%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYN051^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n101.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:37:46 EDT 2014

% Result   : Timeout 290.28s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SYN051^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n101.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:58:31 CDT 2014
% % CPUTime: 290.28 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1473050>, <kernel.Sort object at 0xf5d368>) of role type named p
% Using role type
% Declaring p:Prop
% FOF formula (<kernel.Constant object at 0x14737e8>, <kernel.DependentProduct object at 0x10986c8>) of role type named cF
% Using role type
% Declaring cF:(fofType->Prop)
% FOF formula (((and ((ex fofType) (fun (Xx:fofType)=> (p->(cF Xx))))) ((ex fofType) (fun (Xx:fofType)=> ((cF Xx)->p))))->((ex fofType) (fun (Xx:fofType)=> ((and (p->(cF Xx))) ((cF Xx)->p))))) of role conjecture named cPELL21
% Conjecture to prove = (((and ((ex fofType) (fun (Xx:fofType)=> (p->(cF Xx))))) ((ex fofType) (fun (Xx:fofType)=> ((cF Xx)->p))))->((ex fofType) (fun (Xx:fofType)=> ((and (p->(cF Xx))) ((cF Xx)->p))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and ((ex fofType) (fun (Xx:fofType)=> (p->(cF Xx))))) ((ex fofType) (fun (Xx:fofType)=> ((cF Xx)->p))))->((ex fofType) (fun (Xx:fofType)=> ((and (p->(cF Xx))) ((cF Xx)->p)))))']
% Parameter p:Prop.
% Parameter fofType:Type.
% Parameter cF:(fofType->Prop).
% Trying to prove (((and ((ex fofType) (fun (Xx:fofType)=> (p->(cF Xx))))) ((ex fofType) (fun (Xx:fofType)=> ((cF Xx)->p))))->((ex fofType) (fun (Xx:fofType)=> ((and (p->(cF Xx))) ((cF Xx)->p)))))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x60:=(x6 x00):(cF x5)
% Instantiate: x0:=x5:fofType
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x60:=(x6 x00):(cF x5)
% Instantiate: x4:=x5:fofType
% Found (x6 x00) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x4)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x00:(cF x0)
% Instantiate: x0:=x5:fofType
% Found x00 as proof of (cF x5)
% Found (x6 x00) as proof of p
% Found (fun (x6:((cF x5)->p))=> (x6 x00)) as proof of p
% Found x00:(cF x4)
% Instantiate: x4:=x5:fofType
% Found x00 as proof of (cF x5)
% Found (x6 x00) as proof of p
% Found (fun (x6:((cF x5)->p))=> (x6 x00)) as proof of p
% Found x60:=(x6 x00):(cF x5)
% Found (x6 x00) as proof of (cF x0)
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x60:=(x6 x00):(cF x5)
% Found (x6 x00) as proof of (cF x4)
% Found (x6 x00) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x4)
% Found x40:=(x4 x00):(cF x3)
% Instantiate: x0:=x3:fofType
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x0)
% Found x40:=(x4 x00):(cF x3)
% Instantiate: x2:=x3:fofType
% Found (x4 x00) as proof of (cF x2)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x2)
% Found x60:=(x6 x00):(cF x5)
% Instantiate: x2:=x5:fofType
% Found (x6 x00) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x2)
% Found x00:p
% Found x00 as proof of p
% Found (x6 x00) as proof of (cF x0)
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x00:p
% Found x00 as proof of p
% Found (x6 x00) as proof of (cF x4)
% Found (x6 x00) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x4)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x00:(cF x2)
% Instantiate: x2:=x5:fofType
% Found x00 as proof of (cF x5)
% Found (x6 x00) as proof of p
% Found (fun (x6:((cF x5)->p))=> (x6 x00)) as proof of p
% Found x00:(cF x0)
% Instantiate: x0:=x3:fofType
% Found x00 as proof of (cF x3)
% Found (x4 x00) as proof of p
% Found (fun (x4:((cF x3)->p))=> (x4 x00)) as proof of p
% Found x00:(cF x2)
% Instantiate: x2:=x3:fofType
% Found x00 as proof of (cF x3)
% Found (x4 x00) as proof of p
% Found (fun (x4:((cF x3)->p))=> (x4 x00)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:=(x6 x00):(cF x5)
% Found (x6 x00) as proof of (cF x2)
% Found (x6 x00) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x2)
% Found x5:(cF x4)
% Instantiate: x4:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x40:=(x4 x00):(cF x3)
% Found (x4 x00) as proof of (cF x0)
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x0)
% Found x40:=(x4 x00):(cF x3)
% Found (x4 x00) as proof of (cF x2)
% Found (x4 x00) as proof of (cF x2)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x2)
% Found x00:p
% Found x00 as proof of p
% Found (x6 x00) as proof of (cF x2)
% Found (x6 x00) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x00:p
% Found x00 as proof of p
% Found (x4 x00) as proof of (cF x0)
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x0)
% Found x00:p
% Found x00 as proof of p
% Found (x4 x00) as proof of (cF x2)
% Found (x4 x00) as proof of (cF x2)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x2)
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x40:=(x4 x00):(cF x3)
% Instantiate: x0:=x3:fofType
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x00:(cF x0)
% Instantiate: x0:=x3:fofType
% Found x00 as proof of (cF x3)
% Found (x4 x00) as proof of p
% Found (fun (x4:((cF x3)->p))=> (x4 x00)) as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x40:=(x4 x00):(cF x3)
% Found (x4 x00) as proof of (cF x0)
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x00:p
% Found x00 as proof of p
% Found (x4 x00) as proof of (cF x0)
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (x4 x00)) as proof of (cF x0)
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x1)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x5:(cF x4)
% Instantiate: x4:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x1:p
% Found x1 as proof of p
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:p
% Found (fun (x00:(cF x6))=> x50) as proof of p
% Found (fun (x00:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x30:p
% Found (fun (x00:(cF x6))=> x30) as proof of p
% Found (fun (x00:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x40:=(x4 x00):(cF x3)
% Instantiate: x0:=x3:fofType
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x6:((cF x5)->p))=> (x4 x00)) as proof of (cF x0)
% Found (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)) as proof of (((cF x5)->p)->(cF x0))
% Found (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x5) x2)) (cF x0)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (((fun (P:Prop) (x5:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x5) x2)) (cF x0)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)))) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x60:=(x6 x00):(cF x5)
% Instantiate: x0:=x5:fofType
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x30:p
% Found (fun (x00:(cF x4))=> x30) as proof of p
% Found (fun (x00:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x1)) as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x00:(cF x0)
% Instantiate: x0:=x5:fofType
% Found x00 as proof of (cF x5)
% Found (x6 x00) as proof of p
% Found (fun (x6:((cF x5)->p))=> (x6 x00)) as proof of p
% Found x00:(cF x0)
% Instantiate: x0:=x3:fofType
% Found x00 as proof of (cF x3)
% Found (x4 x00) as proof of p
% Found (fun (x6:(p->(cF x5)))=> (x4 x00)) as proof of p
% Found (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)) as proof of ((p->(cF x5))->p)
% Found (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found ((ex_ind1 p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x5) x1)) p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found (fun (x4:((cF x3)->p))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x5) x1)) p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)))) as proof of p
% Found x40:=(x4 x00):(cF x3)
% Instantiate: x2:=x3:fofType
% Found (x4 x00) as proof of (cF x2)
% Found (fun (x6:((cF x5)->p))=> (x4 x00)) as proof of (cF x2)
% Found (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)) as proof of (((cF x5)->p)->(cF x2))
% Found (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x2)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x5) x1)) (cF x2)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x2)
% Found (fun (x4:(p->(cF x3)))=> (((fun (P:Prop) (x5:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x5) x1)) (cF x2)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)))) as proof of (cF x2)
% Found x60:=(x6 x00):(cF x5)
% Instantiate: x2:=x5:fofType
% Found (x6 x00) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x2)
% Found x40:p
% Found (fun (x00:(cF x2))=> x40) as proof of p
% Found (fun (x00:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x60:=(x6 x00):(cF x5)
% Found (x6 x00) as proof of (cF x0)
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x50:p
% Found (fun (x00:(cF x6))=> x50) as proof of p
% Found (fun (x00:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found ((conj00 x3) (fun (x00:(cF x6))=> x50)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found (((conj0 ((cF x6)->p)) x3) (fun (x00:(cF x6))=> x50)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found ((((conj (p->(cF x6))) ((cF x6)->p)) x3) (fun (x00:(cF x6))=> x50)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found ((((conj (p->(cF x6))) ((cF x6)->p)) x3) (fun (x00:(cF x6))=> x50)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x00:(cF x2)
% Instantiate: x2:=x5:fofType
% Found x00 as proof of (cF x5)
% Found (x6 x00) as proof of p
% Found (fun (x6:((cF x5)->p))=> (x6 x00)) as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x00:(cF x2)
% Instantiate: x2:=x3:fofType
% Found x00 as proof of (cF x3)
% Found (x4 x00) as proof of p
% Found (fun (x6:(p->(cF x5)))=> (x4 x00)) as proof of p
% Found (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)) as proof of ((p->(cF x5))->p)
% Found (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found ((ex_ind1 p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x5) x0)) p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found (fun (x4:((cF x3)->p))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x5) x0)) p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)))) as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x1:p
% Found x1 as proof of p
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x60:=(x6 x00):(cF x5)
% Found (x6 x00) as proof of (cF x2)
% Found (x6 x00) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x2)
% Found x00:p
% Found x00 as proof of p
% Found (x6 x00) as proof of (cF x0)
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x2)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x2))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x2)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x40:=(x4 x00):(cF x3)
% Instantiate: x0:=x3:fofType
% Found (x4 x00) as proof of (cF x0)
% Found (fun (x6:((cF x5)->p))=> (x4 x00)) as proof of (cF x0)
% Found (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)) as proof of (((cF x5)->p)->(cF x0))
% Found (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x5) x2)) (cF x0)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00))) as proof of (cF x0)
% Found (fun (x4:(p->(cF x3)))=> (((fun (P:Prop) (x5:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x5) x2)) (cF x0)) (fun (x5:fofType) (x6:((cF x5)->p))=> (x4 x00)))) as proof of (cF x0)
% Found x60:=(x6 x00):(cF x5)
% Instantiate: x0:=x5:fofType
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found ((conj00 x5) (fun (x7:(cF x6))=> x30)) as proof of ((iff p) (cF x6))
% Found (((conj0 ((cF x6)->p)) x5) (fun (x7:(cF x6))=> x30)) as proof of ((iff p) (cF x6))
% Found ((((conj (p->(cF x6))) ((cF x6)->p)) x5) (fun (x7:(cF x6))=> x30)) as proof of ((iff p) (cF x6))
% Found ((((conj (p->(cF x6))) ((cF x6)->p)) x5) (fun (x7:(cF x6))=> x30)) as proof of ((iff p) (cF x6))
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x00:p
% Found x00 as proof of p
% Found (x6 x00) as proof of (cF x2)
% Found (x6 x00) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x2)
% Found x40:p
% Found (fun (x00:(cF x2))=> x40) as proof of p
% Found (fun (x00:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found (((conj0 ((cF x2)->p)) x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found x3:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x00:(cF x0)
% Instantiate: x0:=x5:fofType
% Found x00 as proof of (cF x5)
% Found (x6 x00) as proof of p
% Found (fun (x6:((cF x5)->p))=> (x6 x00)) as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x00:(cF x0)
% Instantiate: x0:=x3:fofType
% Found x00 as proof of (cF x3)
% Found (x4 x00) as proof of p
% Found (fun (x6:(p->(cF x5)))=> (x4 x00)) as proof of p
% Found (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)) as proof of ((p->(cF x5))->p)
% Found (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found ((ex_ind1 p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x5) x1)) p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00))) as proof of p
% Found (fun (x4:((cF x3)->p))=> (((fun (P:Prop) (x5:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x5) x1)) p) (fun (x5:fofType) (x6:(p->(cF x5)))=> (x4 x00)))) as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x60:=(x6 x00):(cF x5)
% Found (x6 x00) as proof of (cF x0)
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 x3) (fun (x7:(cF x4))=> x60)) as proof of ((iff p) (cF x4))
% Found (((conj0 ((cF x4)->p)) x3) (fun (x7:(cF x4))=> x60)) as proof of ((iff p) (cF x4))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x3) (fun (x7:(cF x4))=> x60)) as proof of ((iff p) (cF x4))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x3) (fun (x7:(cF x4))=> x60)) as proof of ((iff p) (cF x4))
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x1)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)))) as proof of (cF x0)
% Found x70:=(x7 x1):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 x4) (fun (x7:(cF x0))=> x60)) as proof of ((iff p) (cF x0))
% Found (((conj0 ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((iff p) (cF x0))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((iff p) (cF x0))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((iff p) (cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x00:p
% Found x00 as proof of p
% Found (x6 x00) as proof of (cF x0)
% Found (x6 x00) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x00)) as proof of (cF x0)
% Found x1:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x1 as proof of (cF x6)
% Found (x7 x1) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x1)) as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x1)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)))) as proof of p
% Found x70:=(x7 x1):(cF x6)
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x60:=(x6 x40):(cF x5)
% Instantiate: x0:=x5:fofType
% Found (x6 x40) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x0)
% Found x60:=(x6 x30):(cF x5)
% Instantiate: x4:=x5:fofType
% Found (x6 x30) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x30)) as proof of (cF x4)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x1:p
% Found x1 as proof of p
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x30:p
% Found (fun (x00:(cF x4))=> x30) as proof of p
% Found (fun (x00:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 x6) (fun (x00:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found (((conj0 ((cF x4)->p)) x6) (fun (x00:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x00:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found (fun (x6:(p->(cF x5)))=> ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x00:(cF x4))=> x30))) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x60:=(x6 x40):(cF x5)
% Instantiate: x2:=x5:fofType
% Found (x6 x40) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found ((conj00 (fun (x7:(cF x6))=> x50)) x3) as proof of ((iff (cF x6)) p)
% Found (((conj0 (p->(cF x6))) (fun (x7:(cF x6))=> x50)) x3) as proof of ((iff (cF x6)) p)
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x50)) x3) as proof of ((iff (cF x6)) p)
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x50)) x3) as proof of ((iff (cF x6)) p)
% Found x60:=(x6 x30):(cF x5)
% Found (x6 x30) as proof of (cF x4)
% Found (x6 x30) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x30)) as proof of (cF x4)
% Found x60:=(x6 x40):(cF x5)
% Found (x6 x40) as proof of (cF x0)
% Found (x6 x40) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x00:(cF x2))=> x40) as proof of p
% Found (fun (x00:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found (((conj0 ((cF x2)->p)) x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x00:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found (fun (x6:(p->(cF x5)))=> ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x00:(cF x2))=> x40))) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 x6) (fun (x7:(cF x4))=> x30)) as proof of ((iff p) (cF x4))
% Found (((conj0 ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((iff p) (cF x4))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((iff p) (cF x4))
% Found (fun (x6:(p->(cF x5)))=> ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30))) as proof of ((iff p) (cF x4))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 x6) (fun (x7:(cF x0))=> x40)) as proof of ((iff p) (cF x0))
% Found (((conj0 ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((iff p) (cF x0))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((iff p) (cF x0))
% Found (fun (x6:(p->(cF x5)))=> ((((conj (p->(cF x0))) ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40))) as proof of ((iff p) (cF x0))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found x60:=(x6 x40):(cF x5)
% Found (x6 x40) as proof of (cF x2)
% Found (x6 x40) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x2)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found x30:p
% Found x30 as proof of p
% Found (x6 x30) as proof of (cF x4)
% Found (x6 x30) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x30)) as proof of (cF x4)
% Found x40:p
% Found x40 as proof of p
% Found (x6 x40) as proof of (cF x0)
% Found (x6 x40) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x60:=(x6 x40):(cF x5)
% Instantiate: x0:=x5:fofType
% Found (x6 x40) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x0)
% Found x60:=(x6 x30):(cF x5)
% Instantiate: x4:=x5:fofType
% Found (x6 x30) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x30)) as proof of (cF x4)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x2)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x2))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x2)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x70:=(x7 x30):(cF x6)
% Found (x7 x30) as proof of (cF x4)
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 x6) (fun (x7:(cF x2))=> x40)) as proof of ((iff p) (cF x2))
% Found (((conj0 ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((iff p) (cF x2))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((iff p) (cF x2))
% Found (fun (x6:(p->(cF x5)))=> ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40))) as proof of ((iff p) (cF x2))
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x1)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)))) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found x70:=(x7 x1):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found x40:p
% Found x40 as proof of p
% Found (x6 x40) as proof of (cF x2)
% Found (x6 x40) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x2)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x60:=(x6 x40):(cF x5)
% Instantiate: x2:=x5:fofType
% Found (x6 x40) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x2)
% Found x3:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x60:=(x6 x40):(cF x5)
% Found (x6 x40) as proof of (cF x0)
% Found (x6 x40) as proof of (cF x0)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x0)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x60:=(x6 x30):(cF x5)
% Found (x6 x30) as proof of (cF x4)
% Found (x6 x30) as proof of (cF x4)
% Found (fun (x6:(p->(cF x5)))=> (x6 x30)) as proof of (cF x4)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x30:p
% Found x30 as proof of p
% Found (x7 x30) as proof of (cF x4)
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found x1:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x1 as proof of (cF x6)
% Found (x7 x1) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x1)) as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x1)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)))) as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x70:=(x7 x1):(cF x6)
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x60:=(x6 x40):(cF x5)
% Found (x6 x40) as proof of (cF x2)
% Found (x6 x40) as proof of (cF x2)
% Found (fun (x6:(p->(cF x5)))=> (x6 x40)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x30):(cF x6)
% Found (x7 x30) as proof of (cF x4)
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x1:p
% Found x1 as proof of p
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x50:p
% Found (fun (x00:(cF x6))=> x50) as proof of p
% Found (fun (x00:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x30:p
% Found (fun (x00:(cF x6))=> x30) as proof of p
% Found (fun (x00:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x30:p
% Found (fun (x6:(cF x4))=> x30) as proof of p
% Found (fun (x6:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found (conj00 (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x30:p
% Found (fun (x00:(cF x4))=> x30) as proof of p
% Found (fun (x00:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6)) as proof of ((iff (cF x4)) p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x00:p
% Found x00 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((iff (cF x0)) p)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x4)
% Instantiate: x4:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x40:p
% Found (fun (x00:(cF x2))=> x40) as proof of p
% Found (fun (x00:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6)) as proof of ((iff (cF x2)) p)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x1)) as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x50:=(x5 x1):(cF x4)
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x4)
% Instantiate: x4:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x4)
% Instantiate: x4:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x1:p
% Found x1 as proof of p
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x1)) as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x1)) as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x50:=(x5 x1):(cF x4)
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x1:p
% Found x1 as proof of p
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x1:p
% Found x1 as proof of p
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x00:p
% Found x00 as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found ((conj00 x5) (fun (x7:(cF x6))=> x30)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found (((conj0 ((cF x6)->p)) x5) (fun (x7:(cF x6))=> x30)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found ((((conj (p->(cF x6))) ((cF x6)->p)) x5) (fun (x7:(cF x6))=> x30)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found ((((conj (p->(cF x6))) ((cF x6)->p)) x5) (fun (x7:(cF x6))=> x30)) as proof of ((and (p->(cF x6))) ((cF x6)->p))
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x2)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x2))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x2)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x30:p
% Found x30 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x60:p
% Found x60 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x3:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found (((conj0 ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 x3) (fun (x7:(cF x4))=> x60)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found (((conj0 ((cF x4)->p)) x3) (fun (x7:(cF x4))=> x60)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x3) (fun (x7:(cF x4))=> x60)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x3) (fun (x7:(cF x4))=> x60)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found (((conj0 ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found (((conj0 ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found (((conj0 ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found (((conj0 ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x6) (fun (x7:(cF x0))=> x40)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found (((conj0 ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x1)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)))) as proof of (cF x0)
% Found x30:p
% Found x30 as proof of p
% Found x70:=(x7 x1):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found (((conj0 ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found ((((conj (p->(cF x0))) ((cF x0)->p)) x4) (fun (x7:(cF x0))=> x60)) as proof of ((and (p->(cF x0))) ((cF x0)->p))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 x4) (fun (x7:(cF x2))=> x60)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found (((conj0 ((cF x2)->p)) x4) (fun (x7:(cF x2))=> x60)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x4) (fun (x7:(cF x2))=> x60)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x4) (fun (x7:(cF x2))=> x60)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found (((conj0 ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found x1:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x1 as proof of (cF x6)
% Found (x7 x1) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x1)) as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x1)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)))) as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found (((conj0 ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found ((((conj (p->(cF x2))) ((cF x2)->p)) x6) (fun (x7:(cF x2))=> x40)) as proof of ((and (p->(cF x2))) ((cF x2)->p))
% Found x70:=(x7 x1):(cF x6)
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x00:p
% Found x00 as proof of p
% Found x00:p
% Found x00 as proof of p
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x1:p
% Found x1 as proof of p
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found ((conj00 (fun (x7:(cF x6))=> x50)) x3) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found (((conj0 (p->(cF x6))) (fun (x7:(cF x6))=> x50)) x3) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x50)) x3) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x50)) x3) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found ((conj00 (fun (x7:(cF x6))=> x30)) x5) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found (((conj0 (p->(cF x6))) (fun (x7:(cF x6))=> x30)) x5) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x30)) x5) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x30)) x5) as proof of ((and ((cF x6)->p)) (p->(cF x6)))
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found ((conj00 (fun (x7:(cF x6))=> x30)) x5) as proof of ((iff (cF x6)) p)
% Found (((conj0 (p->(cF x6))) (fun (x7:(cF x6))=> x30)) x5) as proof of ((iff (cF x6)) p)
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x30)) x5) as proof of ((iff (cF x6)) p)
% Found ((((conj ((cF x6)->p)) (p->(cF x6))) (fun (x7:(cF x6))=> x30)) x5) as proof of ((iff (cF x6)) p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x30:p
% Found x30 as proof of p
% Found x50:p
% Found x50 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found (((conj0 ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30)) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found (fun (x6:(p->(cF x5)))=> ((((conj (p->(cF x4))) ((cF x4)->p)) x6) (fun (x7:(cF x4))=> x30))) as proof of ((and (p->(cF x4))) ((cF x4)->p))
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x7:p
% Found x7 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x7:p
% Found x7 as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x40:p
% Found x40 as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x2)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x2))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x2)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x2))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x2)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x30):(cF x6)
% Found (x7 x30) as proof of (cF x4)
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((iff (cF x4)) p)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x1)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)))) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x1):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((iff (cF x2)) p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x1)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)))) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x1):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x30:p
% Found x30 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x40:p
% Found x40 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x3:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x30:p
% Found x30 as proof of p
% Found (x7 x30) as proof of (cF x4)
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x1:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x1 as proof of (cF x6)
% Found (x7 x1) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x1)) as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x1:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x1 as proof of (cF x6)
% Found (x7 x1) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x1)) as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x1)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)))) as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x1)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)))) as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((iff (cF x0)) p)
% Found x60:p
% Found x60 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x40:p
% Found x40 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x1):(cF x6)
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x70:=(x7 x1):(cF x6)
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x40:p
% Found x40 as proof of p
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found x40 as proof of p
% Found x70:=(x7 x30):(cF x6)
% Found (x7 x30) as proof of (cF x4)
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x0)
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x1:p
% Found x1 as proof of p
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x1:p
% Found x1 as proof of p
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Found (x7 x40) as proof of (cF x2)
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x30:p
% Found (fun (x6:(cF x4))=> x30) as proof of p
% Found (fun (x6:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found (conj00 (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x7:p
% Found x7 as proof of p
% Found x30:p
% Found (fun (x6:(cF x4))=> x30) as proof of p
% Found (fun (x6:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found (conj00 (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((iff (cF x4)) p))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6)) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((iff (cF x4)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6)) as proof of ((iff (cF x4)) p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((iff (cF x0)) p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((iff (cF x0)) p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((iff (cF x0)) p))
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((iff (cF x0)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((iff (cF x0)) p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((iff (cF x2)) p))
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6)) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((iff (cF x2)) p)
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6)) as proof of ((iff (cF x2)) p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x5:(cF x4)
% Instantiate: x4:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x7:p
% Found x7 as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x3)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x50:=(x5 x3):(cF x4)
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x7:p
% Found x7 as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x5:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x2)
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x2)
% Found x3:p
% Found x3 as proof of p
% Found (x5 x3) as proof of (cF x0)
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x3)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x5 as proof of (cF x6)
% Found (x7 x5) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x5)) as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x5:((cF x4)->p))=> (x5 x1)) as proof of p
% Found x50:=(x5 x1):(cF x4)
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x1:p
% Found x1 as proof of p
% Found (x5 x1) as proof of (cF x0)
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (x5 x1)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x50:p
% Found x50 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x30:p
% Found x30 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x30:p
% Found x30 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x30:p
% Found x30 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x6:=x2:fofType
% Found x3 as proof of ((cF x6)->p)
% Found x5:(p->(cF x4))
% Instantiate: x6:=x4:fofType
% Found x5 as proof of (p->(cF x6))
% Found x5:((cF x4)->p)
% Instantiate: x6:=x4:fofType
% Found x5 as proof of ((cF x6)->p)
% Found x3:(p->(cF x2))
% Instantiate: x6:=x2:fofType
% Found x3 as proof of (p->(cF x6))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x30:p
% Found x30 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x3) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x2)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x0)
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x60:p
% Found x60 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x3:(p->(cF x2))
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (p->(cF x4))
% Found x6:((cF x5)->p)
% Instantiate: x4:=x5:fofType
% Found x6 as proof of ((cF x4)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x50:=(x5 x3):(cF x4)
% Instantiate: x2:=x4:fofType
% Found (x5 x3) as proof of (cF x2)
% Found (fun (x7:((cF x6)->p))=> (x5 x3)) as proof of (cF x2)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (((cF x6)->p)->(cF x2))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x2)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found ((ex_ind1 (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3))) as proof of (cF x2)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x1)) (cF x2)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x3)))) as proof of (cF x2)
% Found x70:=(x7 x3):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x3:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x3:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x1)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x60)) x3) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found x60 as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x50:=(x5 x1):(cF x4)
% Instantiate: x0:=x4:fofType
% Found (x5 x1) as proof of (cF x0)
% Found (fun (x7:((cF x6)->p))=> (x5 x1)) as proof of (cF x0)
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (((cF x6)->p)->(cF x0))
% Found (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)) as proof of (forall (x:fofType), (((cF x)->p)->(cF x0)))
% Found (ex_ind10 (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found ((ex_ind1 (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1))) as proof of (cF x0)
% Found (fun (x5:(p->(cF x4)))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((cF x)->p)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((cF Xx)->p))) P) x6) x3)) (cF x0)) (fun (x6:fofType) (x7:((cF x6)->p))=> (x5 x1)))) as proof of (cF x0)
% Found x70:=(x7 x1):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found x60 as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x60:p
% Found x60 as proof of p
% Found x30:p
% Found x30 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x6:((cF x5)->p)
% Instantiate: x0:=x5:fofType
% Found x6 as proof of ((cF x0)->p)
% Found x4:(p->(cF x3))
% Instantiate: x0:=x3:fofType
% Found x4 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x3:(cF x2)
% Instantiate: x2:=x6:fofType
% Found x3 as proof of (cF x6)
% Found (x7 x3) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x3)) as proof of p
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x3:(cF x2)
% Instantiate: x2:=x4:fofType
% Found x3 as proof of (cF x4)
% Found (x5 x3) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x3)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x0)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x3)))) as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x60)) x4) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x1:(cF x0)
% Instantiate: x0:=x6:fofType
% Found x1 as proof of (cF x6)
% Found (x7 x1) as proof of p
% Found (fun (x7:((cF x6)->p))=> (x7 x1)) as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x1:(cF x0)
% Instantiate: x0:=x4:fofType
% Found x1 as proof of (cF x4)
% Found (x5 x1) as proof of p
% Found (fun (x7:(p->(cF x6)))=> (x5 x1)) as proof of p
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of ((p->(cF x6))->p)
% Found (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)) as proof of (forall (x:fofType), ((p->(cF x))->p))
% Found (ex_ind10 (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found ((ex_ind1 p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1))) as proof of p
% Found (fun (x5:((cF x4)->p))=> (((fun (P:Prop) (x6:(forall (x:fofType), ((p->(cF x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (p->(cF Xx)))) P) x6) x2)) p) (fun (x6:fofType) (x7:(p->(cF x6)))=> (x5 x1)))) as proof of p
% Found x70:=(x7 x3):(cF x6)
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x40:p
% Found x40 as proof of p
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x0)
% Found (x7 x3) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x0)
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x70:=(x7 x1):(cF x6)
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x6:((cF x5)->p)
% Instantiate: x2:=x5:fofType
% Found x6 as proof of ((cF x2)->p)
% Found x4:(p->(cF x3))
% Instantiate: x2:=x3:fofType
% Found x4 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x60)) x4) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x60:p
% Found x60 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x3:p
% Found x3 as proof of p
% Found (x7 x3) as proof of (cF x2)
% Found (x7 x3) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x3)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x1:p
% Found x1 as proof of p
% Found (x7 x1) as proof of (cF x0)
% Found (x7 x1) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x1)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x6:(p->(cF x5))
% Instantiate: x4:=x5:fofType
% Found x6 as proof of (p->(cF x4))
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x30:p
% Found (fun (x6:(cF x4))=> x30) as proof of p
% Found (fun (x6:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found (conj00 (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found (((conj ((cF x4)->p)) (p->(cF x5))) (fun (x6:(cF x4))=> x30)) as proof of ((p->(cF x5))->((and ((cF x4)->p)) (p->(cF x4))))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found ((conj00 (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (((conj0 (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x4)->p)) (p->(cF x4))) (fun (x7:(cF x4))=> x30)) x6)) as proof of ((and ((cF x4)->p)) (p->(cF x4)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x6:(p->(cF x5))
% Instantiate: x0:=x5:fofType
% Found x6 as proof of (p->(cF x0))
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x6:(cF x0))=> x40) as proof of p
% Found (fun (x6:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found (conj00 (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found (((conj ((cF x0)->p)) (p->(cF x5))) (fun (x6:(cF x0))=> x40)) as proof of ((p->(cF x5))->((and ((cF x0)->p)) (p->(cF x0))))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found ((conj00 (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (((conj0 (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x0)->p)) (p->(cF x0))) (fun (x7:(cF x0))=> x40)) x6)) as proof of ((and ((cF x0)->p)) (p->(cF x0)))
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x6:(p->(cF x5))
% Instantiate: x2:=x5:fofType
% Found x6 as proof of (p->(cF x2))
% Found x40:p
% Found (fun (x6:(cF x2))=> x40) as proof of p
% Found (fun (x6:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found (conj00 (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found ((conj0 (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found (((conj ((cF x2)->p)) (p->(cF x5))) (fun (x6:(cF x2))=> x40)) as proof of ((p->(cF x5))->((and ((cF x2)->p)) (p->(cF x2))))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found ((conj00 (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (((conj0 (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found (fun (x6:(p->(cF x5)))=> ((((conj ((cF x2)->p)) (p->(cF x2))) (fun (x7:(cF x2))=> x40)) x6)) as proof of ((and ((cF x2)->p)) (p->(cF x2)))
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x3:((cF x2)->p)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of ((cF x4)->p)
% Found x70:=(x7 x30):(cF x6)
% Instantiate: x4:=x6:fofType
% Found (x7 x30) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x30)) as proof of (cF x4)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x0:=x6:fofType
% Found (x7 x40) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x4)
% Found (x7 x5) as proof of (cF x4)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x4)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x4:((cF x3)->p)
% Instantiate: x2:=x3:fofType
% Found x4 as proof of ((cF x2)->p)
% Found x4:((cF x3)->p)
% Instantiate: x0:=x3:fofType
% Found x4 as proof of ((cF x0)->p)
% Found x70:=(x7 x40):(cF x6)
% Instantiate: x2:=x6:fofType
% Found (x7 x40) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x40)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x5:p
% Found x5 as proof of p
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x30:p
% Found (fun (x7:(cF x6))=> x30) as proof of p
% Found (fun (x7:(cF x6))=> x30) as proof of ((cF x6)->p)
% Found x50:p
% Found (fun (x7:(cF x6))=> x50) as proof of p
% Found (fun (x7:(cF x6))=> x50) as proof of ((cF x6)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x0)
% Found (x7 x5) as proof of (cF x0)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x0)
% Found x7:p
% Found x7 as proof of p
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x70:=(x7 x5):(cF x6)
% Found (x7 x5) as proof of (cF x2)
% Found (x7 x5) as proof of (cF x2)
% Found (fun (x7:(p->(cF x6)))=> (x7 x5)) as proof of (cF x2)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x4))=> x60) as proof of p
% Found (fun (x7:(cF x4))=> x60) as proof of ((cF x4)->p)
% Found x30:p
% Found (fun (x7:(cF x4))=> x30) as proof of p
% Found (fun (x7:(cF x4))=> x30) as proof of ((cF x4)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x2))=> x60) as proof of p
% Found (fun (x7:(cF x2))=> x60) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x0))=> x40) as proof of p
% Found (fun (x7:(cF x0))=> x40) as proof of ((cF x0)->p)
% Found x60:p
% Found (fun (x7:(cF x0))=> x60) as proof of p
% Found (fun (x7:(cF x0))=> x60) as proof of ((cF x0)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x40:p
% Found (fun (x7:(cF x2))=> x40) as proof of p
% Found (fun (x7:(cF x2))=> x40) as proof of ((cF x2)->p)
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x30:p
% Found x30 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x40:p
% Found x40 as proof of p
% Found x60:p
% Found x60 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% Found x7:p
% Found x7 as proof of p
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------