TSTP Solution File: SYO307^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO307^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:08 EDT 2022
% Result : Unknown 20.94s 21.15s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO307^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Mar 12 02:31:10 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.74/0.90 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.74/0.90 FOF formula (<kernel.Constant object at 0x10cf3f8>, <kernel.DependentProduct object at 0x10c5bd8>) of role type named cT
% 0.74/0.90 Using role type
% 0.74/0.90 Declaring cT:(fofType->Prop)
% 0.74/0.90 FOF formula (<kernel.Constant object at 0x10cf440>, <kernel.DependentProduct object at 0x2af2a5045908>) of role type named q
% 0.74/0.90 Using role type
% 0.74/0.90 Declaring q:(fofType->Prop)
% 0.74/0.90 FOF formula (<kernel.Constant object at 0x10cf3f8>, <kernel.DependentProduct object at 0x2af2a5045a70>) of role type named cR
% 0.74/0.90 Using role type
% 0.74/0.90 Declaring cR:(fofType->Prop)
% 0.74/0.90 FOF formula (<kernel.Constant object at 0x10cfd40>, <kernel.DependentProduct object at 0x2af2a5045170>) of role type named p
% 0.74/0.90 Using role type
% 0.74/0.90 Declaring p:(fofType->Prop)
% 0.74/0.90 FOF formula ((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((or (A Xx)) ((and (A Xy)) (A Xz)))->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))))) of role conjecture named cBLEDSOE5F
% 0.74/0.91 Conjecture to prove = ((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((or (A Xx)) ((and (A Xy)) (A Xz)))->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))))):Prop
% 0.74/0.91 Parameter fofType_DUMMY:fofType.
% 0.74/0.91 We need to prove ['((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((or (A Xx)) ((and (A Xy)) (A Xz)))->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))))))']
% 0.74/0.91 Parameter fofType:Type.
% 0.74/0.91 Parameter cT:(fofType->Prop).
% 0.74/0.91 Parameter q:(fofType->Prop).
% 0.74/0.91 Parameter cR:(fofType->Prop).
% 0.74/0.91 Parameter p:(fofType->Prop).
% 0.74/0.91 Trying to prove ((ex (fofType->Prop)) (fun (A:(fofType->Prop))=> (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((or (A Xx)) ((and (A Xy)) (A Xz)))->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))))))
% 0.74/0.91 Found or_introl00:=(or_introl0 ((and (q Xx)) (cT Xz))):((x Xx)->((or (x Xx)) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found (or_introl0 ((and (q Xx)) (cT Xz))) as proof of ((x Xx)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found ((or_introl (x Xx)) ((and (q Xx)) (cT Xz))) as proof of ((x Xx)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found ((or_introl (x Xx)) ((and (q Xx)) (cT Xz))) as proof of ((x Xx)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found ((or_introl (x Xx)) ((and (q Xx)) (cT Xz))) as proof of ((x Xx)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found or_introl00:=(or_introl0 ((and (q Xx)) (cT Xz))):((x Xz)->((or (x Xz)) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found (or_introl0 ((and (q Xx)) (cT Xz))) as proof of ((x Xz)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found ((or_introl (x Xz)) ((and (q Xx)) (cT Xz))) as proof of ((x Xz)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found ((or_introl (x Xz)) ((and (q Xx)) (cT Xz))) as proof of ((x Xz)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz)))) as proof of ((x Xz)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 0.74/0.91 Found (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz)))) as proof of ((x Xy)->((x Xz)->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))))
% 0.74/0.91 Found (and_rect00 (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz))))) as proof of ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))
% 0.74/0.91 Found ((and_rect0 ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))) (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz))))) as proof of ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))
% 0.74/0.91 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))) (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz))))) as proof of ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))
% 0.74/0.91 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))) (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz)))))) as proof of ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))
% 6.03/6.20 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) ((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz)))) (fun (x01:(x Xy))=> ((or_introl (x Xz)) ((and (q Xx)) (cT Xz)))))) as proof of (((and (x Xy)) (x Xz))->((or ((and (p Xx)) (cR Xy))) ((and (q Xx)) (cT Xz))))
% 6.03/6.20 Found or_introl00:=(or_introl0 ((and (p Xx)) (cR Xy))):((x Xx)->((or (x Xx)) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found (or_introl0 ((and (p Xx)) (cR Xy))) as proof of ((x Xx)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found ((or_introl (x Xx)) ((and (p Xx)) (cR Xy))) as proof of ((x Xx)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found ((or_introl (x Xx)) ((and (p Xx)) (cR Xy))) as proof of ((x Xx)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found ((or_introl (x Xx)) ((and (p Xx)) (cR Xy))) as proof of ((x Xx)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found or_intror00:=(or_intror0 (x Xz)):((x Xz)->((or ((and (q Xx)) (cT Xz))) (x Xz)))
% 6.03/6.20 Found (or_intror0 (x Xz)) as proof of ((x Xz)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found ((or_intror ((and (q Xx)) (cT Xz))) (x Xz)) as proof of ((x Xz)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found ((or_intror ((and (q Xx)) (cT Xz))) (x Xz)) as proof of ((x Xz)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz))) as proof of ((x Xz)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz))) as proof of ((x Xy)->((x Xz)->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))))
% 6.03/6.20 Found (and_rect00 (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz)))) as proof of ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))
% 6.03/6.20 Found ((and_rect0 ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))) (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz)))) as proof of ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))
% 6.03/6.20 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))) (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz)))) as proof of ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))
% 6.03/6.20 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))) (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz))))) as proof of ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))
% 6.03/6.20 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) ((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy)))) (fun (x01:(x Xy))=> ((or_intror ((and (q Xx)) (cT Xz))) (x Xz))))) as proof of (((and (x Xy)) (x Xz))->((or ((and (q Xx)) (cT Xz))) ((and (p Xx)) (cR Xy))))
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=q:(fofType->Prop)
% 6.03/6.20 Found x00 as proof of (q Xx)
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=p:(fofType->Prop)
% 6.03/6.20 Found x00 as proof of (p Xx)
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=p:(fofType->Prop)
% 6.03/6.20 Found (fun (x00:(x Xx))=> x00) as proof of (p Xx)
% 6.03/6.20 Found (fun (x00:(x Xx))=> x00) as proof of ((x Xx)->(p Xx))
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=q:(fofType->Prop)
% 6.03/6.20 Found (fun (x00:(x Xx))=> x00) as proof of (q Xx)
% 6.03/6.20 Found (fun (x00:(x Xx))=> x00) as proof of ((x Xx)->(q Xx))
% 6.03/6.20 Found x2:(cR Xy)
% 6.03/6.20 Found x2 as proof of (cR Xy)
% 6.03/6.20 Found x2:(cR Xy)
% 6.03/6.20 Found x2 as proof of (cR Xy)
% 6.03/6.20 Found x2:(cR Xy)
% 6.03/6.20 Found x2 as proof of (cR Xy)
% 6.03/6.20 Found x2:(cR Xy)
% 6.03/6.20 Found x2 as proof of (cR Xy)
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=p:(fofType->Prop)
% 6.03/6.20 Found x00 as proof of (p Xx)
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=q:(fofType->Prop)
% 6.03/6.20 Found x00 as proof of (q Xx)
% 6.03/6.20 Found x2:(cR Xy)
% 6.03/6.20 Found x2 as proof of (cR Xy)
% 6.03/6.20 Found x2:(cR Xy)
% 6.03/6.20 Found x2 as proof of (cR Xy)
% 6.03/6.20 Found x00:(x Xx)
% 6.03/6.20 Instantiate: x:=q:(fofType->Prop)
% 6.03/6.20 Found (fun (x00:(x Xx))=> x00) as proof of (q Xx)
% 6.03/6.20 Found (fun (x00:(x Xx))=> x00) as proof of ((x Xx)->(q Xx))
% 11.35/11.58 Found x00:(x Xx)
% 11.35/11.58 Instantiate: x:=p:(fofType->Prop)
% 11.35/11.58 Found (fun (x00:(x Xx))=> x00) as proof of (p Xx)
% 11.35/11.58 Found (fun (x00:(x Xx))=> x00) as proof of ((x Xx)->(p Xx))
% 11.35/11.58 Found x02:(x Xz)
% 11.35/11.58 Instantiate: x:=cT:(fofType->Prop)
% 11.35/11.58 Found x02 as proof of (cT Xz)
% 11.35/11.58 Found x01:(x Xy)
% 11.35/11.58 Instantiate: x:=cR:(fofType->Prop)
% 11.35/11.58 Found x01 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 11.35/11.58 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 11.35/11.58 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 11.35/11.58 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 11.35/11.58 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 11.35/11.58 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 11.35/11.58 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cT Xz)
% 11.35/11.58 Found x2 as proof of (cT Xz)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cT Xz)
% 11.35/11.58 Found x2 as proof of (cT Xz)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cT Xz)
% 11.35/11.58 Found x2 as proof of (cT Xz)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cT Xz)
% 11.35/11.58 Found x2 as proof of (cT Xz)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cT Xz)
% 11.35/11.58 Found x2 as proof of (cT Xz)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cT Xz)
% 11.35/11.58 Found x2 as proof of (cT Xz)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x2:(cR Xy)
% 11.35/11.58 Found x2 as proof of (cR Xy)
% 11.35/11.58 Found x02:(x Xz)
% 11.35/11.58 Instantiate: x:=cT:(fofType->Prop)
% 11.35/11.58 Found (fun (x02:(x Xz))=> x02) as proof of (cT Xz)
% 11.35/11.58 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xz)->(cT Xz))
% 11.35/11.58 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xy)->((x Xz)->(cT Xz)))
% 11.35/11.58 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.35/11.58 Found ((and_rect0 (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.35/11.58 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.35/11.58 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.35/11.58 Found x01:(x Xy)
% 11.35/11.58 Instantiate: x:=cR:(fofType->Prop)
% 11.35/11.58 Found (fun (x02:(x Xz))=> x01) as proof of (cR Xy)
% 11.35/11.58 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xz)->(cR Xy))
% 11.35/11.58 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xy)->((x Xz)->(cR Xy)))
% 11.35/11.58 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.35/11.58 Found ((and_rect0 (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.35/11.58 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.96/12.18 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.96/12.18 Found x2:(cR Xy)
% 11.96/12.18 Found x2 as proof of (cR Xy)
% 11.96/12.18 Found x2:(cR Xy)
% 11.96/12.18 Found x2 as proof of (cR Xy)
% 11.96/12.18 Found x02:(x Xz)
% 11.96/12.18 Instantiate: x:=cT:(fofType->Prop)
% 11.96/12.18 Found (fun (x02:(x Xz))=> x02) as proof of (cT Xz)
% 11.96/12.18 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xz)->(cT Xz))
% 11.96/12.18 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xy)->((x Xz)->(cT Xz)))
% 11.96/12.18 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.96/12.18 Found ((and_rect0 (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.96/12.18 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 11.96/12.18 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02))) as proof of (cT Xz)
% 11.96/12.18 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02))) as proof of (((and (x Xy)) (x Xz))->(cT Xz))
% 11.96/12.18 Found x01:(x Xy)
% 11.96/12.18 Instantiate: x:=cR:(fofType->Prop)
% 11.96/12.18 Found (fun (x02:(x Xz))=> x01) as proof of (cR Xy)
% 11.96/12.18 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xz)->(cR Xy))
% 11.96/12.18 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xy)->((x Xz)->(cR Xy)))
% 11.96/12.18 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.96/12.18 Found ((and_rect0 (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.96/12.18 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 11.96/12.18 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01))) as proof of (cR Xy)
% 11.96/12.18 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01))) as proof of (((and (x Xy)) (x Xz))->(cR Xy))
% 11.96/12.18 Found x02:(x Xz)
% 11.96/12.18 Instantiate: x:=cT:(fofType->Prop)
% 11.96/12.18 Found x02 as proof of (cT Xz)
% 11.96/12.18 Found x01:(x Xy)
% 11.96/12.18 Instantiate: x:=cR:(fofType->Prop)
% 11.96/12.18 Found x01 as proof of (cR Xy)
% 11.96/12.18 Found x2:(cR Xy)
% 11.96/12.18 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 11.96/12.18 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 11.96/12.18 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 11.96/12.18 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.96/12.18 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.96/12.18 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 11.96/12.18 Found (fun (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2))) as proof of (cR Xy)
% 11.96/12.18 Found (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2))) as proof of ((x Xz)->(cR Xy))
% 11.96/12.18 Found (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2))) as proof of ((x Xy)->((x Xz)->(cR Xy)))
% 11.96/12.18 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 11.96/12.18 Found ((and_rect0 (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 13.68/13.85 Found x2:(cR Xy)
% 13.68/13.85 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 13.68/13.85 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 13.68/13.85 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 13.68/13.85 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found x2:(cT Xz)
% 13.68/13.85 Found (fun (x2:(cT Xz))=> x2) as proof of (cT Xz)
% 13.68/13.85 Found (fun (x1:(q Xz)) (x2:(cT Xz))=> x2) as proof of ((cT Xz)->(cT Xz))
% 13.68/13.85 Found (fun (x1:(q Xz)) (x2:(cT Xz))=> x2) as proof of ((q Xz)->((cT Xz)->(cT Xz)))
% 13.68/13.85 Found (and_rect10 (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found ((and_rect1 (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found x2:(cR Xy)
% 13.68/13.85 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 13.68/13.85 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 13.68/13.85 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 13.68/13.85 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found x2:(cR Xy)
% 13.68/13.85 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 13.68/13.85 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 13.68/13.85 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 13.68/13.85 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 13.68/13.85 Found x2:(cT Xz)
% 13.68/13.85 Found (fun (x2:(cT Xz))=> x2) as proof of (cT Xz)
% 13.68/13.85 Found (fun (x1:(q Xz)) (x2:(cT Xz))=> x2) as proof of ((cT Xz)->(cT Xz))
% 13.68/13.85 Found (fun (x1:(q Xz)) (x2:(cT Xz))=> x2) as proof of ((q Xz)->((cT Xz)->(cT Xz)))
% 13.68/13.85 Found (and_rect10 (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found ((and_rect1 (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 13.68/13.85 Found (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cT Xz)
% 17.09/17.26 Found x4 as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cT Xz)
% 17.09/17.26 Found x4 as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x01:(x Xy)
% 17.09/17.26 Instantiate: x:=cR:(fofType->Prop)
% 17.09/17.26 Found (fun (x02:(x Xz))=> x01) as proof of (cR Xy)
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xz)->(cR Xy))
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xy)->((x Xz)->(cR Xy)))
% 17.09/17.26 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found ((and_rect0 (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found x02:(x Xz)
% 17.09/17.26 Instantiate: x:=cT:(fofType->Prop)
% 17.09/17.26 Found (fun (x02:(x Xz))=> x02) as proof of (cT Xz)
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xz)->(cT Xz))
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xy)->((x Xz)->(cT Xz)))
% 17.09/17.26 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found ((and_rect0 (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found x4:(cT Xz)
% 17.09/17.26 Found x4 as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cT Xz)
% 17.09/17.26 Found x4 as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cT Xz)
% 17.09/17.26 Found x4 as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x4:(cT Xz)
% 17.09/17.26 Found x4 as proof of (cT Xz)
% 17.09/17.26 Found x4:(cR Xy)
% 17.09/17.26 Found x4 as proof of (cR Xy)
% 17.09/17.26 Found x01:(x Xy)
% 17.09/17.26 Instantiate: x:=cR:(fofType->Prop)
% 17.09/17.26 Found (fun (x02:(x Xz))=> x01) as proof of (cR Xy)
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xz)->(cR Xy))
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x01) as proof of ((x Xy)->((x Xz)->(cR Xy)))
% 17.09/17.26 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found ((and_rect0 (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01)) as proof of (cR Xy)
% 17.09/17.26 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01))) as proof of (cR Xy)
% 17.09/17.26 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> x01))) as proof of (((and (x Xy)) (x Xz))->(cR Xy))
% 17.09/17.26 Found x02:(x Xz)
% 17.09/17.26 Instantiate: x:=cT:(fofType->Prop)
% 17.09/17.26 Found (fun (x02:(x Xz))=> x02) as proof of (cT Xz)
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xz)->(cT Xz))
% 17.09/17.26 Found (fun (x01:(x Xy)) (x02:(x Xz))=> x02) as proof of ((x Xy)->((x Xz)->(cT Xz)))
% 17.09/17.26 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found ((and_rect0 (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02)) as proof of (cT Xz)
% 17.09/17.26 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02))) as proof of (cT Xz)
% 17.75/17.92 Found (fun (x00:((and (x Xy)) (x Xz)))=> (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> x02))) as proof of (((and (x Xy)) (x Xz))->(cT Xz))
% 17.75/17.92 Found x4:(cR Xy)
% 17.75/17.92 Found x4 as proof of (cR Xy)
% 17.75/17.92 Found x4:(cR Xy)
% 17.75/17.92 Found x4 as proof of (cR Xy)
% 17.75/17.92 Found x4:(cT Xz)
% 17.75/17.92 Found x4 as proof of (cT Xz)
% 17.75/17.92 Found x4:(cT Xz)
% 17.75/17.92 Found x4 as proof of (cT Xz)
% 17.75/17.92 Found x4:(cR Xy)
% 17.75/17.92 Found x4 as proof of (cR Xy)
% 17.75/17.92 Found x4:(cR Xy)
% 17.75/17.92 Found x4 as proof of (cR Xy)
% 17.75/17.92 Found x2:(cR Xy)
% 17.75/17.92 Found (fun (x2:(cR Xy))=> x2) as proof of (cR Xy)
% 17.75/17.92 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((cR Xy)->(cR Xy))
% 17.75/17.92 Found (fun (x1:(p Xz)) (x2:(cR Xy))=> x2) as proof of ((p Xz)->((cR Xy)->(cR Xy)))
% 17.75/17.92 Found (and_rect10 (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 17.75/17.92 Found ((and_rect1 (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 17.75/17.92 Found (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)) as proof of (cR Xy)
% 17.75/17.92 Found (fun (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2))) as proof of (cR Xy)
% 17.75/17.92 Found (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2))) as proof of ((x Xz)->(cR Xy))
% 17.75/17.92 Found (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2))) as proof of ((x Xy)->((x Xz)->(cR Xy)))
% 17.75/17.92 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 17.75/17.92 Found ((and_rect0 (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 17.75/17.92 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 17.75/17.92 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cR Xy)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((p Xz)->((cR Xy)->P)))=> (((((and_rect (p Xz)) (cR Xy)) P) x1) x02)) (cR Xy)) (fun (x1:(p Xz)) (x2:(cR Xy))=> x2)))) as proof of (cR Xy)
% 17.75/17.92 Found x2:(cT Xz)
% 17.75/17.92 Found (fun (x2:(cT Xz))=> x2) as proof of (cT Xz)
% 17.75/17.92 Found (fun (x1:(q Xz)) (x2:(cT Xz))=> x2) as proof of ((cT Xz)->(cT Xz))
% 17.75/17.92 Found (fun (x1:(q Xz)) (x2:(cT Xz))=> x2) as proof of ((q Xz)->((cT Xz)->(cT Xz)))
% 17.75/17.92 Found (and_rect10 (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 17.75/17.92 Found ((and_rect1 (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 17.75/17.92 Found (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)) as proof of (cT Xz)
% 17.75/17.92 Found (fun (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2))) as proof of (cT Xz)
% 17.75/17.92 Found (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2))) as proof of ((x Xz)->(cT Xz))
% 17.75/17.92 Found (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2))) as proof of ((x Xy)->((x Xz)->(cT Xz)))
% 17.75/17.92 Found (and_rect00 (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)))) as proof of (cT Xz)
% 20.94/21.12 Found ((and_rect0 (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)))) as proof of (cT Xz)
% 20.94/21.12 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)))) as proof of (cT Xz)
% 20.94/21.12 Found (((fun (P:Type) (x1:((x Xy)->((x Xz)->P)))=> (((((and_rect (x Xy)) (x Xz)) P) x1) x00)) (cT Xz)) (fun (x01:(x Xy)) (x02:(x Xz))=> (((fun (P:Type) (x1:((q Xz)->((cT Xz)->P)))=> (((((and_rect (q Xz)) (cT Xz)) P) x1) x02)) (cT Xz)) (fun (x1:(q Xz)) (x2:(cT Xz))=> x2)))) as proof of (cT Xz)
% 20.94/21.12 Found x4:(cR Xy)
% 20.94/21.12 Found x4 as proof of (cR Xy)
% 20.94/21.12 Found x4:(cR Xy)
% 20.94/21.12 Found x4 as proof of (cR Xy)
% 20.94/21.12 % SZS status GaveUp for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------