TSTP Solution File: NUM020^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM020^1 : TPTP v7.0.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n188.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:10:13 EST 2018
% Result : Timeout 292.83s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020^1 : TPTP v7.0.0. Released v3.6.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n188.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Thu Jan 4 14:46:31 CST 2018
% 0.02/0.23 % CPUTime :
% 0.08/0.33 Python 2.7.13
% 0.27/0.77 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.27/0.77 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d29a2dd0>, <kernel.DependentProduct object at 0x2b37d2dfbef0>) of role type named zero
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring zero:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2a814d0>, <kernel.DependentProduct object at 0x2b37d2dfbb48>) of role type named one
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring one:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d29a2dd0>, <kernel.DependentProduct object at 0x2b37d2dfbbd8>) of role type named two
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring two:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2a86248>, <kernel.DependentProduct object at 0x2b37d2dfbef0>) of role type named three
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring three:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d29a2dd0>, <kernel.DependentProduct object at 0x2b37d2dfbbd8>) of role type named four
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring four:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d29a2dd0>, <kernel.DependentProduct object at 0x2b37d2dfbef0>) of role type named five
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring five:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2a84bd8>, <kernel.DependentProduct object at 0x2b37d2dfbcf8>) of role type named six
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring six:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2dfbea8>, <kernel.DependentProduct object at 0x2b37d2dfbef0>) of role type named seven
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring seven:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2dfbfc8>, <kernel.DependentProduct object at 0x2b37d2dfbcf8>) of role type named eight
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring eight:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2dfb9e0>, <kernel.DependentProduct object at 0x2b37d2dfbcb0>) of role type named nine
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring nine:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2dfbef0>, <kernel.DependentProduct object at 0x2b37d2df1b90>) of role type named ten
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring ten:((fofType->fofType)->(fofType->fofType))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2df1a28>, <kernel.DependentProduct object at 0x2b37d2dfbef0>) of role type named succ
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2df1fc8>, <kernel.DependentProduct object at 0x2b37d2dfbb90>) of role type named plus
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.27/0.77 FOF formula (<kernel.Constant object at 0x2b37d2df1a28>, <kernel.DependentProduct object at 0x2b37d2dfbb90>) of role type named mult
% 0.27/0.77 Using role type
% 0.27/0.77 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))
% 0.27/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax
% 0.27/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y))
% 0.27/0.77 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y)
% 0.27/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax
% 0.27/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)))
% 0.27/0.77 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))
% 0.27/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))))
% 0.27/0.79 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))))
% 0.27/0.79 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))) of role definition named four_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))))
% 0.27/0.79 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))) of role definition named five_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))))
% 0.27/0.79 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))) of role definition named six_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))))
% 0.27/0.79 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))) of role definition named seven_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))))
% 0.27/0.79 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))) of role definition named eight_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))))
% 0.27/0.79 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))) of role definition named nine_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.27/0.79 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))
% 0.27/0.79 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))) of role definition named ten_ax
% 0.27/0.79 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))))
% 0.27/0.79 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))
% 0.27/0.79 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))) of role definition named succ_ax
% 0.27/0.79 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))))
% 0.27/0.79 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))
% 0.27/0.79 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))) of role definition named plus_ax
% 0.36/0.80 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))))
% 0.36/0.80 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))
% 0.36/0.80 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))) of role definition named mult_ax
% 0.36/0.80 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)))
% 0.36/0.80 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))
% 0.36/0.80 FOF formula ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) of role conjecture named thm
% 0.36/0.80 Conjecture to prove = ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))):Prop
% 0.36/0.80 Parameter fofType_DUMMY:fofType.
% 0.36/0.80 We need to prove ['((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))']
% 0.36/0.80 Parameter fofType:Type.
% 0.36/0.80 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)).
% 0.36/0.80 Definition succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))).
% 0.36/0.80 Definition plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))).
% 0.36/0.80 Definition mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))).
% 1.86/2.38 Trying to prove ((ex ((fofType->fofType)->(fofType->fofType))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 1.86/2.38 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 1.86/2.38 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 1.86/2.38 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 1.86/2.38 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 1.86/2.38 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 1.86/2.38 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 1.86/2.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 2.27/2.78 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 2.27/2.78 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 2.27/2.78 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 2.27/2.78 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 2.27/2.78 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 2.27/2.78 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 2.27/2.78 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.27/2.78 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 2.37/2.87 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 2.37/2.87 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 2.37/2.87 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.37/2.87 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 2.37/2.87 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 2.47/2.96 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 2.47/2.96 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 2.47/2.96 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.47/2.96 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 2.47/2.96 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 2.57/3.05 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 2.57/3.05 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 2.57/3.05 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 2.57/3.05 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 2.57/3.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 8.56/9.06 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 8.56/9.06 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 8.56/9.06 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 8.56/9.06 Found ((eq_sym10 (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 8.56/9.06 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 8.56/9.06 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 8.56/9.06 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 8.56/9.06 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 8.56/9.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 12.36/12.82 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 12.36/12.82 Found ((eq_sym10 (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 12.36/12.82 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 12.36/12.82 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 12.36/12.82 Found eq_ref00:=(eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 12.36/12.82 Found (eq_ref0 (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) b)
% 12.36/12.82 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) b)
% 12.36/12.82 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) b)
% 12.36/12.82 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six))) b)
% 12.36/12.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 12.36/12.82 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six)))
% 12.36/12.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 12.36/12.82 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 12.36/12.82 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six))
% 14.44/14.88 Found (fun (x:((fofType->fofType)->(fofType->fofType)))=> ((eq_ref Prop) (f x))) as proof of (forall (x:((fofType->fofType)->(fofType->fofType))), (((eq Prop) (f x)) (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) six)))
% 14.44/14.88 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 14.44/14.88 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 14.44/14.88 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 14.44/14.88 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 14.44/14.88 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 14.44/14.88 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 14.44/14.88 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.44/14.88 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 14.95/15.47 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 14.95/15.47 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 14.95/15.47 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 14.95/15.47 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 14.95/15.47 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 14.95/15.47 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 14.95/15.47 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 14.95/15.47 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 15.08/15.58 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 15.08/15.58 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 15.08/15.58 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.08/15.58 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 15.08/15.58 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 15.37/15.87 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 15.37/15.87 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 15.37/15.87 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.37/15.87 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 15.47/15.94 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 15.47/15.94 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 15.47/15.94 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 15.47/15.94 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 15.47/15.94 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.27/18.76 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.27/18.76 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.27/18.76 Found x01:(P ((mult x) three))
% 18.27/18.76 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 18.27/18.76 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 18.27/18.76 Found x01:(P ((mult x) three))
% 18.27/18.76 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 18.27/18.76 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 18.27/18.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 18.27/18.76 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.27/18.76 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.27/18.76 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.27/18.76 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.27/18.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 18.27/18.76 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.27/18.76 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 18.55/18.99 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 18.55/18.99 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 18.55/18.99 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.55/18.99 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 18.55/18.99 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 18.55/18.99 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.55/18.99 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.58/19.07 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.58/19.07 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 18.58/19.07 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 18.58/19.07 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.58/19.07 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.76/19.24 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.76/19.24 Found x01:(P ((mult x) three))
% 18.76/19.24 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 18.76/19.24 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 18.76/19.24 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 18.76/19.24 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 18.76/19.24 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 18.76/19.24 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.76/19.24 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 18.87/19.36 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 18.87/19.36 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 18.87/19.36 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 18.87/19.36 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 18.87/19.36 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.87/19.36 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.87/19.36 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.97/19.45 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 18.97/19.45 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 18.97/19.45 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 18.97/19.45 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 18.97/19.45 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 30.86/31.30 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 30.86/31.30 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 30.86/31.30 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 30.86/31.30 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 30.86/31.30 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 30.86/31.30 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 30.86/31.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 30.86/31.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 30.86/31.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 30.86/31.30 Found eq_ref00:=(eq_ref0 ((mult x) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) ((mult x) three))
% 30.86/31.30 Found (eq_ref0 ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 30.86/31.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 30.86/31.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 30.86/31.30 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 30.86/31.30 Found x01:(P ((mult x) three))
% 30.86/31.30 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 30.86/31.30 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 30.86/31.30 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 30.86/31.30 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 30.86/31.30 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 30.86/31.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 30.86/31.30 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 31.05/31.51 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 31.05/31.51 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 31.05/31.51 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 31.05/31.51 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 31.05/31.51 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 31.05/31.51 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 35.25/35.76 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 35.25/35.76 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 35.25/35.76 Found x01:(P six)
% 35.25/35.76 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 35.25/35.76 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 35.25/35.76 Found x01:(P six)
% 35.25/35.76 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 35.25/35.76 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 35.25/35.76 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 35.25/35.76 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 35.25/35.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 35.25/35.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 35.25/35.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 35.25/35.76 Found eq_ref00:=(eq_ref0 six):(((eq ((fofType->fofType)->(fofType->fofType))) six) six)
% 35.25/35.76 Found (eq_ref0 six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 35.25/35.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 35.25/35.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 35.25/35.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 35.25/35.76 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 35.25/35.76 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.25/35.76 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.25/35.76 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.25/35.76 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.25/35.76 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.25/35.76 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 35.46/35.93 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 35.46/35.93 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 35.46/35.93 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 35.46/35.93 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.46/35.93 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 35.56/36.08 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 35.56/36.08 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 35.56/36.08 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 35.56/36.08 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.56/36.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 35.67/36.15 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 35.67/36.15 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 35.67/36.15 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 35.67/36.15 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 35.67/36.15 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 40.75/41.22 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 40.75/41.22 Found x11:(P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 40.75/41.22 Found x11:(P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 40.75/41.22 Found x01:(P six)
% 40.75/41.22 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 40.75/41.22 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 40.75/41.22 Found x11:(P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 40.75/41.22 Found x11:(P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 40.75/41.22 Found x11:(P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 40.75/41.22 Found x11:(P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 40.75/41.22 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 40.75/41.22 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 40.75/41.22 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 40.75/41.22 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 40.75/41.22 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 40.75/41.22 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 40.75/41.22 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 40.75/41.22 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) b)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found (((eq_trans000 (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 41.16/41.67 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 41.16/41.67 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 41.16/41.67 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 41.16/41.67 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 41.16/41.67 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 41.16/41.67 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 41.16/41.67 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 41.16/41.67 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found (((eq_trans000 (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 41.16/41.67 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found x11:(P ((((mult x) three) x0) y))
% 44.86/45.34 Found (fun (x11:(P ((((mult x) three) x0) y)))=> x11) as proof of (P ((((mult x) three) x0) y))
% 44.86/45.34 Found (fun (x11:(P ((((mult x) three) x0) y)))=> x11) as proof of (P0 ((((mult x) three) x0) y))
% 44.86/45.34 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 44.86/45.34 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 44.86/45.34 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 44.86/45.34 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 44.86/45.34 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 44.86/45.34 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 44.86/45.34 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 45.05/45.50 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 45.05/45.50 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 45.05/45.50 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 45.05/45.50 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 45.05/45.50 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.05/45.50 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 45.15/45.65 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 45.15/45.65 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 45.15/45.65 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 45.15/45.65 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 45.15/45.65 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.65 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 45.15/45.65 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 45.15/45.68 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 45.15/45.68 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 45.15/45.68 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 45.15/45.68 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 47.86/48.39 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 47.86/48.39 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 47.86/48.39 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) y)):(((eq fofType) ((((mult x) three) x0) y)) ((((mult x) three) x0) y))
% 47.86/48.39 Found (eq_ref0 ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 47.86/48.39 Found ((eq_ref fofType) ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 47.86/48.39 Found ((eq_ref fofType) ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 47.86/48.39 Found ((eq_ref fofType) ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 47.86/48.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 47.86/48.39 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) y))
% 47.86/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) y))
% 47.86/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) y))
% 47.86/48.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) y))
% 47.86/48.39 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 47.86/48.39 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 47.86/48.39 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 47.86/48.39 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.05/48.50 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.05/48.50 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.05/48.50 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.50 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.05/48.59 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.05/48.59 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.05/48.59 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.05/48.59 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.05/48.59 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.25/48.72 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.25/48.72 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.25/48.72 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.25/48.72 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.25/48.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.35/48.85 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.35/48.85 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.35/48.85 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.35/48.85 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.35/48.85 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.35/48.85 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.35/48.85 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.45/48.92 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.45/48.92 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.45/48.92 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.45/48.92 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.45/48.92 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.45/48.92 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.45/48.92 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.56/49.04 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.56/49.04 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.56/49.04 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.56/49.04 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.56/49.04 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 48.56/49.04 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.56/49.04 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.66/49.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.66/49.17 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.66/49.17 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 48.66/49.17 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 48.66/49.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 48.66/49.17 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 48.66/49.17 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 54.75/55.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 54.75/55.21 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 54.75/55.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 54.75/55.21 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (six x0)))
% 54.75/55.21 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 54.75/55.21 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 54.75/55.21 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 54.75/55.21 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 54.75/55.21 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 54.75/55.21 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 54.75/55.21 Found (eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found (eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((eq_sym100 x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((eq_sym10 (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((((eq_sym1 (((mult x) three) x0)) (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found (fun (P:((fofType->fofType)->Prop))=> ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 55.26/55.74 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found (eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found (eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((eq_sym100 x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((eq_sym10 (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((((eq_sym1 (((mult x) three) x0)) (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found (fun (P:((fofType->fofType)->Prop))=> ((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) P)) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 55.26/55.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.26/55.74 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.26/55.74 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.36/55.83 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.36/55.83 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.36/55.83 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found ((eq_sym10 (six x0)) (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.36/55.83 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.75/56.26 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.75/56.26 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.75/56.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.75/56.26 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.75/56.26 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 55.86/56.40 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found ((eq_sym10 (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 55.86/56.40 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 55.86/56.40 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 55.86/56.40 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 75.54/76.06 Found x11:(P (six x0))
% 75.54/76.06 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 75.54/76.06 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 75.54/76.06 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 75.54/76.06 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found ((eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((eq_sym100 x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((eq_sym10 (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((((eq_sym1 (((mult x) three) x0)) (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found (fun (P:((fofType->fofType)->Prop))=> (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found x11:(P (six x0))
% 75.54/76.06 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 75.54/76.06 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 75.54/76.06 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 75.54/76.06 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 75.54/76.06 Found ((eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found ((eq_sym1000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 75.54/76.06 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((eq_sym100 x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 83.34/83.86 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((eq_sym10 (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 83.34/83.86 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> ((((eq_sym1 (((mult x) three) x0)) (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 83.34/83.86 Found (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11)) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 83.34/83.86 Found (fun (P:((fofType->fofType)->Prop))=> (((fun (x1:(((eq (fofType->fofType)) (((mult x) three) x0)) (six x0)))=> (((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) x1) (fun (x2:(fofType->fofType))=> ((P (six x0))->(P x2))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (fun (x11:(P (six x0)))=> x11))) as proof of ((P (six x0))->(P (((mult x) three) x0)))
% 83.34/83.86 Found eq_ref00:=(eq_ref0 (six x0)):(((eq (fofType->fofType)) (six x0)) (six x0))
% 83.34/83.86 Found (eq_ref0 (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found ((eq_ref (fofType->fofType)) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found ((eq_ref (fofType->fofType)) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found ((eq_ref (fofType->fofType)) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 83.34/83.86 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found eq_ref00:=(eq_ref0 (six x0)):(((eq (fofType->fofType)) (six x0)) (six x0))
% 83.34/83.86 Found (eq_ref0 (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found ((eq_ref (fofType->fofType)) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found ((eq_ref (fofType->fofType)) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found ((eq_ref (fofType->fofType)) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 83.34/83.86 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 83.34/83.86 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 83.34/83.86 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 83.34/83.86 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 92.53/93.00 Found eta_expansion000:=(eta_expansion00 (six x0)):(((eq (fofType->fofType)) (six x0)) (fun (x:fofType)=> ((six x0) x)))
% 92.53/93.00 Found (eta_expansion00 (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found ((eta_expansion0 fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 92.53/93.00 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 92.53/93.00 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 92.53/93.00 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 92.53/93.00 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 92.53/93.00 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 92.53/93.00 Found eta_expansion000:=(eta_expansion00 (six x0)):(((eq (fofType->fofType)) (six x0)) (fun (x:fofType)=> ((six x0) x)))
% 92.53/93.00 Found (eta_expansion00 (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found ((eta_expansion0 fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x11:(P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P (six x0))
% 92.53/93.00 Found (fun (x11:(P (six x0)))=> x11) as proof of (P0 (six x0))
% 92.53/93.00 Found x21:(P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P0 ((((mult x) three) x0) x1))
% 92.53/93.00 Found x21:(P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P0 ((((mult x) three) x0) x1))
% 92.53/93.00 Found x21:(P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P0 ((((mult x) three) x0) x1))
% 92.53/93.00 Found x21:(P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P ((((mult x) three) x0) x1))
% 92.53/93.00 Found (fun (x21:(P ((((mult x) three) x0) x1)))=> x21) as proof of (P0 ((((mult x) three) x0) x1))
% 92.53/93.00 Found x11:(P ((six x0) y))
% 92.53/93.00 Found (fun (x11:(P ((six x0) y)))=> x11) as proof of (P ((six x0) y))
% 96.73/97.23 Found (fun (x11:(P ((six x0) y)))=> x11) as proof of (P0 ((six x0) y))
% 96.73/97.23 Found eq_ref00:=(eq_ref0 ((six x0) y)):(((eq fofType) ((six x0) y)) ((six x0) y))
% 96.73/97.23 Found (eq_ref0 ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 96.73/97.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 96.73/97.23 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 96.73/97.23 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 96.73/97.23 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 96.73/97.23 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 96.73/97.23 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 96.73/97.23 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 96.73/97.23 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 96.73/97.23 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 96.73/97.23 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 96.73/97.23 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 96.73/97.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 110.11/110.66 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 110.11/110.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 110.11/110.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 110.11/110.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 110.11/110.66 Found eq_ref00:=(eq_ref0 ((six x0) y)):(((eq fofType) ((six x0) y)) ((six x0) y))
% 110.11/110.66 Found (eq_ref0 ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 110.11/110.66 Found ((eq_ref fofType) ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 110.11/110.66 Found ((eq_ref fofType) ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 110.11/110.66 Found ((eq_ref fofType) ((six x0) y)) as proof of (((eq fofType) ((six x0) y)) b)
% 110.11/110.66 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 110.11/110.66 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 110.11/110.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 110.11/110.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 110.11/110.66 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) y))
% 110.11/110.66 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 110.11/110.66 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.11/110.66 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.11/110.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.11/110.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.11/110.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.11/110.66 Found (eq_sym010 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.11/110.66 Found ((eq_sym01 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.11/110.66 Found (((eq_sym0 b) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.11/110.66 Found (((eq_sym0 b) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.11/110.66 Found ((eq_trans0000 (((eq_sym0 b) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.11/110.66 Found (((eq_trans000 (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.11/110.66 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.11/110.66 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.11/110.66 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.11/110.66 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.33/110.81 Found (eq_sym000 ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 110.33/110.81 Found ((eq_sym00 (((mult x) three) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 110.33/110.81 Found (((eq_sym0 (six x0)) (((mult x) three) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 110.33/110.81 Found ((((eq_sym (fofType->fofType)) (six x0)) (((mult x) three) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) ((((eq_sym (fofType->fofType)) (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 110.33/110.81 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 110.33/110.81 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.33/110.81 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.33/110.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.33/110.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.33/110.81 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 110.33/110.81 Found (eq_sym010 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.33/110.81 Found ((eq_sym01 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.33/110.81 Found (((eq_sym0 b) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.33/110.81 Found (((eq_sym0 b) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 110.33/110.81 Found ((eq_trans0000 (((eq_sym0 b) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.33/110.81 Found (((eq_trans000 (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.33/110.81 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 110.33/110.81 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 111.62/112.13 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 111.62/112.13 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 111.62/112.13 Found (eq_sym000 ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 111.62/112.13 Found ((eq_sym00 (((mult x) three) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 111.62/112.13 Found (((eq_sym0 (six x0)) (((mult x) three) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) (((eq_sym0 (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 111.62/112.13 Found ((((eq_sym (fofType->fofType)) (six x0)) (((mult x) three) x0)) ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (x (three x0))) ((((eq_sym (fofType->fofType)) (x (three x0))) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (x (three x0))))) (((eta_expansion fofType) fofType) (x (three x0))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 111.62/112.13 Found eta_expansion000:=(eta_expansion00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 111.62/112.13 Found (eta_expansion00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found ((eta_expansion0 fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 111.62/112.13 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 111.62/112.13 Found (eta_expansion_dep00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.62/112.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 111.73/112.29 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found eta_expansion000:=(eta_expansion00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 111.73/112.29 Found (eta_expansion00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eta_expansion0 fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 111.73/112.29 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found eq_ref00:=(eq_ref0 (b x0)):(((eq (fofType->fofType)) (b x0)) (b x0))
% 111.73/112.29 Found (eq_ref0 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found eta_expansion_dep000:=(eta_expansion_dep00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 111.73/112.29 Found (eta_expansion_dep00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 111.73/112.29 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 111.73/112.29 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 119.42/119.93 Found eq_ref00:=(eq_ref0 (b x0)):(((eq (fofType->fofType)) (b x0)) (b x0))
% 119.42/119.93 Found (eq_ref0 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 119.42/119.93 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 119.42/119.93 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 119.42/119.93 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 119.42/119.93 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 119.42/119.93 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 119.42/119.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 119.42/119.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 119.42/119.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 119.42/119.93 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 119.42/119.93 Found ((eq_sym10 b) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 119.42/119.93 Found (((eq_sym1 (((mult x) three) x0)) b) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 119.42/119.93 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) b) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 119.42/119.93 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) b) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 119.42/119.93 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) b) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 119.42/119.93 Found (((eq_trans000 (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 119.42/119.93 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) three) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 119.42/119.93 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (six x0)) b) (((mult x) three) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 119.42/119.93 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 121.33/121.85 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 121.33/121.85 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 121.33/121.85 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 121.33/121.85 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 121.33/121.85 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 121.33/121.85 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 121.33/121.85 Found ((eq_sym10 b) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 121.33/121.85 Found (((eq_sym1 (((mult x) three) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 121.33/121.85 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 121.33/121.85 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) b) (((mult x) three) x0))
% 121.33/121.85 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) b) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 121.33/121.85 Found (((eq_trans000 (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 121.33/121.85 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (((mult x) three) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 121.33/121.85 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (six x0)) b) (((mult x) three) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 121.33/121.85 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (six x0)) b) (((mult x) three) x0))) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (six x0))) ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (fun (Y:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 Y)))))))) ((eq_ref (fofType->fofType)) (((mult x) three) x0)))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 121.33/121.85 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 121.33/121.85 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.33/121.85 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.33/121.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.33/121.85 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found ((eq_sym10 (b x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found (((eq_sym1 (((mult x) three) x0)) (b x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (b x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 121.42/121.98 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 121.42/121.98 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found ((eq_sym10 (b x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found (((eq_sym1 (((mult x) three) x0)) (b x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (b x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (b x0)) (((mult x) three) x0))
% 121.42/121.98 Found eta_expansion000:=(eta_expansion00 (b x0)):(((eq (fofType->fofType)) (b x0)) (fun (x:fofType)=> ((b x0) x)))
% 121.42/121.98 Found (eta_expansion00 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.42/121.98 Found ((eta_expansion0 fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.42/121.98 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.42/121.98 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.42/121.98 Found (((eta_expansion fofType) fofType) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.42/121.98 Found (eq_sym100 (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 121.42/121.98 Found ((eq_sym10 (six x0)) (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 121.42/121.98 Found (((eq_sym1 (b x0)) (six x0)) (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 121.42/121.98 Found ((((eq_sym (fofType->fofType)) (b x0)) (six x0)) (((eta_expansion fofType) fofType) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 121.42/121.98 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 121.42/121.98 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (six x0)))
% 121.42/121.98 Found ((eta_expansion_dep00 (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 121.52/122.08 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 121.52/122.08 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found eq_ref000:=(eq_ref00 P):((P (b x0))->(P (b x0)))
% 121.52/122.08 Found (eq_ref00 P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found ((eq_ref0 (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (six x0)))
% 121.52/122.08 Found eq_ref00:=(eq_ref0 (b x0)):(((eq (fofType->fofType)) (b x0)) (b x0))
% 121.52/122.08 Found (eq_ref0 (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.52/122.08 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.52/122.08 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.52/122.08 Found ((eq_ref (fofType->fofType)) (b x0)) as proof of (((eq (fofType->fofType)) (b x0)) (six x0))
% 121.52/122.08 Found (eq_sym100 ((eq_ref (fofType->fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 121.52/122.08 Found ((eq_sym10 (six x0)) ((eq_ref (fofType->fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 121.52/122.08 Found (((eq_sym1 (b x0)) (six x0)) ((eq_ref (fofType->fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 122.02/122.51 Found ((((eq_sym (fofType->fofType)) (b x0)) (six x0)) ((eq_ref (fofType->fofType)) (b x0))) as proof of (((eq (fofType->fofType)) (six x0)) (b x0))
% 122.02/122.51 Found eq_ref000:=(eq_ref00 P):((P (b x0))->(P (b x0)))
% 122.02/122.51 Found (eq_ref00 P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((eq_ref0 (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (((eq_ref (fofType->fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found eta_expansion0000:=(eta_expansion000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 122.02/122.51 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((eta_expansion00 (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (((eta_expansion0 fofType) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (b x0)) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 122.02/122.51 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 122.02/122.51 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 122.02/122.51 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((eta_expansion_dep00 (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (b x0)) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.02/122.51 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 122.12/122.65 Found (eta_expansion_dep000 P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 122.12/122.65 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found eta_expansion0000:=(eta_expansion000 P):((P (b x0))->(P (fun (x:fofType)=> ((b x0) x))))
% 122.12/122.65 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((eta_expansion00 (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (((eta_expansion0 fofType) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion fofType) fofType) (b x0)) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (b x0)) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 122.12/122.65 Found (eta_expansion000 P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))):((P (b x0))->(P (b x0)))
% 122.12/122.65 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 122.12/122.65 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 135.72/136.28 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 135.72/136.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 135.72/136.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0)))) as proof of ((P (b x0))->(P (six x0)))
% 135.72/136.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (b x0))))) as proof of ((P (b x0))->(P (six x0)))
% 135.72/136.28 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 135.72/136.28 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 135.72/136.28 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 135.72/136.28 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 135.72/136.28 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 135.72/136.28 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 135.72/136.28 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 135.72/136.28 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 135.72/136.28 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 135.72/136.28 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 136.61/137.12 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 136.61/137.12 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 136.61/137.12 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (six x0))->(P (((mult x) three) x0))))
% 136.61/137.12 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 136.61/137.12 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (eq_sym100 (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found ((eq_sym10 (six x0)) (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion fofType) fofType) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 136.61/137.12 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 136.61/137.12 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 136.61/137.12 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 155.60/156.09 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found (eq_sym100 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found ((eq_sym10 (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 155.60/156.09 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 155.60/156.09 Found (eq_sym100 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found ((eq_sym10 (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found (((eq_sym1 (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found ((((eq_sym (fofType->fofType)) (((mult x) three) x0)) (six x0)) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) as proof of (((eq (fofType->fofType)) (six x0)) (((mult x) three) x0))
% 155.60/156.09 Found x21:(P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P0 ((six x0) x1))
% 155.60/156.09 Found x21:(P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P0 ((six x0) x1))
% 155.60/156.09 Found x21:(P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P0 ((six x0) x1))
% 155.60/156.09 Found x21:(P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P ((six x0) x1))
% 155.60/156.09 Found (fun (x21:(P ((six x0) x1)))=> x21) as proof of (P0 ((six x0) x1))
% 155.60/156.09 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 155.60/156.09 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 155.60/156.09 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 155.60/156.09 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 155.60/156.09 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 155.60/156.09 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.61/158.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 157.61/158.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.61/158.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 157.61/158.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.61/158.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.61/158.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 157.61/158.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 157.61/158.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.61/158.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 157.61/158.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 157.61/158.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.61/158.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 157.61/158.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 179.60/180.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 179.60/180.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found eq_ref00:=(eq_ref0 ((six x0) x1)):(((eq fofType) ((six x0) x1)) ((six x0) x1))
% 179.60/180.10 Found (eq_ref0 ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((six x0) x1)) as proof of (((eq fofType) ((six x0) x1)) b)
% 179.60/180.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 179.60/180.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((mult x) three) x0) x1))
% 179.60/180.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 179.60/180.10 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) y))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) y))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) y))
% 179.60/180.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) y))
% 179.60/180.10 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) y)):(((eq fofType) ((((mult x) three) x0) y)) ((((mult x) three) x0) y))
% 179.60/180.10 Found (eq_ref0 ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 179.60/180.10 Found ((eq_ref fofType) ((((mult x) three) x0) y)) as proof of (((eq fofType) ((((mult x) three) x0) y)) b)
% 179.60/180.10 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 179.60/180.10 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 179.60/180.10 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.60/180.10 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 179.80/180.31 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 179.80/180.31 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 179.80/180.31 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 179.80/180.31 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 179.80/180.31 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 179.80/180.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 179.80/180.31 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.00/180.60 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 180.00/180.60 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 180.00/180.60 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 180.00/180.60 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 180.00/180.60 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.00/180.60 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.00/180.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.10/180.66 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.10/180.66 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.10/180.66 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.10/180.66 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.10/180.66 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.70/181.28 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 180.70/181.28 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.70/181.28 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.70/181.28 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.70/181.28 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.90/181.43 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.90/181.43 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 180.90/181.43 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.90/181.43 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.90/181.43 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.99/181.49 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 180.99/181.49 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 180.99/181.49 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 180.99/181.49 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 185.98/186.54 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 185.98/186.54 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 185.98/186.54 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 185.98/186.54 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 185.98/186.54 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 185.98/186.54 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.10/186.65 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.10/186.65 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.10/186.65 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.10/186.65 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.10/186.65 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.10/186.65 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.19/186.72 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.19/186.72 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.19/186.72 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.19/186.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.28/186.87 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.28/186.87 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.28/186.87 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.28/186.87 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.28/186.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.49/187.08 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.49/187.08 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.49/187.08 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.49/187.08 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.49/187.08 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.49/187.08 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.59/187.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.59/187.17 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.59/187.17 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.59/187.17 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.59/187.17 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.59/187.17 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.59/187.17 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.59/187.17 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.59/187.17 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.70/187.24 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.70/187.24 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.70/187.24 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.70/187.24 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.70/187.24 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.70/187.24 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.70/187.24 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.80/187.35 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.80/187.35 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.80/187.35 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.80/187.35 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.80/187.35 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 186.80/187.35 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.80/187.35 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.89/187.43 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 186.89/187.43 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.89/187.43 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 186.89/187.43 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 186.89/187.43 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 186.89/187.43 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 187.09/187.61 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.09/187.61 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 187.09/187.61 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.09/187.61 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 187.09/187.61 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.61 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.09/187.61 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 187.09/187.69 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.09/187.69 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 187.09/187.69 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.09/187.69 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 187.09/187.69 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.09/187.69 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.09/187.69 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 187.19/187.72 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.19/187.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 187.19/187.72 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.19/187.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 187.19/187.72 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.19/187.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.29/187.83 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 187.29/187.83 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.29/187.83 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 187.29/187.83 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.29/187.83 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 187.29/187.83 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 187.29/187.83 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 187.29/187.83 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 187.29/187.83 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 196.99/197.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 196.99/197.51 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 196.99/197.51 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 196.99/197.51 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 196.99/197.51 Found x01:(P ((mult x) three))
% 196.99/197.51 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 196.99/197.51 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 196.99/197.51 Found eq_ref00:=(eq_ref0 a):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) a)
% 196.99/197.51 Found (eq_ref0 a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 196.99/197.51 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 196.99/197.51 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 196.99/197.51 Found ((eq_ref (((fofType->fofType)->(fofType->fofType))->Prop)) a) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) a) b)
% 196.99/197.51 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (x:((fofType->fofType)->(fofType->fofType)))=> (b x)))
% 196.99/197.51 Found (eta_expansion_dep00 b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 196.99/197.51 Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 196.99/197.51 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 196.99/197.51 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 196.99/197.51 Found (((eta_expansion_dep ((fofType->fofType)->(fofType->fofType))) (fun (x1:((fofType->fofType)->(fofType->fofType)))=> Prop)) b) as proof of (((eq (((fofType->fofType)->(fofType->fofType))->Prop)) b) (fun (N:((fofType->fofType)->(fofType->fofType)))=> (((eq ((fofType->fofType)->(fofType->fofType))) ((mult N) three)) six)))
% 196.99/197.51 Found x01:(P ((mult x) three))
% 196.99/197.51 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 196.99/197.51 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 196.99/197.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 196.99/197.51 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 196.99/197.51 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 197.20/197.72 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 197.20/197.72 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 197.20/197.72 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 197.20/197.72 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.20/197.72 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 197.20/197.72 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.20/197.72 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.20/197.72 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.20/197.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.20/197.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.20/197.72 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 197.29/197.81 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 197.29/197.81 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 197.29/197.81 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 197.29/197.81 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.81 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 197.29/197.89 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 197.29/197.89 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.29/197.89 Found x01:(P ((mult x) three))
% 197.29/197.89 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 197.29/197.89 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 197.29/197.89 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 197.38/197.89 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.38/197.89 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.38/197.89 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.38/197.89 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.38/197.89 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 197.38/197.89 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.38/197.89 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 197.59/198.12 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 197.59/198.12 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 197.59/198.12 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 197.59/198.12 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 197.59/198.12 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found ((eta_expansion00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 197.59/198.12 Found (eta_expansion000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.59/198.12 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 197.69/198.21 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found eq_ref000:=(eq_ref00 P1):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 197.69/198.21 Found (eq_ref00 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((eq_ref0 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (((mult x) three) x0))->(P1 (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 197.69/198.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((eta_expansion_dep00 (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P1 (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 197.69/198.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 197.69/198.21 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P1)) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))):((P1 (((mult x) three) x0))->(P1 (((mult x) three) x0)))
% 203.59/204.18 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0)))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P1 (((mult x) three) x0))))) as proof of ((P1 (((mult x) three) x0))->(P1 (six x0)))
% 203.59/204.18 Found x0:(P ((mult x) three))
% 203.59/204.18 Instantiate: b:=((mult x) three):((fofType->fofType)->(fofType->fofType))
% 203.59/204.18 Found x0 as proof of (P0 b)
% 203.59/204.18 Found eq_ref00:=(eq_ref0 six):(((eq ((fofType->fofType)->(fofType->fofType))) six) six)
% 203.59/204.18 Found (eq_ref0 six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 203.59/204.18 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 203.59/204.18 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 203.59/204.18 Found eq_ref00:=(eq_ref0 ((mult x) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) ((mult x) three))
% 203.59/204.18 Found (eq_ref0 ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 203.59/204.18 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 203.59/204.18 Found x01:(P ((mult x) three))
% 203.59/204.18 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P ((mult x) three))
% 203.59/204.18 Found (fun (x01:(P ((mult x) three)))=> x01) as proof of (P0 ((mult x) three))
% 218.35/218.89 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 218.35/218.89 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 218.35/218.89 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 218.35/218.89 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 218.35/218.89 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 218.35/218.89 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 218.35/218.89 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 218.35/218.89 Found (eq_ref0 b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((six x0) x1))
% 218.35/218.89 Found eq_ref00:=(eq_ref0 ((((mult x) three) x0) x1)):(((eq fofType) ((((mult x) three) x0) x1)) ((((mult x) three) x0) x1))
% 218.35/218.89 Found (eq_ref0 ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found ((eq_ref fofType) ((((mult x) three) x0) x1)) as proof of (((eq fofType) ((((mult x) three) x0) x1)) b)
% 218.35/218.89 Found x0:(P ((mult x) three))
% 218.35/218.89 Instantiate: f:=((mult x) three):((fofType->fofType)->(fofType->fofType))
% 218.35/218.89 Found x0 as proof of (P0 f)
% 218.35/218.89 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 218.35/218.89 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 218.35/218.89 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 218.35/218.89 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 218.35/218.89 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (forall (x:(fofType->fofType)), (((eq (fofType->fofType)) (f x)) (six x)))
% 221.25/221.79 Found x0:(P ((mult x) three))
% 221.25/221.79 Instantiate: f:=((mult x) three):((fofType->fofType)->(fofType->fofType))
% 221.25/221.79 Found x0 as proof of (P0 f)
% 221.25/221.79 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 221.25/221.79 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (fun (x1:(fofType->fofType))=> ((eq_ref (fofType->fofType)) (f x1))) as proof of (forall (x:(fofType->fofType)), (((eq (fofType->fofType)) (f x)) (six x)))
% 221.25/221.79 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 221.25/221.79 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found eta_expansion000:=(eta_expansion00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 221.25/221.79 Found (eta_expansion00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eta_expansion0 fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found eta_expansion000:=(eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x))))))))
% 221.25/221.79 Found (eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 221.25/221.79 Found (eta_expansion_dep00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x))))))))
% 221.25/221.79 Found (eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 221.25/221.79 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found eta_expansion_dep000:=(eta_expansion_dep00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 228.55/229.12 Found (eta_expansion_dep00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x))))))))
% 228.55/229.12 Found (eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found ((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found eta_expansion000:=(eta_expansion00 (f x1)):(((eq (fofType->fofType)) (f x1)) (fun (x:fofType)=> ((f x1) x)))
% 228.55/229.12 Found (eta_expansion00 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found ((eta_expansion0 fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion fofType) fofType) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found eta_expansion000:=(eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))):(((eq (fofType->fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x))))))))
% 228.55/229.12 Found (eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found ((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found (((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (fofType->fofType)) (f x1)) (f x1))
% 228.55/229.12 Found (eq_ref0 (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found ((eq_ref (fofType->fofType)) (f x1)) as proof of (((eq (fofType->fofType)) (f x1)) (six x1))
% 228.55/229.12 Found x0:(P ((mult x) three))
% 228.55/229.12 Instantiate: f:=((mult x) three):((fofType->fofType)->(fofType->fofType))
% 228.55/229.12 Found x0 as proof of (P0 f)
% 228.55/229.12 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 228.55/229.12 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.55/229.12 Found ((eta_expansion_dep00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.55/229.12 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.55/229.12 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.55/229.12 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.55/229.12 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x)))))))))
% 228.66/229.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 228.66/229.21 Found (eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 228.66/229.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((eta_expansion_dep00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x)))))))))
% 228.66/229.21 Found (eta_expansion_dep000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.66/229.21 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 228.69/229.29 Found (eta_expansion_dep000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((eta_expansion_dep00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (((eta_expansion_dep0 (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x3:fofType)=> fofType)) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 228.69/229.29 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((eta_expansion00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (((eta_expansion0 fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x)))))))))
% 228.69/229.29 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found eta_expansion0000:=(eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 228.69/229.29 Found (eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.69/229.29 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (f x1))->(P1 (fun (x:fofType)=> ((f x1) x))))
% 228.96/229.48 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((eta_expansion00 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (((eta_expansion0 fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((((eta_expansion fofType) fofType) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5))))))))->(P1 (fun (x:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x)))))))))
% 228.96/229.48 Found (eta_expansion000 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found eta_expansion0000:=(eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))):((P1 (f x1))->(P1 (f x1)))
% 228.96/229.48 Found (eta_expansion000 (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((eta_expansion00 (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (((eta_expansion0 fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1)))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (fun (P1:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x5:fofType)=> (x1 (x1 (x1 (x1 (x1 (x1 x5)))))))) (fun (x2:(fofType->fofType))=> (P1 (f x1))))) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found eq_ref00:=(eq_ref0 ((f x1) y)):(((eq fofType) ((f x1) y)) ((f x1) y))
% 228.96/229.48 Found (eq_ref0 ((f x1) y)) as proof of (((eq fofType) ((f x1) y)) ((six x1) y))
% 228.96/229.48 Found ((eq_ref fofType) ((f x1) y)) as proof of (((eq fofType) ((f x1) y)) ((six x1) y))
% 228.96/229.48 Found ((eq_ref fofType) ((f x1) y)) as proof of (((eq fofType) ((f x1) y)) ((six x1) y))
% 228.96/229.48 Found (fun (y:fofType)=> ((eq_ref fofType) ((f x1) y))) as proof of (((eq fofType) ((f x1) y)) ((six x1) y))
% 228.96/229.48 Found (fun (x1:(fofType->fofType)) (y:fofType)=> ((eq_ref fofType) ((f x1) y))) as proof of (forall (y:fofType), (((eq fofType) ((f x1) y)) ((six x1) y)))
% 228.96/229.48 Found (fun (x1:(fofType->fofType)) (y:fofType)=> ((eq_ref fofType) ((f x1) y))) as proof of (forall (x:(fofType->fofType)) (y:fofType), (((eq fofType) ((f x) y)) ((six x) y)))
% 228.96/229.48 Found eq_ref000:=(eq_ref00 P1):((P1 (f x1))->(P1 (f x1)))
% 228.96/229.48 Found (eq_ref00 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found ((eq_ref0 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 228.96/229.48 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 237.36/237.90 Found eq_ref000:=(eq_ref00 P1):((P1 (f x1))->(P1 (f x1)))
% 237.36/237.90 Found (eq_ref00 P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 237.36/237.90 Found ((eq_ref0 (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 237.36/237.90 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 237.36/237.90 Found (((eq_ref (fofType->fofType)) (f x1)) P1) as proof of ((P1 (f x1))->(P1 (six x1)))
% 237.36/237.90 Found (fun (P1:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (f x1)) P1)) as proof of ((P1 (f x1))->(P1 (six x1)))
% 237.36/237.90 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 237.36/237.90 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 237.36/237.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 237.36/237.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 237.36/237.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 237.36/237.90 Found eq_ref00:=(eq_ref0 ((mult x) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) ((mult x) three))
% 237.36/237.90 Found (eq_ref0 ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found eta_expansion_dep000:=(eta_expansion_dep00 six):(((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (x:(fofType->fofType))=> (six x)))
% 237.36/237.90 Found (eta_expansion_dep00 six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 237.36/237.90 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> (fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 237.36/237.90 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> (fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 237.36/237.90 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> (fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 237.36/237.90 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> (fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 237.36/237.90 Found x0:(P0 b)
% 237.36/237.90 Instantiate: b:=(fun (X:(fofType->fofType)) (Y:fofType)=> ((x (three X)) Y)):((fofType->fofType)->(fofType->fofType))
% 237.36/237.90 Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((mult x) three))
% 237.36/237.90 Found (fun (P0:(((fofType->fofType)->(fofType->fofType))->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((mult x) three)))
% 237.36/237.90 Found (fun (P0:(((fofType->fofType)->(fofType->fofType))->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 237.36/237.90 Found x0:(P six)
% 237.36/237.90 Instantiate: b:=six:((fofType->fofType)->(fofType->fofType))
% 237.36/237.90 Found x0 as proof of (P0 b)
% 237.36/237.90 Found eta_expansion000:=(eta_expansion00 ((mult x) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) (fun (x0:(fofType->fofType))=> (((mult x) three) x0)))
% 237.36/237.90 Found (eta_expansion00 ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found ((eta_expansion0 (fofType->fofType)) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 237.36/237.90 Found (((eta_expansion (fofType->fofType)) (fofType->fofType)) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 244.85/245.38 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 244.85/245.38 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 244.85/245.38 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 244.85/245.38 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 244.85/245.38 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 244.85/245.38 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 244.85/245.38 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 244.85/245.38 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 245.74/246.31 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 245.74/246.31 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 245.74/246.31 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 245.74/246.31 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 245.74/246.31 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.74/246.31 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 245.89/246.45 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 245.89/246.45 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 245.89/246.45 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 245.89/246.45 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 245.89/246.45 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 245.89/246.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 246.34/246.92 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 246.34/246.92 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 246.34/246.92 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 246.34/246.92 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (b x0))
% 246.34/246.92 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 246.34/246.92 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 246.34/246.92 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.34/246.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 246.57/247.16 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 246.57/247.16 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 246.57/247.16 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 246.57/247.16 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.57/247.16 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 246.66/247.21 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 246.66/247.21 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 246.66/247.21 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 246.66/247.21 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 246.66/247.21 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 259.08/259.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 259.08/259.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 259.08/259.62 Found x01:(P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 259.08/259.62 Found x01:(P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 259.08/259.62 Found x01:(P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 259.08/259.62 Found x01:(P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 259.08/259.62 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 259.08/259.62 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 259.08/259.62 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found eq_ref00:=(eq_ref0 six):(((eq ((fofType->fofType)->(fofType->fofType))) six) six)
% 259.08/259.62 Found (eq_ref0 six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 259.08/259.62 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((mult x) three))
% 259.08/259.62 Found eq_ref00:=(eq_ref0 six):(((eq ((fofType->fofType)->(fofType->fofType))) six) six)
% 259.08/259.62 Found (eq_ref0 six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) six) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) six) b)
% 259.08/259.62 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.08/259.62 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.08/259.62 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.08/259.62 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.08/259.62 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.08/259.62 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.08/259.62 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.17/259.72 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.17/259.72 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.17/259.72 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.17/259.72 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.17/259.72 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.24/259.87 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.24/259.87 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.24/259.87 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.24/259.87 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.24/259.87 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.46/260.00 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.46/260.00 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.46/260.00 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.46/260.00 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.46/260.00 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.54/260.11 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.54/260.11 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.54/260.11 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.54/260.11 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.54/260.11 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.64/260.19 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.64/260.19 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.64/260.19 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.64/260.19 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.77/260.34 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 259.77/260.34 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 259.77/260.34 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 259.77/260.34 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 259.77/260.34 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 260.38/260.97 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 260.38/260.97 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.38/260.97 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.38/260.97 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.38/260.97 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 260.38/260.97 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.45/261.00 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 260.45/261.00 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.45/261.00 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.45/261.00 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.45/261.00 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.58/261.20 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.58/261.20 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.58/261.20 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 260.58/261.20 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.58/261.20 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 260.58/261.20 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.58/261.20 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.58/261.20 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.58/261.20 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.68/261.28 Found eta_expansion0000:=(eta_expansion000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 260.68/261.28 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((eta_expansion00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (((eta_expansion0 fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.68/261.28 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 260.68/261.28 Found (eta_expansion000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.68/261.28 Found eta_expansion0000:=(eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.68/261.28 Found (eta_expansion000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.68/261.28 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.87/261.42 Found eq_ref000:=(eq_ref00 P):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.87/261.42 Found (eq_ref00 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((eq_ref0 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> (((eq_ref (fofType->fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.87/261.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (((mult x) three) x0))->(P (fun (x1:fofType)=> ((((mult x) three) x0) x1))))
% 260.87/261.42 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((eta_expansion_dep00 (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.87/261.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4))))))))->(P (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x)))))))))
% 260.87/261.42 Found (eta_expansion_dep000 P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 260.87/261.42 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) P)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 260.87/261.42 Found eta_expansion_dep0000:=(eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))):((P (((mult x) three) x0))->(P (((mult x) three) x0)))
% 260.87/261.42 Found (eta_expansion_dep000 (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 273.48/274.05 Found ((eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 273.48/274.05 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 273.48/274.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 273.48/274.05 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0)))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 273.48/274.05 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of ((P (((mult x) three) x0))->(P (b x0)))
% 273.48/274.08 Found (fun (P:((fofType->fofType)->Prop))=> ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x1:(fofType->fofType))=> (P (((mult x) three) x0))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (b x0))))
% 273.48/274.08 Found x11:(P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 273.48/274.08 Found x11:(P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 273.48/274.08 Found x11:(P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 273.48/274.08 Found x11:(P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 273.48/274.08 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 273.48/274.08 Found x02:(P ((mult x) three))
% 273.48/274.08 Found (fun (x02:(P ((mult x) three)))=> x02) as proof of (P ((mult x) three))
% 273.48/274.08 Found (fun (x02:(P ((mult x) three)))=> x02) as proof of (P0 ((mult x) three))
% 273.48/274.08 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b)
% 273.48/274.08 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 273.48/274.08 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 273.48/274.08 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 273.48/274.08 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) six)
% 273.48/274.08 Found eq_ref00:=(eq_ref0 ((mult x) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) ((mult x) three))
% 273.48/274.08 Found (eq_ref0 ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 273.48/274.08 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 273.48/274.08 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 273.48/274.08 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b)
% 273.48/274.08 Found x01:(P six)
% 273.48/274.08 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 273.48/274.08 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 273.48/274.08 Found x01:(P six)
% 273.48/274.08 Found (fun (x01:(P six))=> x01) as proof of (P six)
% 273.48/274.08 Found (fun (x01:(P six))=> x01) as proof of (P0 six)
% 273.48/274.08 Found x1:(P (((mult x) three) x0))
% 277.34/277.91 Instantiate: b:=(((mult x) three) x0):(fofType->fofType)
% 277.34/277.91 Found x1 as proof of (P0 b)
% 277.34/277.91 Found eta_expansion000:=(eta_expansion00 (six x0)):(((eq (fofType->fofType)) (six x0)) (fun (x:fofType)=> ((six x0) x)))
% 277.34/277.91 Found (eta_expansion00 (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found ((eta_expansion0 fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found x1:(P (((mult x) three) x0))
% 277.34/277.91 Instantiate: b:=(((mult x) three) x0):(fofType->fofType)
% 277.34/277.91 Found x1 as proof of (P0 b)
% 277.34/277.91 Found eta_expansion000:=(eta_expansion00 (six x0)):(((eq (fofType->fofType)) (six x0)) (fun (x:fofType)=> ((six x0) x)))
% 277.34/277.91 Found (eta_expansion00 (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found ((eta_expansion0 fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found (((eta_expansion fofType) fofType) (six x0)) as proof of (((eq (fofType->fofType)) (six x0)) b)
% 277.34/277.91 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 277.34/277.91 Found (eq_ref0 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.34/277.91 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.34/277.91 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.34/277.91 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.34/277.91 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 277.34/277.91 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 277.34/277.91 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.34/277.91 Found ((eq_trans0000 ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) b)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.34/277.91 Found (((eq_trans000 (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.34/277.91 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.34/277.91 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.68/278.26 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.68/278.26 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (Y:fofType)=> ((x (three x0)) Y))) ((eq_ref (fofType->fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (Y:fofType)=> ((x (three x0)) Y)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.68/278.26 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 277.68/278.26 Found (eta_expansion00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.68/278.26 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.68/278.26 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.68/278.26 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.68/278.26 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.68/278.26 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 277.68/278.26 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 277.68/278.26 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.68/278.26 Found ((eq_trans0000 (((eta_expansion fofType) fofType) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) b)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 277.68/278.26 Found (((eq_trans000 (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 277.68/278.26 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 277.68/278.26 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 277.68/278.26 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion fofType) fofType) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 277.68/278.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 277.98/278.56 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.98/278.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.98/278.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.98/278.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.98/278.56 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.98/278.56 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 277.98/278.56 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% 277.98/278.56 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 277.98/278.56 Found ((eq_trans0000 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) b)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.98/278.56 Found (((eq_trans000 (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.98/278.56 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.98/278.56 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.98/278.56 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.98/278.56 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) ((eq_ref (fofType->fofType)) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 277.98/278.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 277.98/278.56 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 277.98/278.56 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 279.76/280.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 279.76/280.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 279.76/280.40 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) b)
% 279.76/280.40 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 279.76/280.40 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% 279.76/280.40 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (six x0))
% 279.76/280.40 Found ((eq_trans0000 (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) b)) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 279.76/280.40 Found (((eq_trans000 (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 279.76/280.40 Found ((((fun (b:(fofType->fofType))=> ((eq_trans00 b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 279.76/280.40 Found ((((fun (b:(fofType->fofType))=> (((eq_trans0 (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 279.76/280.40 Found ((((fun (b:(fofType->fofType))=> ((((eq_trans (fofType->fofType)) (((mult x) three) x0)) b) (six x0))) (fun (x11:fofType)=> ((x (three x0)) x11))) (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0))) (((eta_expansion fofType) fofType) (fun (x11:fofType)=> ((x (three x0)) x11)))) as proof of (((eq (fofType->fofType)) (((mult x) three) x0)) (six x0))
% 279.76/280.40 Found x11:(P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 279.76/280.40 Found x11:(P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 279.76/280.40 Found x11:(P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 279.76/280.40 Found x11:(P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 279.76/280.40 Found x11:(P (((mult x) three) x0))
% 279.76/280.40 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 292.83/293.43 Found x11:(P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 292.83/293.43 Found x11:(P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 292.83/293.43 Found x11:(P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P (((mult x) three) x0))
% 292.83/293.43 Found (fun (x11:(P (((mult x) three) x0)))=> x11) as proof of (P0 (((mult x) three) x0))
% 292.83/293.43 Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->fofType)->(fofType->fofType))) b0) b0)
% 292.83/293.43 Found (eq_ref0 b0) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b0) six)
% 292.83/293.43 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b0) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b0) six)
% 292.83/293.43 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b0) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b0) six)
% 292.83/293.43 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b0) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b0) six)
% 292.83/293.43 Found eta_expansion_dep000:=(eta_expansion_dep00 ((mult x) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) (fun (x0:(fofType->fofType))=> (((mult x) three) x0)))
% 292.83/293.43 Found (eta_expansion_dep00 ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b0)
% 292.83/293.43 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> (fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b0)
% 292.83/293.43 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> (fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b0)
% 292.83/293.43 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> (fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b0)
% 292.83/293.43 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> (fofType->fofType))) ((mult x) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((mult x) three)) b0)
% 292.83/293.43 Found x11:(P ((((mult x) three) x0) y))
% 292.83/293.43 Found (fun (x11:(P ((((mult x) three) x0) y)))=> x11) as proof of (P ((((mult x) three) x0) y))
% 292.83/293.43 Found (fun (x11:(P ((((mult x) three) x0) y)))=> x11) as proof of (P0 ((((mult x) three) x0) y))
% 292.83/293.43 Found x11:(P ((((mult x) three) x0) y))
% 292.83/293.43 Found (fun (x11:(P ((((mult x) three) x0) y)))=> x11) as proof of (P ((((mult x) three) x0) y))
% 292.83/293.43 Found (fun (x11:(P ((((mult x) three) x0) y)))=> x11) as proof of (P0 ((((mult x) three) x0) y))
% 292.83/293.43 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 292.83/293.43 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.83/293.43 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.83/293.43 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.83/293.43 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.83/293.43 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 292.83/293.43 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.83/293.43 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 292.91/293.48 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 292.91/293.48 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 292.91/293.48 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.91/293.48 Found eq_ref00:=(eq_ref0 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (((mult x) three) x0))
% 292.91/293.48 Found (eq_ref0 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eq_ref (fofType->fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found eta_expansion000:=(eta_expansion00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 292.99/293.62 Found (eta_expansion00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eta_expansion0 fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion fofType) fofType) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found eta_expansion000:=(eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 292.99/293.62 Found (eta_expansion00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eta_expansion0 fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion fofType) fofType) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found eta_expansion_dep000:=(eta_expansion_dep00 (((mult x) three) x0)):(((eq (fofType->fofType)) (((mult x) three) x0)) (fun (x1:fofType)=> ((((mult x) three) x0) x1)))
% 292.99/293.62 Found (eta_expansion_dep00 (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((mult x) three) x0)) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))):(((eq (fofType->fofType)) (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) (fun (x:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x))))))))
% 292.99/293.62 Found (eta_expansion_dep00 (fun (x4:fofType)=> (x0 (x0 (x0 (x0 (x0 (x0 x4)))))))) as proof of (forall (P:((fofType->fofType)->Prop)), ((P (((mult x) three) x0))->(P (six x0))))
% 292.99/293.62 Found ((eta_expa
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