TSTP Solution File: SYO314^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO314^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n024.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 00:51:08 EDT 2022
% Result : Timeout 300.02s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO314^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Sat Mar 12 03:12:04 EST 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.34 Python 2.7.5
% 52.05/52.22 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 52.05/52.22 FOF formula (<kernel.Constant object at 0x2b11a1801ab8>, <kernel.Constant object at 0x2b11a1801cb0>) of role type named z
% 52.05/52.22 Using role type
% 52.05/52.22 Declaring z:fofType
% 52.05/52.22 FOF formula ((iff ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) of role conjecture named cSILLYWFF2
% 52.05/52.22 Conjecture to prove = ((iff ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))):Prop
% 52.05/52.22 We need to prove ['((iff ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))']
% 52.05/52.22 Parameter fofType:Type.
% 52.05/52.22 Parameter z:fofType.
% 52.05/52.22 Trying to prove ((iff ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))
% 52.05/52.22 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.22 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.22 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.22 Found (fun (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.23 Found (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))
% 52.05/52.23 Found (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of (((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))
% 52.05/52.23 Found (and_rect10 (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.23 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.23 Found (((fun (P:Type) (x10:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.25 Found (((fun (P:Type) (x10:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 52.05/52.25 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found (fun (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))
% 52.05/52.25 Found (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of (((and ((x2 z)->False)) (x2 x6))->((x0 x4)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))
% 52.05/52.25 Found (and_rect10 (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found (((fun (P:Type) (x10:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 52.05/52.25 Found (((fun (P:Type) (x10:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.76/77.02 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.76/77.02 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.76/77.02 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.76/77.02 Found (fun (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.76/77.02 Found (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))
% 76.76/77.02 Found (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of (((and ((x2 z)->False)) (x2 x6))->((x0 x4)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))
% 76.76/77.02 Found (and_rect10 (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.85/77.05 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.85/77.05 Found (((fun (P:Type) (x10:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.85/77.05 Found (((fun (P:Type) (x10:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x10:((and ((x2 z)->False)) (x2 x6))) (x11:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 76.85/77.05 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 76.85/77.05 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 76.85/77.05 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 76.85/77.05 Found (fun (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 76.85/77.05 Found (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))
% 76.85/77.05 Found (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of (((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))
% 76.85/77.05 Found (and_rect10 (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 76.85/77.05 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 76.85/77.05 Found (((fun (P:Type) (x10:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found (((fun (P:Type) (x10:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x10) x8)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x10:((and (x0 x4)) ((x0 x6)->False))) (x11:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found (fun (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of (((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))
% 101.97/102.25 Found (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((x0 x4)->(((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))
% 101.97/102.25 Found (and_rect20 (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found (((fun (P:Type) (x12:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 101.97/102.25 Found (((fun (P:Type) (x12:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 102.07/102.29 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 102.07/102.29 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 102.07/102.29 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 102.07/102.29 Found (fun (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 102.07/102.29 Found (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))
% 102.07/102.29 Found (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of (((x2 z)->False)->((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))
% 102.07/102.29 Found (and_rect20 (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.67/119.92 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.67/119.92 Found (((fun (P:Type) (x12:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.67/119.92 Found (((fun (P:Type) (x12:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.67/119.92 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.92 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.92 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.92 Found (fun (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.92 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of ((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))
% 119.67/119.92 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of (((and (x0 x5)) ((x0 x7)->False))->((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))
% 119.67/119.92 Found (and_rect10 (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.92 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.92 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.94 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 119.67/119.94 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.67/119.94 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.67/119.94 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.67/119.94 Found (fun (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.67/119.94 Found (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of ((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))
% 119.67/119.94 Found (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of (((and (x1 x5)) ((x1 x7)->False))->((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))
% 119.67/119.94 Found (and_rect10 (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.75/119.97 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.75/119.97 Found (((fun (P:Type) (x11:(((and (x1 x5)) ((x1 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x1 x5)) ((x1 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.75/119.97 Found (((fun (P:Type) (x11:(((and (x1 x5)) ((x1 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x1 x5)) ((x1 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 119.75/119.97 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found (fun (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))
% 119.75/119.97 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of (((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))
% 119.75/119.97 Found (and_rect10 (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.75/119.97 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 119.76/120.00 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.76/120.00 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.76/120.00 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.76/120.00 Found (fun (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.76/120.00 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x1 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 119.76/120.00 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x3 z)->False)) (x3 x7))->((x1 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.76/120.00 Found (and_rect10 (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.76/120.00 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.79/120.02 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x1 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x1 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.79/120.02 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x1 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x1 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.79/120.02 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.79/120.02 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.79/120.02 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.79/120.02 Found (fun (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.79/120.02 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of ((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))
% 119.81/120.07 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of (((and (x0 x5)) ((x0 x7)->False))->((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))
% 119.81/120.07 Found (and_rect10 (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.81/120.07 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.81/120.07 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.81/120.07 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 119.81/120.07 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.08 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.08 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.08 Found (fun (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.08 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 119.81/120.08 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x6))->((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.81/120.08 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.08 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.08 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.10 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.81/120.10 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.81/120.10 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.81/120.10 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.81/120.10 Found (fun (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.81/120.10 Found (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of ((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))
% 119.81/120.10 Found (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of (((and (x0 x4)) ((x0 x7)->False))->((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))
% 119.90/120.13 Found (and_rect10 (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.90/120.13 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.90/120.13 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.90/120.13 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 119.90/120.13 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found (fun (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 119.90/120.13 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x7))->((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.90/120.13 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.13 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.16 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.16 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.16 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.16 Found (fun (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.16 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 119.90/120.16 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x7))->((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.90/120.16 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.18 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.18 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.18 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.90/120.18 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found (fun (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))
% 119.90/120.18 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of (((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))
% 119.90/120.18 Found (and_rect10 (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.90/120.18 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 119.99/120.21 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.21 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.21 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.21 Found (fun (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.21 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 119.99/120.21 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x3 z)->False)) (x3 x7))->((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 119.99/120.21 Found (and_rect10 (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.21 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found (fun (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 119.99/120.24 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 154.76/155.01 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x6))->((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.76/155.01 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 154.76/155.01 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 154.76/155.01 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 154.76/155.01 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 154.76/155.01 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.76/155.01 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.76/155.01 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.76/155.01 Found (fun (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.76/155.01 Found (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of (((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))
% 154.76/155.01 Found (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False)))))))))))) as proof of ((x0 x4)->(((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))
% 154.76/155.01 Found (and_rect20 (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.76/155.01 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.79/155.09 Found (((fun (P:Type) (x12:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.79/155.09 Found (((fun (P:Type) (x12:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))) (fun (x12:(x0 x4)) (x13:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (Xp Xx))) ((Xp Xy)->False))))))))))
% 154.79/155.09 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))):((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.79/155.09 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.79/155.09 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.79/155.09 Found (fun (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.87/155.10 Found (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))
% 154.87/155.10 Found (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))))) as proof of (((x2 z)->False)->((x2 x6)->((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))
% 154.87/155.10 Found (and_rect20 (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.87/155.10 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.87/155.10 Found (((fun (P:Type) (x12:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 154.87/155.10 Found (((fun (P:Type) (x12:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x12) x10)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) (fun (x12:((x2 z)->False)) (x13:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xp:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (Xp Xx)) ((Xp Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.04/170.34 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.04/170.34 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.04/170.34 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.04/170.34 Found (fun (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.04/170.34 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x1 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 170.04/170.34 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x3 z)->False)) (x3 x7))->((x1 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.04/170.34 Found (and_rect10 (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.13/170.37 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.13/170.37 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x1 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x1 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.13/170.37 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x1 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x1 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x1 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.13/170.37 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.37 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.37 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.37 Found (fun (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.38 Found (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of ((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))
% 170.13/170.38 Found (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of (((and (x0 x4)) ((x0 x7)->False))->((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))
% 170.13/170.38 Found (and_rect10 (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.38 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.38 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.13/170.38 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 170.14/170.41 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.14/170.41 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.14/170.41 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.14/170.41 Found (fun (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.14/170.41 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 170.14/170.41 Found (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x3 z)->False)) (x3 x7))->((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.14/170.41 Found (and_rect10 (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.14/170.41 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found (((fun (P:Type) (x11:(((and ((x3 z)->False)) (x3 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x3 z)->False)) (x3 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x3 z)->False)) (x3 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found (fun (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.44 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 170.18/170.47 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x7))->((x0 x5)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.18/170.47 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.47 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.47 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.47 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x5)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x5)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x5))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.18/170.47 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.48 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.48 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.48 Found (fun (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.48 Found (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of ((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))
% 170.18/170.48 Found (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of (((and (x1 x5)) ((x1 x7)->False))->((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))
% 170.18/170.48 Found (and_rect10 (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.48 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.48 Found (((fun (P:Type) (x11:(((and (x1 x5)) ((x1 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x1 x5)) ((x1 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.51 Found (((fun (P:Type) (x11:(((and (x1 x5)) ((x1 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x1 x5)) ((x1 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x11:((and (x1 x5)) ((x1 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 170.18/170.51 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.18/170.51 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.18/170.51 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.18/170.51 Found (fun (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.18/170.51 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))
% 170.18/170.51 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of (((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))
% 170.27/170.54 Found (and_rect10 (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.27/170.54 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.27/170.54 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.27/170.54 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 170.27/170.54 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found (fun (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 170.27/170.54 Found (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x7))->((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.27/170.54 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.54 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x7))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x7))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x7))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.27/170.57 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.27/170.57 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.27/170.57 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.27/170.57 Found (fun (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.27/170.57 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of ((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))
% 170.27/170.57 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of (((and (x0 x5)) ((x0 x7)->False))->((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))
% 170.27/170.57 Found (and_rect10 (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.35/170.61 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.35/170.61 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.35/170.61 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x2 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x2 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 170.35/170.61 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found (fun (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 170.35/170.61 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x6))->((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.35/170.61 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.61 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.35/170.64 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.64 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.64 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.64 Found (fun (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.64 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))
% 170.35/170.64 Found (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of (((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))
% 170.35/170.64 Found (and_rect10 (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.64 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.67 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.67 Found (((fun (P:Type) (x11:(((and (x0 x4)) ((x0 x6)->False))->((x2 x6)->P)))=> (((((and_rect ((and (x0 x4)) ((x0 x6)->False))) (x2 x6)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x11:((and (x0 x4)) ((x0 x6)->False))) (x12:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 170.35/170.67 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.35/170.67 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.35/170.67 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.35/170.67 Found (fun (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.35/170.67 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of ((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))
% 170.46/170.70 Found (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of (((and (x0 x5)) ((x0 x7)->False))->((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))
% 170.46/170.70 Found (and_rect10 (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.46/170.70 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.46/170.70 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.46/170.70 Found (((fun (P:Type) (x11:(((and (x0 x5)) ((x0 x7)->False))->((x3 x7)->P)))=> (((((and_rect ((and (x0 x5)) ((x0 x7)->False))) (x3 x7)) P) x11) x9)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x11:((and (x0 x5)) ((x0 x7)->False))) (x12:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 170.46/170.70 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.46/170.70 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.46/170.71 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.46/170.71 Found (fun (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.46/170.71 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 170.46/170.71 Found (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((and ((x2 z)->False)) (x2 x6))->((x0 x4)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 170.46/170.71 Found (and_rect10 (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.46/170.71 Found ((and_rect1 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 170.46/170.71 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.42/217.70 Found (((fun (P:Type) (x11:(((and ((x2 z)->False)) (x2 x6))->((x0 x4)->P)))=> (((((and_rect ((and ((x2 z)->False)) (x2 x6))) (x0 x4)) P) x11) x8)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x11:((and ((x2 z)->False)) (x2 x6))) (x12:(x0 x4))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.42/217.70 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.42/217.70 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.42/217.70 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.42/217.70 Found (fun (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.42/217.70 Found (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of (((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))
% 217.42/217.70 Found (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False)))))))))) as proof of ((x0 x4)->(((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))
% 217.44/217.74 Found (and_rect20 (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.44/217.74 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.44/217.74 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.44/217.74 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x8 Xx))) ((x8 Xy)->False))))))))
% 217.44/217.74 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.74 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.74 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.75 Found (fun (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.75 Found (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of (((x0 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))
% 217.44/217.75 Found (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False)))))))))) as proof of ((x0 x5)->(((x0 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))
% 217.44/217.75 Found (and_rect20 (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.75 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.75 Found (((fun (P:Type) (x13:((x0 x5)->(((x0 x7)->False)->P)))=> (((((and_rect (x0 x5)) ((x0 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.75 Found (((fun (P:Type) (x13:((x0 x5)->(((x0 x7)->False)->P)))=> (((((and_rect (x0 x5)) ((x0 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))) (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x4 Xx))) ((x4 Xy)->False))))))))
% 217.44/217.79 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.44/217.79 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.44/217.79 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.44/217.79 Found (fun (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.44/217.79 Found (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False)))))))))) as proof of (((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False)))))))))
% 217.44/217.79 Found (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False)))))))))) as proof of ((x0 x4)->(((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))))
% 217.44/217.79 Found (and_rect20 (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.44/217.79 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.55/217.84 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x13) x10)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.55/217.84 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x13) x10)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x12 Xx))) ((x12 Xy)->False))))))))
% 217.55/217.84 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.84 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.84 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.84 Found (fun (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.84 Found (fun (x13:(x0 x4)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of (((x0 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))
% 217.55/217.89 Found (fun (x13:(x0 x4)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False)))))))))) as proof of ((x0 x4)->(((x0 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))
% 217.55/217.89 Found (and_rect20 (fun (x13:(x0 x4)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.89 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.89 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x7)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.89 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x7)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x6 Xx))) ((x6 Xy)->False))))))))
% 217.55/217.89 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.55/217.89 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.55/217.89 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.55/217.89 Found (fun (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.55/217.89 Found (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of (((x0 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))
% 217.55/217.89 Found (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False)))))))))) as proof of ((x0 x5)->(((x0 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))
% 217.55/217.89 Found (and_rect20 (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.55/217.89 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.55/217.89 Found (((fun (P:Type) (x13:((x0 x5)->(((x0 x7)->False)->P)))=> (((((and_rect (x0 x5)) ((x0 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.64/217.94 Found (((fun (P:Type) (x13:((x0 x5)->(((x0 x7)->False)->P)))=> (((((and_rect (x0 x5)) ((x0 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))) (fun (x13:(x0 x5)) (x14:((x0 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x2 Xx))) ((x2 Xy)->False))))))))
% 217.64/217.94 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.94 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.94 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.94 Found (fun (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.94 Found (fun (x13:(x1 x5)) (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of (((x1 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))
% 217.64/217.94 Found (fun (x13:(x1 x5)) (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False)))))))))) as proof of ((x1 x5)->(((x1 x7)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))
% 217.64/217.94 Found (and_rect20 (fun (x13:(x1 x5)) (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.98 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x13:(x1 x5)) (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.98 Found (((fun (P:Type) (x13:((x1 x5)->(((x1 x7)->False)->P)))=> (((((and_rect (x1 x5)) ((x1 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x13:(x1 x5)) (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.98 Found (((fun (P:Type) (x13:((x1 x5)->(((x1 x7)->False)->P)))=> (((((and_rect (x1 x5)) ((x1 x7)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))) (fun (x13:(x1 x5)) (x14:((x1 x7)->False))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x0 Xx))) ((x0 Xy)->False))))))))
% 217.64/217.98 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found (fun (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of (((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))
% 217.64/217.98 Found (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False)))))))))) as proof of ((x0 x4)->(((x0 x6)->False)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))
% 217.64/217.98 Found (and_rect20 (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.64/217.98 Found (((fun (P:Type) (x13:((x0 x4)->(((x0 x6)->False)->P)))=> (((((and_rect (x0 x4)) ((x0 x6)->False)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))) (fun (x13:(x0 x4)) (x14:((x0 x6)->False))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and ((Xq z)->False)) (Xq Xy))) (x10 Xx))) ((x10 Xy)->False))))))))
% 217.73/218.03 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.03 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.03 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.03 Found (fun (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.03 Found (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 217.73/218.03 Found (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x2 z)->False)->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 217.73/218.03 Found (and_rect20 (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.03 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x10 Xx)) ((x10 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found (fun (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.73/218.08 Found (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 217.73/218.08 Found (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x2 z)->False)->((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 217.82/218.13 Found (and_rect20 (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x7)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x7)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x7)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x7)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x6 Xx)) ((x6 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (fun (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 217.82/218.13 Found (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x3 z)->False)->((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 217.82/218.13 Found (and_rect20 (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (((fun (P:Type) (x13:(((x3 z)->False)->((x3 x7)->P)))=> (((((and_rect ((x3 z)->False)) (x3 x7)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.13 Found (((fun (P:Type) (x13:(((x3 z)->False)->((x3 x7)->P)))=> (((((and_rect ((x3 z)->False)) (x3 x7)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x0 Xx)) ((x0 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.18 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.18 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.18 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.18 Found (fun (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.18 Found (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 217.82/218.18 Found (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x2 z)->False)->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 217.82/218.18 Found (and_rect20 (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.82/218.18 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x8 Xx)) ((x8 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found (fun (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.23 Found (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 217.94/218.27 Found (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x2 z)->False)->((x2 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 217.94/218.27 Found (and_rect20 (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.27 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.27 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x7)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x7)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.27 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x7)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x7)) P) x13) x11)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x4 Xx)) ((x4 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.27 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.28 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.28 Found ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.28 Found (fun (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.28 Found (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 217.94/218.28 Found (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x2 z)->False)->((x2 x6)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))
% 217.94/218.28 Found (and_rect20 (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.28 Found ((and_rect2 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 217.94/218.28 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x13) x10)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 218.03/218.32 Found (((fun (P:Type) (x13:(((x2 z)->False)->((x2 x6)->P)))=> (((((and_rect ((x2 z)->False)) (x2 x6)) P) x13) x10)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) (fun (x13:((x2 z)->False)) (x14:(x2 x6))=> ((fun (P:Type)=> ((False_rect P) x90)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x12 Xx)) ((x12 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 218.03/218.32 Found False_rect00:=(False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))):((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 218.03/218.32 Found (False_rect0 ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 218.03/218.32 Found ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 218.03/218.32 Found (fun (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False))))))))
% 218.03/218.32 Found (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of ((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))
% 218.03/218.32 Found (fun (x13:((x3 z)->False)) (x14:(x3 x7))=> ((fun (P:Type)=> ((False_rect P) x100)) ((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (x2 Xx)) ((x2 Xy)->False))) (Xq Xy))) ((Xq z)->False)))))))))) as proof of (((x3 z)->False)->((x3 x7)->((ex (fofType->Prop)) (fun (Xq:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((and (
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