TSTP Solution File: SEV235^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV235^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n111.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 13:33:55 EDT 2014
% Result : Unknown 2.09s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV235^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n111.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 08:34:51 CDT 2014
% % CPUTime : 2.09
% 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 0x1093050>, <kernel.DependentProduct object at 0x10931b8>) of role type named cE
% Using role type
% Declaring cE:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xcd6440>, <kernel.DependentProduct object at 0x10934d0>) of role type named cD
% Using role type
% Declaring cD:(fofType->Prop)
% FOF formula (forall (Xx:(fofType->Prop)), ((iff (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))) ((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))))) of role conjecture named cTHM46A_pme
% Conjecture to prove = (forall (Xx:(fofType->Prop)), ((iff (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))) ((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xx:(fofType->Prop)), ((iff (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))) ((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))))']
% Parameter fofType:Type.
% Parameter cE:(fofType->Prop).
% Parameter cD:(fofType->Prop).
% Trying to prove (forall (Xx:(fofType->Prop)), ((iff (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))) ((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))))
% Found x200:=(x20 x0):(cE Xx0)
% Found (x20 x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found x100:=(x10 x0):(cD Xx0)
% Found (x10 x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((conj10 ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((conj1 (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))->((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0))))
% Found (and_rect00 (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((and_rect0 ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))->(forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))))
% Found x200:=(x20 x0):(cE Xx0)
% Found (x20 x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found x100:=(x10 x0):(cD Xx0)
% Found (x10 x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((conj10 ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((conj1 (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))->((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0))))
% Found (and_rect00 (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((and_rect0 ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))->(forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))))
% Found x100:=(x10 x0):(cD Xx0)
% Found (x10 x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found x200:=(x20 x0):(cE Xx0)
% Found (x20 x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((conj10 ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((conj1 (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))->((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0))))
% Found (and_rect00 (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((and_rect0 ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))->(forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))))
% Found x100:=(x10 x0):(cD Xx0)
% Found (x10 x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found x200:=(x20 x0):(cE Xx0)
% Found (x20 x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((conj10 ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((conj1 (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))->((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0))))
% Found (and_rect00 (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((and_rect0 ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))->(forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))))
% Found x100:=(x10 x0):(cD Xx0)
% Found (x10 x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found x200:=(x20 x0):(cE Xx0)
% Found (x20 x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((conj10 ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((conj1 (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))->((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0))))
% Found (and_rect00 (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((and_rect0 ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))->(forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))))
% Found x200:=(x20 x0):(cE Xx0)
% Found (x20 x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found ((x2 Xx0) x0) as proof of (cE Xx0)
% Found x100:=(x10 x0):(cD Xx0)
% Found (x10 x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((x1 Xx0) x0) as proof of (cD Xx0)
% Found ((conj10 ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((conj1 (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))) as proof of ((forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))->((forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00)))->((and (cD Xx0)) (cE Xx0))))
% Found (and_rect00 (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found ((and_rect0 ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0)))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((and (cD Xx0)) (cE Xx0))
% Found (fun (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0))))
% Found (fun (x:((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))) (Xx0:fofType) (x0:(Xx Xx0))=> (((fun (P:Type) (x1:((forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))->((forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))->P)))=> (((((and_rect (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0)))) P) x1) x)) ((and (cD Xx0)) (cE Xx0))) (fun (x1:(forall (Xx00:fofType), ((Xx Xx00)->(cD Xx00)))) (x2:(forall (Xx00:fofType), ((Xx Xx00)->(cE Xx00))))=> ((((conj (cD Xx0)) (cE Xx0)) ((x1 Xx0) x0)) ((x2 Xx0) x0))))) as proof of (((and (forall (Xx0:fofType), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:fofType), ((Xx Xx0)->(cE Xx0))))->(forall (Xx0:fofType), ((Xx Xx0)->((and (cD Xx0)) (cE Xx0)))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------