TSTP Solution File: SYN059^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYN059^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n097.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:37:48 EDT 2014
% Result : Unknown 19.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SYN059^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n097.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:06:21 CDT 2014
% % CPUTime: 19.02
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1b31bd8>, <kernel.DependentProduct object at 0x1b31b48>) of role type named cJ
% Using role type
% Declaring cJ:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1f6bf80>, <kernel.DependentProduct object at 0x1b319e0>) of role type named cG
% Using role type
% Declaring cG:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1b31c20>, <kernel.DependentProduct object at 0x1b316c8>) of role type named cH
% Using role type
% Declaring cH:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1b317e8>, <kernel.DependentProduct object at 0x1b31830>) of role type named cF
% Using role type
% Declaring cF:(fofType->Prop)
% FOF formula (((and ((ex fofType) (fun (Xx:fofType)=> (cF Xx)))) ((ex fofType) (fun (Xx:fofType)=> (cG Xx))))->((and (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))) ((forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))->(forall (Xx:fofType), ((cG Xx)->(cJ Xx)))))) of role conjecture named cPELL29
% Conjecture to prove = (((and ((ex fofType) (fun (Xx:fofType)=> (cF Xx)))) ((ex fofType) (fun (Xx:fofType)=> (cG Xx))))->((and (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))) ((forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))->(forall (Xx:fofType), ((cG Xx)->(cJ Xx)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and ((ex fofType) (fun (Xx:fofType)=> (cF Xx)))) ((ex fofType) (fun (Xx:fofType)=> (cG Xx))))->((and (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))) ((forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))->(forall (Xx:fofType), ((cG Xx)->(cJ Xx))))))']
% Parameter fofType:Type.
% Parameter cJ:(fofType->Prop).
% Parameter cG:(fofType->Prop).
% Parameter cH:(fofType->Prop).
% Parameter cF:(fofType->Prop).
% Trying to prove (((and ((ex fofType) (fun (Xx:fofType)=> (cF Xx)))) ((ex fofType) (fun (Xx:fofType)=> (cG Xx))))->((and (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))) ((forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))->(forall (Xx:fofType), ((cG Xx)->(cJ Xx))))))
% Found x30:=(x3 Xy):((cG Xy)->(cJ Xy))
% Found (x3 Xy) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x4:(cF Xx))=> (x3 Xy)) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x4:(cF Xx))=> (x3 Xy)) as proof of ((cF Xx)->((cG Xy)->(cJ Xy)))
% Found (and_rect10 (fun (x4:(cF Xx))=> (x3 Xy))) as proof of (cJ Xy)
% Found ((and_rect1 (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))) as proof of (cJ Xy)
% Found x200:=(x20 x4):(cH Xx)
% Found (x20 x4) as proof of (cH Xx)
% Found ((x2 Xx) x4) as proof of (cH Xx)
% Found (fun (x5:(cG Xy))=> ((x2 Xx) x4)) as proof of (cH Xx)
% Found (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)) as proof of ((cG Xy)->(cH Xx))
% Found (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)) as proof of ((cF Xx)->((cG Xy)->(cH Xx)))
% Found (and_rect10 (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4))) as proof of (cH Xx)
% Found ((and_rect1 (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4))) as proof of (cH Xx)
% Found (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4))) as proof of (cH Xx)
% Found (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4))) as proof of (cH Xx)
% Found ((conj10 (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((conj1 (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))) as proof of ((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy)))
% Found (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))) as proof of ((forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))->((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy))))
% Found (and_rect00 (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((and_rect0 ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((fun (P:Type) (x2:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x2) x0)) ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x1:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x2) x0)) ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (Xy:fofType) (x1:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x2) x0)) ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))))) as proof of (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x1:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x2) x0)) ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))))) as proof of (forall (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x0:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x1:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x2) x0)) ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x0:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x1:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x2) x0)) ((and (cH Xx)) (cJ Xy))) (fun (x2:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x3:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cH Xx)) (fun (x4:(cF Xx)) (x5:(cG Xy))=> ((x2 Xx) x4)))) (((fun (P:Type) (x4:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x4) x1)) (cJ Xy)) (fun (x4:(cF Xx))=> (x3 Xy))))))) as proof of (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))
% Found x50:=(x5 Xy):((cG Xy)->(cJ Xy))
% Found (x5 Xy) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x6:(cF Xx))=> (x5 Xy)) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x6:(cF Xx))=> (x5 Xy)) as proof of ((cF Xx)->((cG Xy)->(cJ Xy)))
% Found (and_rect20 (fun (x6:(cF Xx))=> (x5 Xy))) as proof of (cJ Xy)
% Found ((and_rect2 (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))) as proof of (cJ Xy)
% Found x400:=(x40 x6):(cH Xx)
% Found (x40 x6) as proof of (cH Xx)
% Found ((x4 Xx) x6) as proof of (cH Xx)
% Found (fun (x7:(cG Xy))=> ((x4 Xx) x6)) as proof of (cH Xx)
% Found (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)) as proof of ((cG Xy)->(cH Xx))
% Found (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)) as proof of ((cF Xx)->((cG Xy)->(cH Xx)))
% Found (and_rect20 (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6))) as proof of (cH Xx)
% Found ((and_rect2 (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6))) as proof of (cH Xx)
% Found (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6))) as proof of (cH Xx)
% Found (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6))) as proof of (cH Xx)
% Found ((conj10 (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((conj1 (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))) as proof of ((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy)))
% Found (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))) as proof of ((forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))->((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy))))
% Found (and_rect10 (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((and_rect1 ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((fun (P:Type) (x4:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x4) x2)) ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x3:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x4:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x4) x2)) ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (Xy:fofType) (x3:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x4:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x4) x2)) ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))))) as proof of (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x3:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x4:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x4) x2)) ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))))) as proof of (forall (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x2:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x3:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x4:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x4) x2)) ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x2:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x3:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x4:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x4) x2)) ((and (cH Xx)) (cJ Xy))) (fun (x4:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x5:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cH Xx)) (fun (x6:(cF Xx)) (x7:(cG Xy))=> ((x4 Xx) x6)))) (((fun (P:Type) (x6:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x6) x3)) (cJ Xy)) (fun (x6:(cF Xx))=> (x5 Xy))))))) as proof of (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))
% Found x70:=(x7 Xy):((cG Xy)->(cJ Xy))
% Found (x7 Xy) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x8:(cF Xx))=> (x7 Xy)) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x8:(cF Xx))=> (x7 Xy)) as proof of ((cF Xx)->((cG Xy)->(cJ Xy)))
% Found (and_rect20 (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found ((and_rect2 (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found x70:=(x7 Xy):((cG Xy)->(cJ Xy))
% Found (x7 Xy) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x8:(cF Xx))=> (x7 Xy)) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x8:(cF Xx))=> (x7 Xy)) as proof of ((cF Xx)->((cG Xy)->(cJ Xy)))
% Found (and_rect20 (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found ((and_rect2 (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))) as proof of (cJ Xy)
% Found x600:=(x60 x8):(cH Xx)
% Found (x60 x8) as proof of (cH Xx)
% Found ((x6 Xx) x8) as proof of (cH Xx)
% Found (fun (x9:(cG Xy))=> ((x6 Xx) x8)) as proof of (cH Xx)
% Found (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)) as proof of ((cG Xy)->(cH Xx))
% Found (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)) as proof of ((cF Xx)->((cG Xy)->(cH Xx)))
% Found (and_rect20 (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found ((and_rect2 (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found ((conj10 (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((conj1 (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))) as proof of ((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy)))
% Found (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))) as proof of ((forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))->((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy))))
% Found (and_rect10 (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((and_rect1 ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (forall (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x4:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x4:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))
% Found x600:=(x60 x8):(cH Xx)
% Found (x60 x8) as proof of (cH Xx)
% Found ((x6 Xx) x8) as proof of (cH Xx)
% Found (fun (x9:(cG Xy))=> ((x6 Xx) x8)) as proof of (cH Xx)
% Found (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)) as proof of ((cG Xy)->(cH Xx))
% Found (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)) as proof of ((cF Xx)->((cG Xy)->(cH Xx)))
% Found (and_rect20 (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found ((and_rect2 (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8))) as proof of (cH Xx)
% Found ((conj10 (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((conj1 (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))) as proof of ((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy)))
% Found (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))) as proof of ((forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))->((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy))))
% Found (and_rect10 (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((and_rect1 ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (forall (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x4:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x4:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x5:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x6:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x6) x4)) ((and (cH Xx)) (cJ Xy))) (fun (x6:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x7:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cH Xx)) (fun (x8:(cF Xx)) (x9:(cG Xy))=> ((x6 Xx) x8)))) (((fun (P:Type) (x8:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x8) x5)) (cJ Xy)) (fun (x8:(cF Xx))=> (x7 Xy))))))) as proof of (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))
% Found x90:=(x9 Xy):((cG Xy)->(cJ Xy))
% Found (x9 Xy) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x10:(cF Xx))=> (x9 Xy)) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x10:(cF Xx))=> (x9 Xy)) as proof of ((cF Xx)->((cG Xy)->(cJ Xy)))
% Found (and_rect20 (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found ((and_rect2 (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found x90:=(x9 Xy):((cG Xy)->(cJ Xy))
% Found (x9 Xy) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x10:(cF Xx))=> (x9 Xy)) as proof of ((cG Xy)->(cJ Xy))
% Found (fun (x10:(cF Xx))=> (x9 Xy)) as proof of ((cF Xx)->((cG Xy)->(cJ Xy)))
% Found (and_rect20 (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found ((and_rect2 (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))) as proof of (cJ Xy)
% Found x800:=(x80 x10):(cH Xx)
% Found (x80 x10) as proof of (cH Xx)
% Found ((x8 Xx) x10) as proof of (cH Xx)
% Found (fun (x11:(cG Xy))=> ((x8 Xx) x10)) as proof of (cH Xx)
% Found (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)) as proof of ((cG Xy)->(cH Xx))
% Found (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)) as proof of ((cF Xx)->((cG Xy)->(cH Xx)))
% Found (and_rect20 (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found ((and_rect2 (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found ((conj10 (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((conj1 (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))) as proof of ((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy)))
% Found (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))) as proof of ((forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))->((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy))))
% Found (and_rect10 (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((and_rect1 ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (forall (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x6:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x6:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))
% Found x800:=(x80 x10):(cH Xx)
% Found (x80 x10) as proof of (cH Xx)
% Found ((x8 Xx) x10) as proof of (cH Xx)
% Found (fun (x11:(cG Xy))=> ((x8 Xx) x10)) as proof of (cH Xx)
% Found (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)) as proof of ((cG Xy)->(cH Xx))
% Found (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)) as proof of ((cF Xx)->((cG Xy)->(cH Xx)))
% Found (and_rect20 (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found ((and_rect2 (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10))) as proof of (cH Xx)
% Found ((conj10 (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((conj1 (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))) as proof of ((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy)))
% Found (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))) as proof of ((forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))->((forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0)))->((and (cH Xx)) (cJ Xy))))
% Found (and_rect10 (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found ((and_rect1 ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy)))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of ((and (cH Xx)) (cJ Xy))
% Found (fun (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))
% Found (fun (Xx:fofType) (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (forall (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x6:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy))))
% Found (fun (x6:((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))) (Xx:fofType) (Xy:fofType) (x7:((and (cF Xx)) (cG Xy)))=> (((fun (P:Type) (x8:((forall (Xx:fofType), ((cF Xx)->(cH Xx)))->((forall (Xx:fofType), ((cG Xx)->(cJ Xx)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx)))) P) x8) x6)) ((and (cH Xx)) (cJ Xy))) (fun (x8:(forall (Xx0:fofType), ((cF Xx0)->(cH Xx0)))) (x9:(forall (Xx0:fofType), ((cG Xx0)->(cJ Xx0))))=> ((((conj (cH Xx)) (cJ Xy)) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cH Xx)) (fun (x10:(cF Xx)) (x11:(cG Xy))=> ((x8 Xx) x10)))) (((fun (P:Type) (x10:((cF Xx)->((cG Xy)->P)))=> (((((and_rect (cF Xx)) (cG Xy)) P) x10) x7)) (cJ Xy)) (fun (x10:(cF Xx))=> (x9 Xy))))))) as proof of (((and (forall (Xx:fofType), ((cF Xx)->(cH Xx)))) (forall (Xx:fofType), ((cG Xx)->(cJ Xx))))->(forall (Xx:fofType) (Xy:fofType), (((and (cF Xx)) (cG Xy))->((and (cH Xx)) (cJ Xy)))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------