Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x3)) Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found (fun (x00:(x2 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x3)) Xx0) x4)) Xx)) as proof of (cP Xx)
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x2 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x3)) Xx0) x4)) Xx)) as proof of ((x2 (f Xx))->(cP Xx))
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x2 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x3)) Xx0) x4)) Xx)) as proof of (forall (Xx:fofType), ((x2 (f Xx))->(cP Xx)))
% 3.13/3.32 Found x000:=(x00 Xx):(cP Xx)
% 3.13/3.32 Found (x00 Xx) as proof of (cP Xx)
% 3.13/3.32 Found (x00 Xx) as proof of (cP Xx)
% 3.13/3.32 Found (fun (x00:(x6 (f Xx)))=> (x00 Xx)) as proof of (cP Xx)
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x6 (f Xx)))=> (x00 Xx)) as proof of ((x6 (f Xx))->(cP Xx))
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x6 (f Xx)))=> (x00 Xx)) as proof of (forall (Xx:fofType), ((x6 (f Xx))->(cP Xx)))
% 3.13/3.32 Found x0000000:=(x000000 Xx):(cP Xx)
% 3.13/3.32 Found (x000000 Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> ((x00000 Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x0000 Xx0) x2)) Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x000 Xx0) x3)) Xx0) x2)) Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x1)) Xx0) x3)) Xx0) x2)) Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x1)) Xx0) x3)) Xx0) x2)) Xx0) x4)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found (fun (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x1)) Xx0) x3)) Xx0) x2)) Xx0) x4)) Xx)) as proof of (cP Xx)
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x1)) Xx0) x3)) Xx0) x2)) Xx0) x4)) Xx)) as proof of ((x0 (f Xx))->(cP Xx))
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x1)) Xx0) x3)) Xx0) x2)) Xx0) x4)) Xx)) as proof of (forall (Xx:fofType), ((x0 (f Xx))->(cP Xx)))
% 3.13/3.32 Found x00000:=(x0000 Xx):(cP Xx)
% 3.13/3.32 Found (x0000 Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> ((x000 Xx0) x5)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x6)) Xx0) x5)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x6)) Xx0) x5)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found (fun (x00:(x4 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x6)) Xx0) x5)) Xx)) as proof of (cP Xx)
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x4 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x6)) Xx0) x5)) Xx)) as proof of ((x4 (f Xx))->(cP Xx))
% 3.13/3.32 Found (fun (Xx:fofType) (x00:(x4 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x6)) Xx0) x5)) Xx)) as proof of (forall (Xx:fofType), ((x4 (f Xx))->(cP Xx)))
% 3.13/3.32 Found x0000000:=(x000000 Xx):(cP Xx)
% 3.13/3.32 Found (x000000 Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> ((x00000 Xx0) x5)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x0000 Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x000 Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 3.13/3.32 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x4)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x4)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found (fun (x00:(x2 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x4)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx)) as proof of (cP Xx)
% 4.87/5.05 Found (fun (Xx:fofType) (x00:(x2 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x4)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx)) as proof of ((x2 (f Xx))->(cP Xx))
% 4.87/5.05 Found (fun (Xx:fofType) (x00:(x2 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x4)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx)) as proof of (forall (Xx:fofType), ((x2 (f Xx))->(cP Xx)))
% 4.87/5.05 Found x000000000:=(x00000000 Xx):(cP Xx)
% 4.87/5.05 Found (x00000000 Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> ((x0000000 Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x000000 Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00000 Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x0000 Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x000 Xx0) x4)) Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x4)) Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x4)) Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx) as proof of (cP Xx)
% 4.87/5.05 Found (fun (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x4)) Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx)) as proof of (cP Xx)
% 4.87/5.05 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x4)) Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx)) as proof of ((x0 (f Xx))->(cP Xx))
% 4.87/5.05 Found (fun (Xx:fofType) (x00:(x0 (f Xx)))=> ((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> (((fun (Xx0:fofType)=> ((x00 Xx0) x2)) Xx0) x4)) Xx0) x1)) Xx0) x6)) Xx0) x3)) Xx0) x5)) Xx)) as proof of (forall (Xx:fofType), ((x0 (f Xx))->(cP Xx)))
% 4.87/5.05 Found x3:(cP a)
% 4.87/5.05 Instantiate: x7:=a:fofType
% 4.87/5.05 Found x3 as proof of (x6 x7)
% 4.87/5.05 Found x3 as proof of (x6 x7)
% 4.87/5.05 Found (ex_intro100 x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x6 Xz)))
% 4.87/5.05 Found ((ex_intro10 a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x6 Xz)))
% 4.87/5.05 Found (((ex_intro1 (fun (Xz:fofType)=> (x6 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x6 Xz)))
% 4.87/5.05 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x6 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x6 Xz)))
% 4.87/5.05 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x6 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x6 Xz)))
% 4.87/5.05 Found x4:(cP a)
% 4.87/5.05 Instantiate: x7:=a:fofType
% 4.87/5.05 Found x4 as proof of (x2 x7)
% 4.87/5.05 Found x4 as proof of (x2 x7)
% 4.87/5.05 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 4.87/5.05 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 4.87/5.05 Found (((ex_intro1 (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 4.87/5.05 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.43 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.43 Found x3:(cP a)
% 5.25/5.43 Instantiate: x7:=a:fofType
% 5.25/5.43 Found x3 as proof of (x4 x7)
% 5.25/5.43 Found x3 as proof of (x4 x7)
% 5.25/5.43 Found (ex_intro100 x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found ((ex_intro10 a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found (((ex_intro1 (fun (Xz:fofType)=> (x4 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found x4:(cP a)
% 5.25/5.43 Instantiate: x7:=a:fofType
% 5.25/5.43 Found x4 as proof of (x0 x7)
% 5.25/5.43 Found x4 as proof of (x0 x7)
% 5.25/5.43 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.43 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.43 Found (((ex_intro1 (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.43 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.43 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.43 Found x3:(cP a)
% 5.25/5.43 Instantiate: x7:=a:fofType
% 5.25/5.43 Found x3 as proof of (x4 x7)
% 5.25/5.43 Found x3 as proof of (x4 x7)
% 5.25/5.43 Found (ex_intro100 x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found ((ex_intro10 a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found (((ex_intro1 (fun (Xz:fofType)=> (x4 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found (fun (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3)) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3)) as proof of ((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x4 Xz))))
% 5.25/5.43 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3)) as proof of ((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))))
% 5.25/5.43 Found (and_rect20 (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found ((and_rect2 ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x2)) ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.43 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x2)) ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x4 Xz))) a) x3))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x4 Xz)))
% 5.25/5.44 Found x4:(cP a)
% 5.25/5.44 Instantiate: x7:=a:fofType
% 5.25/5.44 Found x4 as proof of (x0 x7)
% 5.25/5.44 Found x4 as proof of (x0 x7)
% 5.25/5.44 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (((ex_intro1 (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (fun (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz))))
% 5.25/5.44 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))))
% 5.25/5.44 Found (and_rect20 (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found ((and_rect2 ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found x4:(cP a)
% 5.25/5.44 Instantiate: x7:=a:fofType
% 5.25/5.44 Found x4 as proof of (x0 x7)
% 5.25/5.44 Found x4 as proof of (x0 x7)
% 5.25/5.44 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (((ex_intro1 (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (fun (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz))))
% 5.25/5.44 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))))
% 5.25/5.44 Found (and_rect20 (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found ((and_rect2 ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (fun (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.44 Found (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))) as proof of ((cP a)->((ex fofType) (fun (Xz:fofType)=> (x0 Xz))))
% 5.25/5.44 Found (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))) as proof of (((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))))
% 5.25/5.45 Found (and_rect10 (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.45 Found ((and_rect1 ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.45 Found (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.45 Found (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.45 Found x4:(cP a)
% 5.25/5.45 Instantiate: x7:=a:fofType
% 5.25/5.45 Found x4 as proof of (x2 x7)
% 5.25/5.45 Found x4 as proof of (x2 x7)
% 5.25/5.45 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (((ex_intro1 (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (fun (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)) as proof of ((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x2 Xz))))
% 5.25/5.45 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)) as proof of ((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))))
% 5.25/5.45 Found (and_rect20 (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found ((and_rect2 ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found x4:(cP a)
% 5.25/5.45 Instantiate: x7:=a:fofType
% 5.25/5.45 Found x4 as proof of (x2 x7)
% 5.25/5.45 Found x4 as proof of (x2 x7)
% 5.25/5.45 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (((ex_intro1 (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (fun (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.45 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)) as proof of ((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x2 Xz))))
% 5.25/5.45 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)) as proof of ((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))))
% 5.25/5.46 Found (and_rect20 (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found ((and_rect2 ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found (fun (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)))) as proof of ((cP a)->((ex fofType) (fun (Xz:fofType)=> (x2 Xz))))
% 5.25/5.46 Found (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4)))) as proof of (((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))))
% 5.25/5.46 Found (and_rect10 (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found ((and_rect1 ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x0)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x0)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x2 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x2 Xz)))
% 5.25/5.46 Found x4:(cP a)
% 5.25/5.46 Instantiate: x7:=a:fofType
% 5.25/5.46 Found x4 as proof of (x0 x7)
% 5.25/5.46 Found x4 as proof of (x0 x7)
% 5.25/5.46 Found (ex_intro100 x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.46 Found ((ex_intro10 a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.46 Found (((ex_intro1 (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.46 Found ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.46 Found (fun (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.46 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz))))
% 5.25/5.47 Found (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)) as proof of ((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))))
% 5.25/5.47 Found (and_rect20 (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found ((and_rect2 ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (fun (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))) as proof of ((cP a)->((ex fofType) (fun (Xz:fofType)=> (x0 Xz))))
% 5.25/5.47 Found (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))) as proof of (((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))))
% 5.25/5.47 Found (and_rect10 (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found ((and_rect1 ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (fun (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (fun (x1:((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))))) as proof of ((forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz))))
% 5.25/5.47 Found (fun (x1:((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4)))))) as proof of (((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))->((forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz)))->((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))))
% 5.25/5.47 Found (and_rect00 (fun (x1:((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found ((and_rect0 ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x1:((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (((fun (P:Type) (x1:(((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))->((forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz)))->P)))=> (((((and_rect ((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz)))) P) x1) x)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x1:((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 5.25/5.47 Found (((fun (P:Type) (x1:(((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))->((forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz)))->P)))=> (((((and_rect ((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz)))) P) x1) x)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x1:((and ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a))) (x2:(forall (Xy:fofType) (Xz:fofType), (((cEQ (f Xy)) (f Xz))->((cEQ Xy) Xz))))=> (((fun (P:Type) (x3:(((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (cP a)) P) x3) x1)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x3:((and (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))) (x4:(cP a))=> (((fun (P:Type) (x5:((forall (Xx:fofType), ((cEQ Xx) Xx))->((forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cEQ Xx) Xx))) (forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy)))) P) x5) x3)) ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))) (fun (x5:(forall (Xx:fofType), ((cEQ Xx) Xx))) (x6:(forall (Xx:fofType) (Xy:fofType), (((and ((cEQ Xx) Xy)) (cP Xx))->(cP Xy))))=> ((((ex_intro fofType) (fun (Xz:fofType)=> (x0 Xz))) a) x4))))))) as proof of ((ex fofType) (fun (Xz:fofType)=> (x0 Xz)))
% 10.33/10.54 Found x3:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x3 as proof of (cP Xx0)
% 10.33/10.54 Found x40:=(x4 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x4 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x4 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x4 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x4:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x4 as proof of (cP Xx0)
% 10.33/10.54 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x4:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x4 as proof of (cP Xx0)
% 10.33/10.54 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x3:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x3 as proof of (cP Xx0)
% 10.33/10.54 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x5:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x5 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x3:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x3 as proof of (cP Xx0)
% 10.33/10.54 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x3:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x3 as proof of (cP Xx0)
% 10.33/10.54 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x4:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x4 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x4:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x4 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x3:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x3 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x4:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x4 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x5:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x5 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x5:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x5 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found x5:(cP a)
% 10.33/10.54 Instantiate: Xx0:=a:fofType
% 10.33/10.54 Found x5 as proof of (cP Xx0)
% 10.33/10.54 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 10.33/10.54 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x4:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x4 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x3:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x3 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x4:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x4 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x4:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x4 as proof of (cP Xx0)
% 11.30/11.47 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x4:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x4 as proof of (cP Xx0)
% 11.30/11.47 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x4:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x4 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x40:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x40 as proof of (cP Xx0)
% 11.30/11.47 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x4:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x4 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x40:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x40 as proof of (cP Xx0)
% 11.30/11.47 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found x5:(cP a)
% 11.30/11.47 Instantiate: Xx0:=a:fofType
% 11.30/11.47 Found x5 as proof of (cP Xx0)
% 11.30/11.47 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 11.30/11.47 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x40:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x40 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x4:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x4 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x5:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x5 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x4:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x4 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x5:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x5 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x40:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x40 as proof of (cP Xx0)
% 15.81/16.01 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x40:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x40 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x40:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x40 as proof of (cP Xx0)
% 15.81/16.01 Found x51:=(x5 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x40:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x40 as proof of (cP Xx0)
% 15.81/16.01 Found x51:=(x5 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x40:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x40 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x3:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x3 as proof of (cP Xx0)
% 15.81/16.01 Found x40:=(x4 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x4 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x4 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x4 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x4:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x4 as proof of (cP Xx0)
% 15.81/16.01 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x3:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x3 as proof of (cP Xx0)
% 15.81/16.01 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x4:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x4 as proof of (cP Xx0)
% 15.81/16.01 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x5:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x5 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x4:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x4 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x4:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x4 as proof of (cP Xx0)
% 15.81/16.01 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 15.81/16.01 Found x5:(cP a)
% 15.81/16.01 Instantiate: Xx0:=a:fofType
% 15.81/16.01 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x3:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x3 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x4:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x4 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x3:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x3 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x5:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x5 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x4:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x4 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x3:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x3 as proof of (cP Xx0)
% 17.43/17.61 Found x51:=(x5 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x3:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x3 as proof of (cP Xx0)
% 17.43/17.61 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x4:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x4 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x4:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x4 as proof of (cP Xx0)
% 17.43/17.61 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 17.43/17.61 Found x4:(cP a)
% 17.43/17.61 Instantiate: Xx0:=a:fofType
% 17.43/17.61 Found x4 as proof of (cP Xx0)
% 17.43/17.61 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 17.43/17.61 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x4:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x4 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x51:=(x5 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x51:=(x5 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x5:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x5 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x4:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x4 as proof of (cP Xx0)
% 20.82/21.02 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x4:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x4 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x5:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x5 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x5:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x5 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x4:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x4 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x5:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x5 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x50:=(x5 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x5 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x60:=(x6 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x6 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found x40:(cP a)
% 20.82/21.02 Instantiate: Xx0:=a:fofType
% 20.82/21.02 Found x40 as proof of (cP Xx0)
% 20.82/21.02 Found x500:=(x50 Xx0):((cEQ Xx0) Xx0)
% 20.82/21.02 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 Found (x50 Xx0) as proof of ((cEQ Xx0) Xx)
% 20.82/21.02 % SZS status GaveUp for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------