TSTP Solution File: SYO326^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO326^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 00:51:10 EDT 2022
% Result : Theorem 1.07s 1.31s
% Output : Proof 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO326^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sat Mar 12 03:53:12 EST 2022
% 0.17/0.33 % CPUTime :
% 0.17/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.17/0.34 Python 2.7.5
% 0.71/0.88 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.71/0.88 FOF formula (<kernel.Constant object at 0x14afd40>, <kernel.DependentProduct object at 0x2b7829d45d88>) of role type named cC
% 0.71/0.88 Using role type
% 0.71/0.88 Declaring cC:(fofType->Prop)
% 0.71/0.88 FOF formula (<kernel.Constant object at 0x14afd40>, <kernel.DependentProduct object at 0x2b7829d456c8>) of role type named f
% 0.71/0.88 Using role type
% 0.71/0.88 Declaring f:(fofType->fofType)
% 0.71/0.88 FOF formula (<kernel.Constant object at 0x14abc20>, <kernel.DependentProduct object at 0x2b7829d45440>) of role type named cB
% 0.71/0.88 Using role type
% 0.71/0.88 Declaring cB:(fofType->(fofType->Prop))
% 0.71/0.88 FOF formula (<kernel.Constant object at 0x14abc20>, <kernel.DependentProduct object at 0x2b7829d458c0>) of role type named cA
% 0.71/0.88 Using role type
% 0.71/0.88 Declaring cA:(fofType->Prop)
% 0.71/0.88 FOF formula ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))) of role conjecture named cSV8
% 0.71/0.88 Conjecture to prove = ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))):Prop
% 0.71/0.88 Parameter fofType_DUMMY:fofType.
% 0.71/0.88 We need to prove ['((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))']
% 0.71/0.88 Parameter fofType:Type.
% 0.71/0.88 Parameter cC:(fofType->Prop).
% 0.71/0.88 Parameter f:(fofType->fofType).
% 0.71/0.88 Parameter cB:(fofType->(fofType->Prop)).
% 0.71/0.88 Parameter cA:(fofType->Prop).
% 0.71/0.88 Trying to prove ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))
% 0.71/0.88 Found x00:((x Xx) Xy)
% 0.71/0.88 Instantiate: x:=Xv:(fofType->(fofType->Prop))
% 0.71/0.88 Found x00 as proof of ((Xv Xx) Xy)
% 0.71/0.88 Found (fun (x00:((x Xx) Xy))=> x00) as proof of ((Xv Xx) Xy)
% 0.71/0.88 Found (fun (Xy:fofType) (x00:((x Xx) Xy))=> x00) as proof of (((x Xx) Xy)->((Xv Xx) Xy))
% 0.71/0.88 Found (fun (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> x00) as proof of (forall (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))
% 0.71/0.88 Found (fun (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> x00) as proof of (forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))
% 0.71/0.88 Found x0000:=(x000 x0):((Xv Xx) Xy)
% 0.71/0.88 Found (x000 x0) as proof of ((Xv Xx) Xy)
% 0.71/0.88 Found ((x00 Xv) x0) as proof of ((Xv Xx) Xy)
% 0.71/0.88 Found ((x00 Xv) x0) as proof of ((Xv Xx) Xy)
% 0.71/0.88 Found (fun (x00:((x Xx) Xy))=> ((x00 Xv) x0)) as proof of ((Xv Xx) Xy)
% 0.71/0.88 Found (fun (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0)) as proof of (((x Xx) Xy)->((Xv Xx) Xy))
% 0.71/0.88 Found (fun (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0)) as proof of (forall (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))
% 1.07/1.25 Found (fun (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0)) as proof of (forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))
% 1.07/1.25 Found (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0)) as proof of (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy))))
% 1.07/1.25 Found (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0)) as proof of (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))))
% 1.07/1.25 Found x200:=(x20 x0):((Xv Xz) Xz)
% 1.07/1.25 Found (x20 x0) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found ((x2 Xz) x0) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found (fun (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)) as proof of ((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->((Xv Xz) Xz))
% 1.07/1.25 Found (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)) as proof of ((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->((Xv Xz) Xz)))
% 1.07/1.25 Found (and_rect00 (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found ((and_rect0 ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found (fun (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))) as proof of ((Xv Xz) Xz)
% 1.07/1.25 Found (fun (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))) as proof of (((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))->((Xv Xz) Xz))
% 1.07/1.27 Found (fun (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))) as proof of ((x Xz) Xz)
% 1.07/1.27 Found (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))) as proof of ((cC Xz)->((x Xz) Xz))
% 1.07/1.27 Found (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))) as proof of (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))
% 1.07/1.27 Found x1000:=(x100 x0):((Xv (f Xw)) Xz)
% 1.07/1.27 Found (x100 x0) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found ((x10 Xz) x0) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found (((x1 Xw) Xz) x0) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found (fun (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)) as proof of ((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->((Xv (f Xw)) Xz))
% 1.07/1.27 Found (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)) as proof of ((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->((Xv (f Xw)) Xz)))
% 1.07/1.27 Found (and_rect00 (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found ((and_rect0 ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found (fun (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)))) as proof of ((Xv (f Xw)) Xz)
% 1.07/1.27 Found (fun (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)))) as proof of (((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))->((Xv (f Xw)) Xz))
% 1.07/1.27 Found (fun (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)))) as proof of ((x (f Xw)) Xz)
% 1.07/1.27 Found (fun (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)))) as proof of (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz))
% 1.07/1.27 Found (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)))) as proof of (forall (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))
% 1.07/1.27 Found (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0)))) as proof of (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))
% 1.07/1.27 Found ((conj10 (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))))) as proof of ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))
% 1.07/1.27 Found (((conj1 (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))))) as proof of ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))
% 1.07/1.28 Found ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))))) as proof of ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))
% 1.07/1.28 Found ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0))))) as proof of ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))
% 1.07/1.28 Found ((conj00 ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0))) as proof of ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy))))))
% 1.07/1.28 Found (((conj0 (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0))) as proof of ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy))))))
% 1.07/1.28 Found ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0))) as proof of ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy))))))
% 1.07/1.29 Found ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0))) as proof of ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy))))))
% 1.07/1.29 Found (ex_intro000 ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((x Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((x (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((x Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:((x Xx) Xy))=> ((x00 Xv) x0)))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))
% 1.07/1.29 Found ((ex_intro00 (fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1))))) ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), ((((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy))=> ((x00 Xv) x0)))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))
% 1.07/1.29 Found (((ex_intro0 (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))) (fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1))))) ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), ((((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy))=> ((x00 Xv) x0)))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))
% 1.07/1.30 Found ((((ex_intro (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))) (fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1))))) ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), ((((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy))=> ((x00 Xv) x0)))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))
% 1.07/1.30 Found ((((ex_intro (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))) (fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1))))) ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), ((((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy))=> ((x00 Xv) x0)))) as proof of ((ex (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy))))))))
% 1.07/1.30 Got proof ((((ex_intro (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))) (fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1))))) ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), ((((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy))=> ((x00 Xv) x0))))
% 1.07/1.31 Time elapsed = 0.684992s
% 1.07/1.31 node=97 cost=850.000000 depth=27
% 1.07/1.31 ::::::::::::::::::::::
% 1.07/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/1.31 ((((ex_intro (fofType->(fofType->Prop))) (fun (Xu:(fofType->(fofType->Prop)))=> ((and ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xu (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xu Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), (((Xu Xx) Xy)->((Xv Xx) Xy)))))))) (fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1))))) ((((conj ((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz))))) (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->(forall (Xx:fofType) (Xy:fofType), ((((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy)->((Xv Xx) Xy)))))) ((((conj (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xz) Xz)))) (fun (Xw:fofType) (Xz:fofType) (x0:((and (cA Xw)) ((cB Xz) Xw))) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv (f Xw)) Xz)) (fun (x1:(forall (Xw0:fofType) (Xz0:fofType), (((and (cA Xw0)) ((cB Xz0) Xw0))->((Xv (f Xw0)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> (((x1 Xw) Xz) x0))))) (fun (Xz:fofType) (x0:(cC Xz)) (Xv:(fofType->(fofType->Prop))) (x00:((and (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))))=> (((fun (P:Type) (x1:((forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))->((forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))->P)))=> (((((and_rect (forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0)))) P) x1) x00)) ((Xv Xz) Xz)) (fun (x1:(forall (Xw:fofType) (Xz0:fofType), (((and (cA Xw)) ((cB Xz0) Xw))->((Xv (f Xw)) Xz0)))) (x2:(forall (Xz0:fofType), ((cC Xz0)->((Xv Xz0) Xz0))))=> ((x2 Xz) x0)))))) (fun (Xv:(fofType->(fofType->Prop))) (x0:((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))) (Xx:fofType) (Xy:fofType) (x00:(((fun (a0:fofType) (a1:fofType)=> (forall (Xv:(fofType->(fofType->Prop))), (((and (forall (Xw:fofType) (Xz:fofType), (((and (cA Xw)) ((cB Xz) Xw))->((Xv (f Xw)) Xz)))) (forall (Xz:fofType), ((cC Xz)->((Xv Xz) Xz))))->((Xv a0) a1)))) Xx) Xy))=> ((x00 Xv) x0))))
% 1.16/1.31 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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