TSTP Solution File: SYO137^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO137^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 00:50:43 EDT 2022
% Result : Unknown 9.19s 9.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYO137^5 : TPTP v7.5.0. Released v4.0.0.
% 0.04/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Fri Mar 11 16:29:14 EST 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 1.91/2.09 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.91/2.09 FOF formula (<kernel.Constant object at 0x1be5e60>, <kernel.DependentProduct object at 0x1bbfea8>) of role type named cN
% 1.91/2.09 Using role type
% 1.91/2.09 Declaring cN:(fofType->Prop)
% 1.91/2.09 FOF formula (<kernel.Constant object at 0x1be5e60>, <kernel.DependentProduct object at 0x1bbf9e0>) of role type named cM
% 1.91/2.09 Using role type
% 1.91/2.09 Declaring cM:(fofType->Prop)
% 1.91/2.09 FOF formula ((iff ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))) (forall (Xx:fofType), (cN Xx))) of role conjecture named cX2304
% 1.91/2.09 Conjecture to prove = ((iff ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))) (forall (Xx:fofType), (cN Xx))):Prop
% 1.91/2.09 Parameter fofType_DUMMY:fofType.
% 1.91/2.09 We need to prove ['((iff ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))) (forall (Xx:fofType), (cN Xx)))']
% 1.91/2.09 Parameter fofType:Type.
% 1.91/2.09 Parameter cN:(fofType->Prop).
% 1.91/2.09 Parameter cM:(fofType->Prop).
% 1.91/2.09 Trying to prove ((iff ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))) (forall (Xx:fofType), (cN Xx)))
% 1.91/2.09 Found x00:=(x0 x10):(forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x10) as proof of (forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x10) as proof of (forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found x00:=(x0 x10):(forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x10) as proof of (forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x10) as proof of (forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x01 (x1 x00)) as proof of (cM Xx0)
% 1.91/2.09 Found ((fun (x2:(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0))))=> ((x0 x2) Xx0)) (x1 x00)) as proof of (cM Xx0)
% 1.91/2.09 Found ((fun (x2:(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0))))=> ((x0 x2) Xx0)) (x1 x00)) as proof of (cM Xx0)
% 1.91/2.09 Found x00:=(x0 x11):(forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x11) as proof of (forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x11) as proof of (forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 1.91/2.09 Found (x01 (x1 x00)) as proof of (cM Xx0)
% 1.91/2.09 Found ((fun (x2:(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0))))=> ((x0 x2) Xx0)) (x1 x00)) as proof of (cM Xx0)
% 1.91/2.09 Found ((fun (x2:(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0))))=> ((x0 x2) Xx0)) (x1 x00)) as proof of (cM Xx0)
% 1.91/2.09 Found x00:=(x0 x11):(forall (Xx0:fofType), (cM Xx0))
% 1.91/2.09 Found (x0 x11) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found (x0 x11) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x00:=(x0 x12):(forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found (x0 x12) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found (x0 x12) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x00:=(x0 x12):(forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found (x0 x12) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found (x0 x12) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.18/3.42 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.18/3.42 Found x3:=(x Xx0):(cN Xx0)
% 3.18/3.42 Found (x Xx0) as proof of (cN Xx0)
% 3.18/3.42 Found (x Xx0) as proof of (cN Xx0)
% 3.18/3.42 Found (x2 (x Xx0)) as proof of (cM Xx)
% 3.18/3.42 Found (x2 (x Xx0)) as proof of (cM Xx)
% 3.18/3.42 Found (fun (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (cM Xx)
% 3.18/3.42 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cN Xx0)->(cM Xx0))->(cM Xx))
% 3.18/3.42 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->(cM Xx)))
% 3.18/3.42 Found (and_rect00 (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 3.18/3.42 Found ((and_rect0 (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 3.18/3.42 Found (((fun (P:Type) (x1:(((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->P)))=> (((((and_rect ((cM Xx0)->(cN Xx0))) ((cN Xx0)->(cM Xx0))) P) x1) x00)) (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 3.18/3.42 Found (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))) as proof of (cM Xx)
% 3.18/3.42 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (cM Xx)
% 3.18/3.42 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (forall (Xx:fofType), (cM Xx))
% 3.90/4.06 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))
% 3.90/4.06 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found x3:=(x Xx0):(cN Xx0)
% 3.90/4.06 Found (x Xx0) as proof of (cN Xx0)
% 3.90/4.06 Found (x Xx0) as proof of (cN Xx0)
% 3.90/4.06 Found (x2 (x Xx0)) as proof of (cM Xx)
% 3.90/4.06 Found (x2 (x Xx0)) as proof of (cM Xx)
% 3.90/4.06 Found (fun (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (cM Xx)
% 3.90/4.06 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cN Xx0)->(cM Xx0))->(cM Xx))
% 3.90/4.06 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->(cM Xx)))
% 3.90/4.06 Found (and_rect00 (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 3.90/4.06 Found ((and_rect0 (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 3.90/4.06 Found (((fun (P:Type) (x1:(((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->P)))=> (((((and_rect ((cM Xx0)->(cN Xx0))) ((cN Xx0)->(cM Xx0))) P) x1) x00)) (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 3.90/4.06 Found (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))) as proof of (cM Xx)
% 3.90/4.06 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (cM Xx)
% 3.90/4.06 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (forall (Xx:fofType), (cM Xx))
% 3.90/4.06 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))
% 3.90/4.06 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found x00:=(x0 x13):(forall (Xx0:fofType), (cM Xx0))
% 3.90/4.06 Found (x0 x13) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.90/4.06 Found (x0 x13) as proof of (forall (Xx0:fofType), (cM Xx0))
% 3.90/4.06 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 3.90/4.06 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 4.31/4.48 Found x3:=(x Xx0):(cN Xx0)
% 4.31/4.48 Found (x Xx0) as proof of (cN Xx0)
% 4.31/4.48 Found (x Xx0) as proof of (cN Xx0)
% 4.31/4.48 Found (x2 (x Xx0)) as proof of (cM Xx)
% 4.31/4.48 Found (x2 (x Xx0)) as proof of (cM Xx)
% 4.31/4.48 Found (fun (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (cM Xx)
% 4.31/4.48 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cN Xx0)->(cM Xx0))->(cM Xx))
% 4.31/4.48 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->(cM Xx)))
% 4.31/4.48 Found (and_rect00 (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 4.31/4.48 Found ((and_rect0 (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 4.31/4.48 Found (((fun (P:Type) (x1:(((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->P)))=> (((((and_rect ((cM Xx0)->(cN Xx0))) ((cN Xx0)->(cM Xx0))) P) x1) x00)) (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 4.31/4.48 Found (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))) as proof of (cM Xx)
% 4.31/4.48 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (cM Xx)
% 4.31/4.48 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (forall (Xx:fofType), (cM Xx))
% 4.31/4.48 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))
% 4.31/4.48 Found x000:=(x00 Xx0):(cM Xx0)
% 4.31/4.48 Found (x00 Xx0) as proof of (cM Xx0)
% 4.31/4.48 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of (cM Xx0)
% 4.31/4.48 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 4.31/4.48 Found x00:=(x0 Xx):(cM Xx)
% 4.31/4.48 Found (x0 Xx) as proof of (cM Xx)
% 4.31/4.48 Found (fun (x1:(cN Xx))=> (x0 Xx)) as proof of (cM Xx)
% 4.31/4.48 Found (fun (x1:(cN Xx))=> (x0 Xx)) as proof of ((cN Xx)->(cM Xx))
% 4.31/4.48 Found x2:=(x Xx):(cN Xx)
% 4.31/4.48 Found (x Xx) as proof of (cN Xx)
% 4.31/4.48 Found (fun (x1:(cM Xx))=> (x Xx)) as proof of (cN Xx)
% 4.31/4.48 Found (fun (x1:(cM Xx))=> (x Xx)) as proof of ((cM Xx)->(cN Xx))
% 4.31/4.48 Found ((conj20 (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 4.31/4.48 Found (((conj2 ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 4.31/4.48 Found ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 4.31/4.48 Found ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 4.31/4.48 Found (fun (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of ((iff (cM Xx)) (cN Xx))
% 4.31/4.48 Found (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))
% 4.31/4.48 Found (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))
% 4.31/4.49 Found ((conj10 (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 4.31/4.49 Found (((conj1 ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 4.31/4.49 Found ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 4.31/4.49 Found ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 4.31/4.49 Found (fun (x:(forall (Xx:fofType), (cN Xx)))=> ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))
% 4.31/4.49 Found (fun (x:(forall (Xx:fofType), (cN Xx)))=> ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))))) as proof of ((forall (Xx:fofType), (cN Xx))->((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx))))
% 5.10/5.26 Found x000:=(x00 Xx0):(cM Xx0)
% 5.10/5.26 Found (x00 Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found x000:=(x00 Xx0):(cM Xx0)
% 5.10/5.26 Found (x00 Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 5.10/5.26 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x000:=(x00 Xx0):(cM Xx0)
% 5.10/5.26 Found (x00 Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found x000:=(x00 Xx0):(cM Xx0)
% 5.10/5.26 Found (x00 Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 5.10/5.26 Found x000:=(x00 Xx0):(cM Xx0)
% 5.10/5.26 Found (x00 Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 5.10/5.26 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x00:=(x0 x14):(forall (Xx0:fofType), (cM Xx0))
% 5.10/5.26 Found (x0 x14) as proof of (forall (Xx0:fofType), (cM Xx0))
% 5.10/5.26 Found (x0 x14) as proof of (forall (Xx0:fofType), (cM Xx0))
% 5.10/5.26 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x00:=(x0 x13):(forall (Xx0:fofType), (cM Xx0))
% 5.10/5.26 Found (x0 x13) as proof of (forall (Xx0:fofType), (cM Xx0))
% 5.10/5.26 Found (x0 x13) as proof of (forall (Xx0:fofType), (cM Xx0))
% 5.10/5.26 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x000:=(x00 Xx0):(cM Xx0)
% 5.10/5.26 Found (x00 Xx0) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of (cM Xx0)
% 5.10/5.26 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 5.10/5.26 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 5.10/5.26 Found x3:=(x Xx0):(cN Xx0)
% 5.10/5.26 Found (x Xx0) as proof of (cN Xx0)
% 5.10/5.26 Found (x Xx0) as proof of (cN Xx0)
% 5.10/5.26 Found (x2 (x Xx0)) as proof of (cM Xx)
% 5.10/5.26 Found (x2 (x Xx0)) as proof of (cM Xx)
% 5.11/5.29 Found (fun (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (cM Xx)
% 5.11/5.29 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cN Xx0)->(cM Xx0))->(cM Xx))
% 5.11/5.29 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->(cM Xx)))
% 5.11/5.29 Found (and_rect00 (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 5.11/5.29 Found ((and_rect0 (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 5.11/5.29 Found (((fun (P:Type) (x1:(((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->P)))=> (((((and_rect ((cM Xx0)->(cN Xx0))) ((cN Xx0)->(cM Xx0))) P) x1) x00)) (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 5.11/5.29 Found (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))) as proof of (cM Xx)
% 5.11/5.29 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (cM Xx)
% 5.11/5.29 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (forall (Xx:fofType), (cM Xx))
% 5.11/5.29 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))
% 5.11/5.29 Found x00:=(x0 Xx):(cM Xx)
% 5.11/5.29 Found (x0 Xx) as proof of (cM Xx)
% 5.11/5.29 Found (fun (x1:(cN Xx))=> (x0 Xx)) as proof of (cM Xx)
% 5.11/5.29 Found (fun (x1:(cN Xx))=> (x0 Xx)) as proof of ((cN Xx)->(cM Xx))
% 5.11/5.29 Found x2:=(x Xx):(cN Xx)
% 5.11/5.29 Found (x Xx) as proof of (cN Xx)
% 5.11/5.29 Found (fun (x1:(cM Xx))=> (x Xx)) as proof of (cN Xx)
% 5.11/5.29 Found (fun (x1:(cM Xx))=> (x Xx)) as proof of ((cM Xx)->(cN Xx))
% 5.11/5.29 Found ((conj20 (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 5.11/5.29 Found (((conj2 ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 5.11/5.29 Found ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 5.11/5.29 Found ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 5.11/5.29 Found (fun (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of ((iff (cM Xx)) (cN Xx))
% 5.11/5.29 Found (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))
% 5.11/5.29 Found (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))
% 5.11/5.29 Found ((conj10 (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 5.11/5.29 Found (((conj1 ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 5.11/5.29 Found ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 5.11/5.29 Found ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 5.11/5.29 Found (fun (x:(forall (Xx:fofType), (cN Xx)))=> ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))
% 5.11/5.29 Found (fun (x:(forall (Xx:fofType), (cN Xx)))=> ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))))) as proof of ((forall (Xx:fofType), (cN Xx))->((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx))))
% 6.44/6.60 Found x000:=(x00 Xx0):(cM Xx0)
% 6.44/6.60 Found (x00 Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found x000:=(x00 Xx0):(cM Xx0)
% 6.44/6.60 Found (x00 Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 6.44/6.60 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 6.44/6.60 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x000:=(x00 Xx0):(cM Xx0)
% 6.44/6.60 Found (x00 Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found x000:=(x00 Xx0):(cM Xx0)
% 6.44/6.60 Found (x00 Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 6.44/6.60 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 6.44/6.60 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x00:=(x0 x14):(forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x14) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x14) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x000:=(x00 Xx0):(cM Xx0)
% 6.44/6.60 Found (x00 Xx0) as proof of (cM Xx0)
% 6.44/6.60 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of (cM Xx0)
% 6.44/6.60 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 6.44/6.60 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x10:=(x1 x05):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x05) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x05) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x00:=(x0 x15):(forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x15) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x15) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x10:=(x1 x05):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x05) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x05) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x00:=(x0 x15):(forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x15) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x15) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x00:=(x0 x10):(forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x10) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found (x0 x10) as proof of (forall (Xx0:fofType), (cM Xx0))
% 6.44/6.60 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 6.44/6.60 Found x000:=(x00 Xx0):(cM Xx0)
% 7.67/7.86 Found (x00 Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found x000:=(x00 Xx0):(cM Xx0)
% 7.67/7.86 Found (x00 Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 7.67/7.86 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 7.67/7.86 Found x10:=(x1 x06):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x06) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x06) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x000:=(x00 Xx0):(cM Xx0)
% 7.67/7.86 Found (x00 Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found x000:=(x00 Xx0):(cM Xx0)
% 7.67/7.86 Found (x00 Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 7.67/7.86 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 7.67/7.86 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 7.67/7.86 Found x10:=(x1 x06):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x06) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x06) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x10:=(x1 x00):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x00) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x01 (x1 x00)) as proof of (cM Xx0)
% 7.67/7.86 Found ((fun (x2:(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0))))=> ((x0 x2) Xx0)) (x1 x00)) as proof of (cM Xx0)
% 7.67/7.86 Found ((fun (x2:(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0))))=> ((x0 x2) Xx0)) (x1 x00)) as proof of (cM Xx0)
% 7.67/7.86 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x00:=(x0 x11):(forall (Xx0:fofType), (cM Xx0))
% 7.67/7.86 Found (x0 x11) as proof of (forall (Xx0:fofType), (cM Xx0))
% 7.67/7.86 Found (x0 x11) as proof of (forall (Xx0:fofType), (cM Xx0))
% 7.67/7.86 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x10:=(x1 x01):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x01) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x00:=(x0 x12):(forall (Xx0:fofType), (cM Xx0))
% 7.67/7.86 Found (x0 x12) as proof of (forall (Xx0:fofType), (cM Xx0))
% 7.67/7.86 Found (x0 x12) as proof of (forall (Xx0:fofType), (cM Xx0))
% 7.67/7.86 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 7.67/7.86 Found x3:=(x Xx0):(cN Xx0)
% 7.67/7.86 Found (x Xx0) as proof of (cN Xx0)
% 7.67/7.86 Found (x Xx0) as proof of (cN Xx0)
% 7.67/7.86 Found (x2 (x Xx0)) as proof of (cM Xx)
% 7.67/7.86 Found (x2 (x Xx0)) as proof of (cM Xx)
% 7.67/7.86 Found (fun (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (cM Xx)
% 7.67/7.86 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cN Xx0)->(cM Xx0))->(cM Xx))
% 7.67/7.86 Found (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0))) as proof of (((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->(cM Xx)))
% 7.67/7.86 Found (and_rect00 (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 7.67/7.86 Found ((and_rect0 (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 8.12/8.29 Found (((fun (P:Type) (x1:(((cM Xx0)->(cN Xx0))->(((cN Xx0)->(cM Xx0))->P)))=> (((((and_rect ((cM Xx0)->(cN Xx0))) ((cN Xx0)->(cM Xx0))) P) x1) x00)) (cM Xx)) (fun (x1:((cM Xx0)->(cN Xx0))) (x2:((cN Xx0)->(cM Xx0)))=> (x2 (x Xx0)))) as proof of (cM Xx)
% 8.12/8.29 Found (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))) as proof of (cM Xx)
% 8.12/8.29 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (cM Xx)
% 8.12/8.29 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of (forall (Xx:fofType), (cM Xx))
% 8.12/8.29 Found (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx))))) as proof of ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))
% 8.12/8.29 Found x10:=(x1 x02):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found (x1 x02) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found x00:=(x0 x13):(forall (Xx0:fofType), (cM Xx0))
% 8.12/8.29 Found (x0 x13) as proof of (forall (Xx0:fofType), (cM Xx0))
% 8.12/8.29 Found (x0 x13) as proof of (forall (Xx0:fofType), (cM Xx0))
% 8.12/8.29 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 8.12/8.29 Found x000:=(x00 Xx0):(cM Xx0)
% 8.12/8.29 Found (x00 Xx0) as proof of (cM Xx0)
% 8.12/8.29 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of (cM Xx0)
% 8.12/8.29 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 8.12/8.29 Found x00:=(x0 Xx):(cM Xx)
% 8.12/8.29 Found (x0 Xx) as proof of (cM Xx)
% 8.12/8.29 Found (fun (x1:(cN Xx))=> (x0 Xx)) as proof of (cM Xx)
% 8.12/8.29 Found (fun (x1:(cN Xx))=> (x0 Xx)) as proof of ((cN Xx)->(cM Xx))
% 8.12/8.29 Found x2:=(x Xx):(cN Xx)
% 8.12/8.29 Found (x Xx) as proof of (cN Xx)
% 8.12/8.29 Found (fun (x1:(cM Xx))=> (x Xx)) as proof of (cN Xx)
% 8.12/8.29 Found (fun (x1:(cM Xx))=> (x Xx)) as proof of ((cM Xx)->(cN Xx))
% 8.12/8.29 Found ((conj20 (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 8.12/8.29 Found (((conj2 ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 8.12/8.29 Found ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 8.12/8.29 Found ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))) as proof of ((and ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx)))
% 8.12/8.29 Found (fun (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of ((iff (cM Xx)) (cN Xx))
% 8.12/8.29 Found (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))
% 8.12/8.29 Found (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))) as proof of ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))
% 8.12/8.30 Found ((conj10 (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 8.12/8.30 Found (((conj1 ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 8.12/8.30 Found ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 8.12/8.30 Found ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx))))) as proof of ((and ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))))
% 8.12/8.30 Found (fun (x:(forall (Xx:fofType), (cN Xx)))=> ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx)))
% 8.12/8.30 Found (fun (x:(forall (Xx:fofType), (cN Xx)))=> ((((conj ((forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))->(forall (Xx:fofType), (cM Xx)))) ((forall (Xx:fofType), (cM Xx))->(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx))))) (fun (x0:(forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (Xx:fofType)=> (((fun (P:Type) (x1:(((cM Xx)->(cN Xx))->(((cN Xx)->(cM Xx))->P)))=> (((((and_rect ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) P) x1) (x0 Xx))) (cM Xx)) (fun (x1:((cM Xx)->(cN Xx))) (x2:((cN Xx)->(cM Xx)))=> (x2 (x Xx)))))) (fun (x0:(forall (Xx:fofType), (cM Xx))) (Xx:fofType)=> ((((conj ((cM Xx)->(cN Xx))) ((cN Xx)->(cM Xx))) (fun (x1:(cM Xx))=> (x Xx))) (fun (x1:(cN Xx))=> (x0 Xx)))))) as proof of ((forall (Xx:fofType), (cN Xx))->((iff (forall (Xx:fofType), ((iff (cM Xx)) (cN Xx)))) (forall (Xx:fofType), (cM Xx))))
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 9.12/9.29 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 9.12/9.29 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 9.12/9.29 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 9.12/9.29 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x00:=(x0 x14):(forall (Xx0:fofType), (cM Xx0))
% 9.12/9.29 Found (x0 x14) as proof of (forall (Xx0:fofType), (cM Xx0))
% 9.12/9.29 Found (x0 x14) as proof of (forall (Xx0:fofType), (cM Xx0))
% 9.12/9.29 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of (cM Xx0)
% 9.12/9.29 Found (fun (x1:(cN Xx0))=> (x00 Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 9.12/9.29 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x10:=(x1 x03):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x03) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x10:=(x1 x04):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x04) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x10:=(x1 x05):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x05) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x05) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x00:=(x0 x15):(forall (Xx0:fofType), (cM Xx0))
% 9.12/9.29 Found (x0 x15) as proof of (forall (Xx0:fofType), (cM Xx0))
% 9.12/9.29 Found (x0 x15) as proof of (forall (Xx0:fofType), (cM Xx0))
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found x10:=(x1 x06):(forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x06) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found (x1 x06) as proof of (forall (Xx0:fofType), ((iff (cM Xx0)) (cN Xx0)))
% 9.12/9.29 Found x000:=(x00 Xx0):(cM Xx0)
% 9.12/9.29 Found (x00 Xx0) as proof of (cM Xx0)
% 9.12/9.29 Found ((x0 x10) Xx0) as proof of (cM Xx0)
% 9.19/9.42 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of (cM Xx0)
% 9.19/9.42 Found (fun (x2:(cN Xx0))=> ((x0 x10) Xx0)) as proof of ((cN Xx0)->(cM Xx0))
% 9.19/9.42 % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------