TSTP Solution File: SYO313^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO313^5 : 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 00:51:08 EDT 2022
% Result : Unknown 5.27s 5.47s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO313^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n019.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 03:04:42 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
% 2.92/3.09 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 2.92/3.09 FOF formula (<kernel.Constant object at 0x257d1b8>, <kernel.DependentProduct object at 0x257d488>) of role type named cELESS
% 2.92/3.09 Using role type
% 2.92/3.09 Declaring cELESS:(fofType->(fofType->Prop))
% 2.92/3.09 FOF formula (forall (A:(fofType->Prop)), (((and ((ex fofType) (fun (Xr:fofType)=> (A Xr)))) ((ex fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))))->((ex fofType) (fun (Xl:fofType)=> ((and (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xl)))) (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS Xl) Xy)))))))) of role conjecture named cELUB
% 2.92/3.09 Conjecture to prove = (forall (A:(fofType->Prop)), (((and ((ex fofType) (fun (Xr:fofType)=> (A Xr)))) ((ex fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))))->((ex fofType) (fun (Xl:fofType)=> ((and (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xl)))) (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS Xl) Xy)))))))):Prop
% 2.92/3.09 Parameter fofType_DUMMY:fofType.
% 2.92/3.09 We need to prove ['(forall (A:(fofType->Prop)), (((and ((ex fofType) (fun (Xr:fofType)=> (A Xr)))) ((ex fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))))->((ex fofType) (fun (Xl:fofType)=> ((and (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xl)))) (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS Xl) Xy))))))))']
% 2.92/3.09 Parameter fofType:Type.
% 2.92/3.09 Parameter cELESS:(fofType->(fofType->Prop)).
% 2.92/3.09 Trying to prove (forall (A:(fofType->Prop)), (((and ((ex fofType) (fun (Xr:fofType)=> (A Xr)))) ((ex fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))))->((ex fofType) (fun (Xl:fofType)=> ((and (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xl)))) (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS Xl) Xy))))))))
% 2.92/3.09 Found x3:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x2)))
% 2.92/3.09 Instantiate: x4:=x2:fofType
% 2.92/3.09 Found x3 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x4)))
% 2.92/3.09 Found x4:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x3)))
% 2.92/3.09 Instantiate: x0:=x3:fofType
% 2.92/3.09 Found x4 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x0)))
% 2.92/3.09 Found x4:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x3)))
% 2.92/3.09 Instantiate: x2:=x3:fofType
% 2.92/3.09 Found x4 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x2)))
% 2.92/3.09 Found x3:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x2)))
% 2.92/3.09 Instantiate: x6:=x2:fofType
% 2.92/3.09 Found x3 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x6)))
% 2.92/3.09 Found x5:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x4)))
% 2.92/3.09 Instantiate: x6:=x4:fofType
% 2.92/3.09 Found x5 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x6)))
% 2.92/3.09 Found x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5)))
% 2.92/3.09 Instantiate: x4:=x5:fofType
% 2.92/3.09 Found x6 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x4)))
% 2.92/3.09 Found x4:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x3)))
% 2.92/3.09 Instantiate: x0:=x3:fofType
% 2.92/3.09 Found x4 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x0)))
% 2.92/3.09 Found x3:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x2)))
% 2.92/3.09 Instantiate: x4:=x2:fofType
% 2.92/3.09 Found x3 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x4)))
% 2.92/3.09 Found x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5)))
% 2.92/3.09 Instantiate: x0:=x5:fofType
% 2.92/3.09 Found x6 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x0)))
% 2.92/3.09 Found x3:(A x2)
% 2.92/3.09 Instantiate: x4:=x2:fofType
% 2.92/3.09 Found x3 as proof of (A x4)
% 2.92/3.09 Found (x000 x3) as proof of ((cELESS x4) Xy)
% 2.92/3.09 Found ((x00 x4) x3) as proof of ((cELESS x4) Xy)
% 2.92/3.09 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x3)) as proof of ((cELESS x4) Xy)
% 2.92/3.09 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x3)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x4) Xy))
% 2.92/3.09 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x3)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x4) Xy)))
% 2.92/3.09 Found x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5)))
% 2.92/3.09 Instantiate: x2:=x5:fofType
% 3.62/3.80 Found x6 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x2)))
% 3.62/3.80 Found x4:(A x3)
% 3.62/3.80 Instantiate: x0:=x3:fofType
% 3.62/3.80 Found x4 as proof of (A x0)
% 3.62/3.80 Found (x000 x4) as proof of ((cELESS x0) Xy)
% 3.62/3.80 Found ((x00 x0) x4) as proof of ((cELESS x0) Xy)
% 3.62/3.80 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x4)) as proof of ((cELESS x0) Xy)
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x0) Xy))
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x4)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x0) Xy)))
% 3.62/3.80 Found x4:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x3)))
% 3.62/3.80 Instantiate: x2:=x3:fofType
% 3.62/3.80 Found x4 as proof of (forall (Xx:fofType), ((A Xx)->((cELESS Xx) x2)))
% 3.62/3.80 Found x4:(A x3)
% 3.62/3.80 Instantiate: x2:=x3:fofType
% 3.62/3.80 Found x4 as proof of (A x2)
% 3.62/3.80 Found (x000 x4) as proof of ((cELESS x2) Xy)
% 3.62/3.80 Found ((x00 x2) x4) as proof of ((cELESS x2) Xy)
% 3.62/3.80 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x4)) as proof of ((cELESS x2) Xy)
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x2) Xy))
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x4)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x2) Xy)))
% 3.62/3.80 Found x000:=(x00 x5):((A x5)->((cELESS x5) Xy))
% 3.62/3.80 Found (x00 x5) as proof of ((A x5)->((cELESS x4) Xy))
% 3.62/3.80 Found (x00 x5) as proof of ((A x5)->((cELESS x4) Xy))
% 3.62/3.80 Found x000:=(x00 x5):((A x5)->((cELESS x5) Xy))
% 3.62/3.80 Found (x00 x5) as proof of ((A x5)->((cELESS x0) Xy))
% 3.62/3.80 Found (x00 x5) as proof of ((A x5)->((cELESS x0) Xy))
% 3.62/3.80 Found x3:(A x2)
% 3.62/3.80 Instantiate: x6:=x2:fofType
% 3.62/3.80 Found x3 as proof of (A x6)
% 3.62/3.80 Found (x000 x3) as proof of ((cELESS x6) Xy)
% 3.62/3.80 Found ((x00 x6) x3) as proof of ((cELESS x6) Xy)
% 3.62/3.80 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x6) x3)) as proof of ((cELESS x6) Xy)
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x6) x3)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x6) Xy))
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x6) x3)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x6) Xy)))
% 3.62/3.80 Found x5:(A x4)
% 3.62/3.80 Instantiate: x6:=x4:fofType
% 3.62/3.80 Found x5 as proof of (A x6)
% 3.62/3.80 Found (x000 x5) as proof of ((cELESS x6) Xy)
% 3.62/3.80 Found ((x00 x6) x5) as proof of ((cELESS x6) Xy)
% 3.62/3.80 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x6) x5)) as proof of ((cELESS x6) Xy)
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x6) x5)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x6) Xy))
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x6) x5)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x6) Xy)))
% 3.62/3.80 Found x000:=(x00 x3):((A x3)->((cELESS x3) Xy))
% 3.62/3.80 Found (x00 x3) as proof of ((A x3)->((cELESS x0) Xy))
% 3.62/3.80 Found (x00 x3) as proof of ((A x3)->((cELESS x0) Xy))
% 3.62/3.80 Found x000:=(x00 x3):((A x3)->((cELESS x3) Xy))
% 3.62/3.80 Found (x00 x3) as proof of ((A x3)->((cELESS x2) Xy))
% 3.62/3.80 Found (x00 x3) as proof of ((A x3)->((cELESS x2) Xy))
% 3.62/3.80 Found x000:=(x00 x5):((A x5)->((cELESS x5) Xy))
% 3.62/3.80 Found (x00 x5) as proof of ((A x5)->((cELESS x2) Xy))
% 3.62/3.80 Found (x00 x5) as proof of ((A x5)->((cELESS x2) Xy))
% 3.62/3.80 Found x6:(A x5)
% 3.62/3.80 Instantiate: x0:=x5:fofType
% 3.62/3.80 Found x6 as proof of (A x0)
% 3.62/3.80 Found (x000 x6) as proof of ((cELESS x0) Xy)
% 3.62/3.80 Found ((x00 x0) x6) as proof of ((cELESS x0) Xy)
% 3.62/3.80 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x6)) as proof of ((cELESS x0) Xy)
% 3.62/3.80 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x6)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x0) Xy))
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x6)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x0) Xy)))
% 3.90/4.10 Found x3:(A x2)
% 3.90/4.10 Instantiate: x4:=x2:fofType
% 3.90/4.10 Found x3 as proof of (A x4)
% 3.90/4.10 Found (x000 x3) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found ((x00 x4) x3) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x3)) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x3)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x4) Xy))
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x3)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x4) Xy)))
% 3.90/4.10 Found x6:(A x5)
% 3.90/4.10 Instantiate: x4:=x5:fofType
% 3.90/4.10 Found x6 as proof of (A x4)
% 3.90/4.10 Found (x000 x6) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found ((x00 x4) x6) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x6)) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x6)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x4) Xy))
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x4) x6)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x4) Xy)))
% 3.90/4.10 Found x4:(A x3)
% 3.90/4.10 Instantiate: x0:=x3:fofType
% 3.90/4.10 Found x4 as proof of (A x0)
% 3.90/4.10 Found (x000 x4) as proof of ((cELESS x0) Xy)
% 3.90/4.10 Found ((x00 x0) x4) as proof of ((cELESS x0) Xy)
% 3.90/4.10 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x4)) as proof of ((cELESS x0) Xy)
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x0) Xy))
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x0) x4)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x0) Xy)))
% 3.90/4.10 Found x6:(A x5)
% 3.90/4.10 Instantiate: x2:=x5:fofType
% 3.90/4.10 Found x6 as proof of (A x2)
% 3.90/4.10 Found (x000 x6) as proof of ((cELESS x2) Xy)
% 3.90/4.10 Found ((x00 x2) x6) as proof of ((cELESS x2) Xy)
% 3.90/4.10 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x6)) as proof of ((cELESS x2) Xy)
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x6)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x2) Xy))
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x6)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x2) Xy)))
% 3.90/4.10 Found x4:(A x3)
% 3.90/4.10 Instantiate: x2:=x3:fofType
% 3.90/4.10 Found x4 as proof of (A x2)
% 3.90/4.10 Found (x000 x4) as proof of ((cELESS x2) Xy)
% 3.90/4.10 Found ((x00 x2) x4) as proof of ((cELESS x2) Xy)
% 3.90/4.10 Found (fun (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x4)) as proof of ((cELESS x2) Xy)
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x2) Xy))
% 3.90/4.10 Found (fun (Xy:fofType) (x00:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy))))=> ((x00 x2) x4)) as proof of (forall (Xy:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xy)))->((cELESS x2) Xy)))
% 3.90/4.10 Found x6:(A x5)
% 3.90/4.10 Instantiate: x0:=x5:fofType
% 3.90/4.10 Found x6 as proof of (A x0)
% 3.90/4.10 Found (x000 x6) as proof of ((cELESS x0) Xy)
% 3.90/4.10 Found ((x00 x0) x6) as proof of ((cELESS x0) Xy)
% 3.90/4.10 Found (fun (x6:(A x5))=> ((x00 x0) x6)) as proof of ((cELESS x0) Xy)
% 3.90/4.10 Found x6:(A x5)
% 3.90/4.10 Instantiate: x4:=x5:fofType
% 3.90/4.10 Found x6 as proof of (A x4)
% 3.90/4.10 Found (x000 x6) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found ((x00 x4) x6) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found (fun (x6:(A x5))=> ((x00 x4) x6)) as proof of ((cELESS x4) Xy)
% 3.90/4.10 Found x600:=(x60 x00):((cELESS Xx) x5)
% 3.90/4.10 Found (x60 x00) as proof of ((cELESS Xx) x4)
% 3.90/4.10 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found x600:=(x60 x00):((cELESS Xx) x5)
% 4.31/4.53 Found (x60 x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found x6:(A x5)
% 4.31/4.53 Instantiate: x0:=x5:fofType
% 4.31/4.53 Found (fun (x6:(A x5))=> x6) as proof of (A x0)
% 4.31/4.53 Found x6:(A x5)
% 4.31/4.53 Instantiate: x4:=x5:fofType
% 4.31/4.53 Found (fun (x6:(A x5))=> x6) as proof of (A x4)
% 4.31/4.53 Found x00:(A Xx)
% 4.31/4.53 Found x00 as proof of (A Xx)
% 4.31/4.53 Found (x60 x00) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x4)
% 4.31/4.53 Found x00:(A Xx)
% 4.31/4.53 Found x00 as proof of (A Xx)
% 4.31/4.53 Found (x60 x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found x6:(A x5)
% 4.31/4.53 Instantiate: x2:=x5:fofType
% 4.31/4.53 Found x6 as proof of (A x2)
% 4.31/4.53 Found (x000 x6) as proof of ((cELESS x2) Xy)
% 4.31/4.53 Found ((x00 x2) x6) as proof of ((cELESS x2) Xy)
% 4.31/4.53 Found (fun (x6:(A x5))=> ((x00 x2) x6)) as proof of ((cELESS x2) Xy)
% 4.31/4.53 Found x600:=(x60 x00):((cELESS Xx) x5)
% 4.31/4.53 Found (x60 x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found x6:(A x5)
% 4.31/4.53 Instantiate: x2:=x5:fofType
% 4.31/4.53 Found (fun (x6:(A x5))=> x6) as proof of (A x2)
% 4.31/4.53 Found x00:(A Xx)
% 4.31/4.53 Found x00 as proof of (A Xx)
% 4.31/4.53 Found (x60 x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found x000:=(x00 x3):((A x3)->((cELESS x3) Xy))
% 4.31/4.53 Found (x00 x3) as proof of ((A x3)->((cELESS x0) Xy))
% 4.31/4.53 Found (x00 x3) as proof of ((A x3)->((cELESS x0) Xy))
% 4.31/4.53 Found x4:(A x3)
% 4.31/4.53 Instantiate: x0:=x3:fofType
% 4.31/4.53 Found x4 as proof of (A x0)
% 4.31/4.53 Found (x000 x4) as proof of ((cELESS x0) Xy)
% 4.31/4.53 Found ((x00 x0) x4) as proof of ((cELESS x0) Xy)
% 4.31/4.53 Found (fun (x4:(A x3))=> ((x00 x0) x4)) as proof of ((cELESS x0) Xy)
% 4.31/4.53 Found x4:(A x3)
% 4.31/4.53 Instantiate: x2:=x3:fofType
% 4.31/4.53 Found x4 as proof of (A x2)
% 4.31/4.53 Found (x000 x4) as proof of ((cELESS x2) Xy)
% 4.31/4.53 Found ((x00 x2) x4) as proof of ((cELESS x2) Xy)
% 4.31/4.53 Found (fun (x4:(A x3))=> ((x00 x2) x4)) as proof of ((cELESS x2) Xy)
% 4.31/4.53 Found x400:=(x40 x00):((cELESS Xx) x3)
% 4.31/4.53 Found (x40 x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found x400:=(x40 x00):((cELESS Xx) x3)
% 4.31/4.53 Found (x40 x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found x4:(A x3)
% 4.31/4.53 Instantiate: x0:=x3:fofType
% 4.31/4.53 Found (fun (x4:(A x3))=> x4) as proof of (A x0)
% 4.31/4.53 Found x4:(A x3)
% 4.31/4.53 Instantiate: x2:=x3:fofType
% 4.31/4.53 Found (fun (x4:(A x3))=> x4) as proof of (A x2)
% 4.31/4.53 Found x00:(A Xx)
% 4.31/4.53 Found x00 as proof of (A Xx)
% 4.31/4.53 Found (x40 x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x0)
% 4.31/4.53 Found x00:(A Xx)
% 4.31/4.53 Found x00 as proof of (A Xx)
% 4.31/4.53 Found (x40 x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x2)
% 4.31/4.53 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.12/5.31 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x2)
% 5.12/5.31 Found x400:=(x40 x00):((cELESS Xx) x3)
% 5.12/5.31 Found (x40 x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found x4:(A x3)
% 5.12/5.31 Instantiate: x0:=x3:fofType
% 5.12/5.31 Found x4 as proof of (A x0)
% 5.12/5.31 Found (x000 x4) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found ((x00 x0) x4) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found (fun (x4:(A x3))=> ((x00 x0) x4)) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found x4:(A x3)
% 5.12/5.31 Instantiate: x0:=x3:fofType
% 5.12/5.31 Found (fun (x4:(A x3))=> x4) as proof of (A x0)
% 5.12/5.31 Found x4:(A x3)
% 5.12/5.31 Instantiate: x0:=x3:fofType
% 5.12/5.31 Found (fun (x4:(A x3))=> x4) as proof of (A x0)
% 5.12/5.31 Found x00:(A Xx)
% 5.12/5.31 Found x00 as proof of (A Xx)
% 5.12/5.31 Found (x40 x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found x000:=(x00 x5):((A x5)->((cELESS x5) Xy))
% 5.12/5.31 Found (x00 x5) as proof of ((A x5)->((cELESS x0) Xy))
% 5.12/5.31 Found (x00 x5) as proof of ((A x5)->((cELESS x0) Xy))
% 5.12/5.31 Found x000:=(x00 x5):((A x5)->((cELESS x5) Xy))
% 5.12/5.31 Found (x00 x5) as proof of ((A x5)->((cELESS x2) Xy))
% 5.12/5.31 Found (x00 x5) as proof of ((A x5)->((cELESS x2) Xy))
% 5.12/5.31 Found x000:=(x00 x5):((A x5)->((cELESS x5) Xy))
% 5.12/5.31 Found (x00 x5) as proof of ((A x5)->((cELESS x0) Xy))
% 5.12/5.31 Found (x00 x5) as proof of ((A x5)->((cELESS x0) Xy))
% 5.12/5.31 Found x4:(A x3)
% 5.12/5.31 Instantiate: x0:=x3:fofType
% 5.12/5.31 Found x4 as proof of (A x0)
% 5.12/5.31 Found (x000 x4) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found ((x00 x0) x4) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found (fun (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5)))->((cELESS x0) Xy))
% 5.12/5.31 Found (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)) as proof of (forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->((cELESS x0) Xy)))
% 5.12/5.31 Found (ex_ind10 (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4))) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found ((ex_ind1 ((cELESS x0) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4))) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found (((fun (P:Prop) (x5:(forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->P)))=> (((((ex_ind fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))) P) x5) x2)) ((cELESS x0) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4))) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found (fun (x4:(A x3))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->P)))=> (((((ex_ind fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))) P) x5) x2)) ((cELESS x0) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)))) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found x6:(A x5)
% 5.12/5.31 Instantiate: x0:=x5:fofType
% 5.12/5.31 Found x6 as proof of (A x0)
% 5.12/5.31 Found (x000 x6) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found ((x00 x0) x6) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found (fun (x6:(A x5))=> ((x00 x0) x6)) as proof of ((cELESS x0) Xy)
% 5.12/5.31 Found x600:=(x60 x00):((cELESS Xx) x5)
% 5.12/5.31 Found (x60 x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found x400:=(x40 x00):((cELESS Xx) x3)
% 5.12/5.31 Found (x40 x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found (fun (x6:(A x5))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.12/5.31 Found (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)) as proof of ((A x5)->((cELESS Xx) x0))
% 5.21/5.38 Found (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)) as proof of (forall (x:fofType), ((A x)->((cELESS Xx) x0)))
% 5.21/5.38 Found (ex_ind10 (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x0)
% 5.21/5.38 Found ((ex_ind1 ((cELESS Xx) x0)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x0)
% 5.21/5.38 Found (((fun (P:Prop) (x5:(forall (x:fofType), ((A x)->P)))=> (((((ex_ind fofType) (fun (Xr:fofType)=> (A Xr))) P) x5) x1)) ((cELESS Xx) x0)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x0)
% 5.21/5.38 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((A x)->P)))=> (((((ex_ind fofType) (fun (Xr:fofType)=> (A Xr))) P) x5) x1)) ((cELESS Xx) x0)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)))) as proof of ((cELESS Xx) x0)
% 5.21/5.38 Found x6:(A x5)
% 5.21/5.38 Instantiate: x0:=x5:fofType
% 5.21/5.38 Found (fun (x6:(A x5))=> x6) as proof of (A x0)
% 5.21/5.38 Found x4:(A x3)
% 5.21/5.38 Instantiate: x2:=x3:fofType
% 5.21/5.38 Found x4 as proof of (A x2)
% 5.21/5.38 Found (x000 x4) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found ((x00 x2) x4) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found (fun (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4)) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5)))->((cELESS x2) Xy))
% 5.21/5.38 Found (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4)) as proof of (forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->((cELESS x2) Xy)))
% 5.21/5.38 Found (ex_ind10 (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4))) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found ((ex_ind1 ((cELESS x2) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4))) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found (((fun (P:Prop) (x5:(forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->P)))=> (((((ex_ind fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))) P) x5) x1)) ((cELESS x2) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4))) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found (fun (x4:(A x3))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->P)))=> (((((ex_ind fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))) P) x5) x1)) ((cELESS x2) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x2) x4)))) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found x6:(A x5)
% 5.21/5.38 Instantiate: x2:=x5:fofType
% 5.21/5.38 Found x6 as proof of (A x2)
% 5.21/5.38 Found (x000 x6) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found ((x00 x2) x6) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found (fun (x6:(A x5))=> ((x00 x2) x6)) as proof of ((cELESS x2) Xy)
% 5.21/5.38 Found x6:(A x5)
% 5.21/5.38 Instantiate: x0:=x5:fofType
% 5.21/5.38 Found (fun (x6:(A x5))=> x6) as proof of (A x0)
% 5.21/5.38 Found x600:=(x60 x00):((cELESS Xx) x5)
% 5.21/5.38 Found (x60 x00) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found x400:=(x40 x00):((cELESS Xx) x3)
% 5.21/5.38 Found (x40 x00) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found (fun (x6:(A x5))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)) as proof of ((A x5)->((cELESS Xx) x2))
% 5.21/5.38 Found (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)) as proof of (forall (x:fofType), ((A x)->((cELESS Xx) x2)))
% 5.21/5.38 Found (ex_ind10 (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found ((ex_ind1 ((cELESS Xx) x2)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x2)
% 5.21/5.38 Found (((fun (P:Prop) (x5:(forall (x:fofType), ((A x)->P)))=> (((((ex_ind fofType) (fun (Xr:fofType)=> (A Xr))) P) x5) x0)) ((cELESS Xx) x2)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x2)
% 5.21/5.42 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((A x)->P)))=> (((((ex_ind fofType) (fun (Xr:fofType)=> (A Xr))) P) x5) x0)) ((cELESS Xx) x2)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)))) as proof of ((cELESS Xx) x2)
% 5.21/5.42 Found x00:(A Xx)
% 5.21/5.42 Found x00 as proof of (A Xx)
% 5.21/5.42 Found (x60 x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found x6:(A x5)
% 5.21/5.42 Instantiate: x2:=x5:fofType
% 5.21/5.42 Found (fun (x6:(A x5))=> x6) as proof of (A x2)
% 5.21/5.42 Found x6:(A x5)
% 5.21/5.42 Instantiate: x2:=x5:fofType
% 5.21/5.42 Found (fun (x6:(A x5))=> x6) as proof of (A x2)
% 5.21/5.42 Found x00:(A Xx)
% 5.21/5.42 Found x00 as proof of (A Xx)
% 5.21/5.42 Found (x60 x00) as proof of ((cELESS Xx) x2)
% 5.21/5.42 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.21/5.42 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x2)
% 5.21/5.42 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x2)
% 5.21/5.42 Found x4:(A x3)
% 5.21/5.42 Instantiate: x0:=x3:fofType
% 5.21/5.42 Found x4 as proof of (A x0)
% 5.21/5.42 Found (x000 x4) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found ((x00 x0) x4) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found (fun (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)) as proof of ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5)))->((cELESS x0) Xy))
% 5.21/5.42 Found (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)) as proof of (forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->((cELESS x0) Xy)))
% 5.21/5.42 Found (ex_ind10 (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4))) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found ((ex_ind1 ((cELESS x0) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4))) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found (((fun (P:Prop) (x5:(forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->P)))=> (((((ex_ind fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))) P) x5) x2)) ((cELESS x0) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4))) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found (fun (x4:(A x3))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((forall (Xx:fofType), ((A Xx)->((cELESS Xx) x)))->P)))=> (((((ex_ind fofType) (fun (Xu:fofType)=> (forall (Xx:fofType), ((A Xx)->((cELESS Xx) Xu))))) P) x5) x2)) ((cELESS x0) Xy)) (fun (x5:fofType) (x6:(forall (Xx:fofType), ((A Xx)->((cELESS Xx) x5))))=> ((x00 x0) x4)))) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found x6:(A x5)
% 5.21/5.42 Instantiate: x0:=x5:fofType
% 5.21/5.42 Found x6 as proof of (A x0)
% 5.21/5.42 Found (x000 x6) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found ((x00 x0) x6) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found (fun (x6:(A x5))=> ((x00 x0) x6)) as proof of ((cELESS x0) Xy)
% 5.21/5.42 Found x600:=(x60 x00):((cELESS Xx) x5)
% 5.21/5.42 Found (x60 x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found x400:=(x40 x00):((cELESS Xx) x3)
% 5.21/5.42 Found (x40 x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((x4 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found (fun (x6:(A x5))=> ((x4 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)) as proof of ((A x5)->((cELESS Xx) x0))
% 5.21/5.42 Found (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)) as proof of (forall (x:fofType), ((A x)->((cELESS Xx) x0)))
% 5.21/5.42 Found (ex_ind10 (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found ((ex_ind1 ((cELESS Xx) x0)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x0)
% 5.21/5.42 Found (((fun (P:Prop) (x5:(forall (x:fofType), ((A x)->P)))=> (((((ex_ind fofType) (fun (Xr:fofType)=> (A Xr))) P) x5) x1)) ((cELESS Xx) x0)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00))) as proof of ((cELESS Xx) x0)
% 5.27/5.46 Found (fun (x4:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x3))))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((A x)->P)))=> (((((ex_ind fofType) (fun (Xr:fofType)=> (A Xr))) P) x5) x1)) ((cELESS Xx) x0)) (fun (x5:fofType) (x6:(A x5))=> ((x4 Xx) x00)))) as proof of ((cELESS Xx) x0)
% 5.27/5.46 Found x6:(A x5)
% 5.27/5.46 Instantiate: x0:=x5:fofType
% 5.27/5.46 Found (fun (x6:(A x5))=> x6) as proof of (A x0)
% 5.27/5.46 Found x6:(A x5)
% 5.27/5.46 Instantiate: x0:=x5:fofType
% 5.27/5.46 Found (fun (x6:(A x5))=> x6) as proof of (A x0)
% 5.27/5.46 Found x6:(A x5)
% 5.27/5.46 Instantiate: x0:=x5:fofType
% 5.27/5.46 Found (fun (x6:(A x5))=> x6) as proof of (A x0)
% 5.27/5.46 Found x00:(A Xx)
% 5.27/5.46 Found x00 as proof of (A Xx)
% 5.27/5.46 Found (x60 x00) as proof of ((cELESS Xx) x0)
% 5.27/5.46 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.27/5.46 Found ((x6 Xx) x00) as proof of ((cELESS Xx) x0)
% 5.27/5.46 Found (fun (x6:(forall (Xx0:fofType), ((A Xx0)->((cELESS Xx0) x5))))=> ((x6 Xx) x00)) as proof of ((cELESS Xx) x0)
% 5.27/5.46 % SZS status GaveUp for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------